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7d89a42b56
SourceSDK mathlib port with light modifications. Renamed Vector to Vector3D (to avoid confusion with std::vector (declared as vector) and Vector2D/Vector4D).
4458 lines
114 KiB
C++
4458 lines
114 KiB
C++
//========= Copyright Valve Corporation, All rights reserved. ============//
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//
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// Purpose: Math primitives.
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//
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//===========================================================================//
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/// FIXME: As soon as all references to mathlib.c are gone, include it in here
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#include "core/stdafx.h"
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#include <math.h>
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#include <float.h> // Needed for FLT_EPSILON
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#include "tier0/basetypes.h"
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#include <memory.h>
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#include "tier0/dbg.h"
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//#define _VPROF_MATHLIB
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#pragma warning(disable:4244) // "conversion from 'const int' to 'float', possible loss of data"
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#pragma warning(disable:4730) // "mixing _m64 and floating point expressions may result in incorrect code"
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#include "mathlib/bits.h"
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#include "mathlib/vplane.h"
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#include "mathlib/Vector.h"
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#include "mathlib/Vector2d.h"
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#include "mathlib/mathlib.h"
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#include "mathlib/ssemath.h"
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#include "mathlib/math_pfns.h"
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#include <tier0/cpu.h>
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bool s_bMathlibInitialized = false;
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#ifdef PARANOID
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// User must provide an implementation of Sys_Error()
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void Sys_Error(char* error, ...);
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#endif
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const Vector3D vec3_origin(0, 0, 0);
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const QAngle vec3_angle(0, 0, 0);
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const Vector3D vec3_invalid(FLT_MAX, FLT_MAX, FLT_MAX);
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const int nanmask = 255 << 23;
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//-----------------------------------------------------------------------------
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// Standard C implementations of optimized routines:
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//-----------------------------------------------------------------------------
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float _sqrtf(float _X)
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{
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Assert(s_bMathlibInitialized);
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return sqrtf(_X);
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}
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float _rsqrtf(float x)
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{
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Assert(s_bMathlibInitialized);
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return 1.f / _sqrtf(x);
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}
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float FASTCALL _VectorNormalize(Vector3D& vec)
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{
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#ifdef _VPROF_MATHLIB
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VPROF_BUDGET("_Vector3Normalize", "Mathlib");
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#endif
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Assert(s_bMathlibInitialized);
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float radius = sqrtf(vec.x * vec.x + vec.y * vec.y + vec.z * vec.z);
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// FLT_EPSILON is added to the radius to eliminate the possibility of divide by zero.
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float iradius = 1.f / (radius + FLT_EPSILON);
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vec.x *= iradius;
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vec.y *= iradius;
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vec.z *= iradius;
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return radius;
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}
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// TODO: Add fast C VectorNormalizeFast.
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// Perhaps use approximate rsqrt trick, if the accuracy isn't too bad.
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void FASTCALL _VectorNormalizeFast(Vector3D& vec)
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{
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Assert(s_bMathlibInitialized);
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// FLT_EPSILON is added to the radius to eliminate the possibility of divide by zero.
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float iradius = 1.f / (sqrtf(vec.x * vec.x + vec.y * vec.y + vec.z * vec.z) + FLT_EPSILON);
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vec.x *= iradius;
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vec.y *= iradius;
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vec.z *= iradius;
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}
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float _InvRSquared(const float* v)
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{
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Assert(s_bMathlibInitialized);
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float r2 = DotProduct(v, v);
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return r2 < 1.f ? 1.f : 1 / r2;
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}
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//-----------------------------------------------------------------------------
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// Function pointers selecting the appropriate implementation
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//-----------------------------------------------------------------------------
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float (*pfSqrt)(float x) = _sqrtf;
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float (*pfRSqrt)(float x) = _rsqrtf;
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float (*pfRSqrtFast)(float x) = _rsqrtf;
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float (FASTCALL* pfVectorNormalize)(Vector3D& v) = _VectorNormalize;
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void (FASTCALL* pfVectorNormalizeFast)(Vector3D& v) = _VectorNormalizeFast;
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float (*pfInvRSquared)(const float* v) = _InvRSquared;
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void (*pfFastSinCos)(float x, float* s, float* c) = SinCos;
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float (*pfFastCos)(float x) = cosf;
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float SinCosTable[SIN_TABLE_SIZE];
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void InitSinCosTable()
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{
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for (int i = 0; i < SIN_TABLE_SIZE; i++)
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{
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SinCosTable[i] = sin(i * 2.0 * M_PI / SIN_TABLE_SIZE);
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}
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}
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qboolean VectorsEqual(const float* v1, const float* v2)
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{
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Assert(s_bMathlibInitialized);
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return ((v1[0] == v2[0]) &&
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(v1[1] == v2[1]) &&
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(v1[2] == v2[2]));
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}
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//-----------------------------------------------------------------------------
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// Purpose: Generates Euler angles given a left-handed orientation matrix. The
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// columns of the matrix contain the forward, left, and up Vector3s.
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// Input : matrix - Left-handed orientation matrix.
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// angles[PITCH, YAW, ROLL]. Receives right-handed counterclockwise
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// rotations in degrees around Y, Z, and X respectively.
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//-----------------------------------------------------------------------------
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void MatrixAngles(const matrix3x4_t& matrix, RadianEuler& angles, Vector3D& position)
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{
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MatrixGetColumn(matrix, 3, position);
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MatrixAngles(matrix, angles);
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}
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void MatrixAngles(const matrix3x4_t& matrix, Quaternion& q, Vector3D& pos)
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{
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#ifdef _VPROF_MATHLIB
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VPROF_BUDGET("MatrixQuaternion", "Mathlib");
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#endif
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float trace;
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trace = matrix[0][0] + matrix[1][1] + matrix[2][2] + 1.0f;
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if (trace > 1.0f + FLT_EPSILON)
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{
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// VPROF_INCREMENT_COUNTER("MatrixQuaternion A",1);
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q.x = (matrix[2][1] - matrix[1][2]);
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q.y = (matrix[0][2] - matrix[2][0]);
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q.z = (matrix[1][0] - matrix[0][1]);
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q.w = trace;
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}
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else if (matrix[0][0] > matrix[1][1] && matrix[0][0] > matrix[2][2])
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{
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// VPROF_INCREMENT_COUNTER("MatrixQuaternion B",1);
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trace = 1.0f + matrix[0][0] - matrix[1][1] - matrix[2][2];
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q.x = trace;
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q.y = (matrix[1][0] + matrix[0][1]);
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q.z = (matrix[0][2] + matrix[2][0]);
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q.w = (matrix[2][1] - matrix[1][2]);
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}
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else if (matrix[1][1] > matrix[2][2])
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{
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// VPROF_INCREMENT_COUNTER("MatrixQuaternion C",1);
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trace = 1.0f + matrix[1][1] - matrix[0][0] - matrix[2][2];
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q.x = (matrix[0][1] + matrix[1][0]);
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q.y = trace;
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q.z = (matrix[2][1] + matrix[1][2]);
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q.w = (matrix[0][2] - matrix[2][0]);
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}
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else
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{
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// VPROF_INCREMENT_COUNTER("MatrixQuaternion D",1);
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trace = 1.0f + matrix[2][2] - matrix[0][0] - matrix[1][1];
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q.x = (matrix[0][2] + matrix[2][0]);
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q.y = (matrix[2][1] + matrix[1][2]);
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q.z = trace;
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q.w = (matrix[1][0] - matrix[0][1]);
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}
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QuaternionNormalize(q);
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#if 0
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// check against the angle version
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RadianEuler ang;
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MatrixAngles(matrix, ang);
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Quaternion test;
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AngleQuaternion(ang, test);
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float d = QuaternionDotProduct(q, test);
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Assert(fabs(d) > 0.99 && fabs(d) < 1.01);
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#endif
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MatrixGetColumn(matrix, 3, pos);
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}
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void MatrixAngles(const matrix3x4_t& matrix, float* angles)
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{
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#ifdef _VPROF_MATHLIB
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VPROF_BUDGET("MatrixAngles", "Mathlib");
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#endif
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Assert(s_bMathlibInitialized);
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float forward[3];
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float left[3];
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float up[3];
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//
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// Extract the basis Vector3s from the matrix. Since we only need the Z
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// component of the up Vector3, we don't get X and Y.
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//
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forward[0] = matrix[0][0];
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forward[1] = matrix[1][0];
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forward[2] = matrix[2][0];
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left[0] = matrix[0][1];
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left[1] = matrix[1][1];
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left[2] = matrix[2][1];
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up[2] = matrix[2][2];
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float xyDist = sqrtf(forward[0] * forward[0] + forward[1] * forward[1]);
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// enough here to get angles?
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if (xyDist > 0.001f)
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{
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// (yaw) y = ATAN( forward.y, forward.x ); -- in our space, forward is the X axis
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angles[1] = RAD2DEG(atan2f(forward[1], forward[0]));
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// (pitch) x = ATAN( -forward.z, sqrt(forward.x*forward.x+forward.y*forward.y) );
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angles[0] = RAD2DEG(atan2f(-forward[2], xyDist));
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// (roll) z = ATAN( left.z, up.z );
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angles[2] = RAD2DEG(atan2f(left[2], up[2]));
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}
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else // forward is mostly Z, gimbal lock-
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{
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// (yaw) y = ATAN( -left.x, left.y ); -- forward is mostly z, so use right for yaw
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angles[1] = RAD2DEG(atan2f(-left[0], left[1]));
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// (pitch) x = ATAN( -forward.z, sqrt(forward.x*forward.x+forward.y*forward.y) );
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angles[0] = RAD2DEG(atan2f(-forward[2], xyDist));
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// Assume no roll in this case as one degree of freedom has been lost (i.e. yaw == roll)
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angles[2] = 0;
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}
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}
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// transform in1 by the matrix in2
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void VectorTransform(const float* in1, const matrix3x4_t& in2, float* out)
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{
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Assert(s_bMathlibInitialized);
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Assert(in1 != out);
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out[0] = DotProduct(in1, in2[0]) + in2[0][3];
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out[1] = DotProduct(in1, in2[1]) + in2[1][3];
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out[2] = DotProduct(in1, in2[2]) + in2[2][3];
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}
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// assuming the matrix is orthonormal, transform in1 by the transpose (also the inverse in this case) of in2.
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void VectorITransform(const float* in1, const matrix3x4_t& in2, float* out)
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{
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Assert(s_bMathlibInitialized);
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float in1t[3];
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in1t[0] = in1[0] - in2[0][3];
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in1t[1] = in1[1] - in2[1][3];
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in1t[2] = in1[2] - in2[2][3];
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out[0] = in1t[0] * in2[0][0] + in1t[1] * in2[1][0] + in1t[2] * in2[2][0];
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out[1] = in1t[0] * in2[0][1] + in1t[1] * in2[1][1] + in1t[2] * in2[2][1];
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out[2] = in1t[0] * in2[0][2] + in1t[1] * in2[1][2] + in1t[2] * in2[2][2];
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}
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// assume in2 is a rotation and rotate the input Vector3D
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void VectorRotate(const float* in1, const matrix3x4_t& in2, float* out)
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{
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Assert(s_bMathlibInitialized);
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Assert(in1 != out);
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out[0] = DotProduct(in1, in2[0]);
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out[1] = DotProduct(in1, in2[1]);
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out[2] = DotProduct(in1, in2[2]);
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}
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// assume in2 is a rotation and rotate the input Vector3D
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void VectorRotate(const Vector3D& in1, const QAngle& in2, Vector3D& out)
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{
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matrix3x4_t matRotate;
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AngleMatrix(in2, matRotate);
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VectorRotate(in1, matRotate, out);
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}
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// assume in2 is a rotation and rotate the input Vector3D
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void VectorRotate(const Vector3D& in1, const Quaternion& in2, Vector3D& out)
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{
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matrix3x4_t matRotate;
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QuaternionMatrix(in2, matRotate);
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VectorRotate(in1, matRotate, out);
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}
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// rotate by the inverse of the matrix
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void VectorIRotate(const float* in1, const matrix3x4_t& in2, float* out)
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{
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Assert(s_bMathlibInitialized);
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Assert(in1 != out);
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out[0] = in1[0] * in2[0][0] + in1[1] * in2[1][0] + in1[2] * in2[2][0];
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out[1] = in1[0] * in2[0][1] + in1[1] * in2[1][1] + in1[2] * in2[2][1];
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out[2] = in1[0] * in2[0][2] + in1[1] * in2[1][2] + in1[2] * in2[2][2];
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}
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#ifndef Vector_NO_SLOW_OPERATIONS
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// transform a set of angles in the output space of parentMatrix to the input space
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QAngle TransformAnglesToLocalSpace(const QAngle& angles, const matrix3x4_t& parentMatrix)
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{
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matrix3x4_t angToWorld, worldToParent, localMatrix;
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MatrixInvert(parentMatrix, worldToParent);
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AngleMatrix(angles, angToWorld);
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ConcatTransforms(worldToParent, angToWorld, localMatrix);
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QAngle out;
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MatrixAngles(localMatrix, out);
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return out;
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}
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// transform a set of angles in the input space of parentMatrix to the output space
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QAngle TransformAnglesToWorldSpace(const QAngle& angles, const matrix3x4_t& parentMatrix)
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{
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matrix3x4_t angToParent, angToWorld;
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AngleMatrix(angles, angToParent);
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ConcatTransforms(parentMatrix, angToParent, angToWorld);
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QAngle out;
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MatrixAngles(angToWorld, out);
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return out;
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}
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#endif // Vector3D_NO_SLOW_OPERATIONS
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void MatrixInitialize(matrix3x4_t& mat, const Vector3D& vecOrigin, const Vector3D& vecXAxis, const Vector3D& vecYAxis, const Vector3D& vecZAxis)
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{
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MatrixSetColumn(vecXAxis, 0, mat);
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MatrixSetColumn(vecYAxis, 1, mat);
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MatrixSetColumn(vecZAxis, 2, mat);
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MatrixSetColumn(vecOrigin, 3, mat);
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}
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void MatrixCopy(const matrix3x4_t& in, matrix3x4_t& out)
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{
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Assert(s_bMathlibInitialized);
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memcpy(out.Base(), in.Base(), sizeof(float) * 3 * 4);
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}
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//-----------------------------------------------------------------------------
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// Matrix equality test
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//-----------------------------------------------------------------------------
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bool MatricesAreEqual(const matrix3x4_t& src1, const matrix3x4_t& src2, float flTolerance)
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{
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for (int i = 0; i < 3; ++i)
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{
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for (int j = 0; j < 4; ++j)
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{
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if (fabs(src1[i][j] - src2[i][j]) > flTolerance)
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return false;
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}
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}
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return true;
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}
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// NOTE: This is just the transpose not a general inverse
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void MatrixInvert(const matrix3x4_t& in, matrix3x4_t& out)
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{
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Assert(s_bMathlibInitialized);
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if (&in == &out)
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{
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V_swap(out[0][1], out[1][0]);
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V_swap(out[0][2], out[2][0]);
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V_swap(out[1][2], out[2][1]);
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}
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else
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{
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// transpose the matrix
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out[0][0] = in[0][0];
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out[0][1] = in[1][0];
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out[0][2] = in[2][0];
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out[1][0] = in[0][1];
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out[1][1] = in[1][1];
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out[1][2] = in[2][1];
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out[2][0] = in[0][2];
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out[2][1] = in[1][2];
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out[2][2] = in[2][2];
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}
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// now fix up the translation to be in the other space
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float tmp[3];
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tmp[0] = in[0][3];
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tmp[1] = in[1][3];
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tmp[2] = in[2][3];
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out[0][3] = -DotProduct(tmp, out[0]);
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out[1][3] = -DotProduct(tmp, out[1]);
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out[2][3] = -DotProduct(tmp, out[2]);
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}
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void MatrixGetColumn(const matrix3x4_t& in, int column, Vector3D& out)
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{
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out.x = in[0][column];
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out.y = in[1][column];
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out.z = in[2][column];
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}
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void MatrixSetColumn(const Vector3D& in, int column, matrix3x4_t& out)
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{
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out[0][column] = in.x;
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out[1][column] = in.y;
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out[2][column] = in.z;
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}
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void MatrixScaleBy(const float flScale, matrix3x4_t& out)
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{
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out[0][0] *= flScale;
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out[1][0] *= flScale;
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out[2][0] *= flScale;
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out[0][1] *= flScale;
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out[1][1] *= flScale;
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out[2][1] *= flScale;
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out[0][2] *= flScale;
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out[1][2] *= flScale;
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out[2][2] *= flScale;
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}
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void MatrixScaleByZero(matrix3x4_t& out)
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{
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out[0][0] = 0.0f;
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out[1][0] = 0.0f;
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out[2][0] = 0.0f;
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out[0][1] = 0.0f;
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out[1][1] = 0.0f;
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out[2][1] = 0.0f;
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out[0][2] = 0.0f;
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out[1][2] = 0.0f;
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out[2][2] = 0.0f;
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}
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int VectorCompare(const float* v1, const float* v2)
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{
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Assert(s_bMathlibInitialized);
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int i;
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for (i = 0; i < 3; i++)
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if (v1[i] != v2[i])
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return 0;
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return 1;
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}
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|
|
void CrossProduct(const float* v1, const float* v2, float* cross)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Assert(v1 != cross);
|
|
Assert(v2 != cross);
|
|
cross[0] = v1[1] * v2[2] - v1[2] * v2[1];
|
|
cross[1] = v1[2] * v2[0] - v1[0] * v2[2];
|
|
cross[2] = v1[0] * v2[1] - v1[1] * v2[0];
|
|
}
|
|
|
|
int Q_log2(int val)
|
|
{
|
|
int answer = 0;
|
|
while (val >>= 1)
|
|
answer++;
|
|
return answer;
|
|
}
|
|
|
|
// Matrix is right-handed x=forward, y=left, z=up. We a left-handed convention for Vector3Ds in the game code (forward, right, up)
|
|
void MatrixVectors(const matrix3x4_t& matrix, Vector3D* pForward, Vector3D* pRight, Vector3D* pUp)
|
|
{
|
|
MatrixGetColumn(matrix, 0, *pForward);
|
|
MatrixGetColumn(matrix, 1, *pRight);
|
|
MatrixGetColumn(matrix, 2, *pUp);
|
|
*pRight *= -1.0f;
|
|
}
|
|
|
|
|
|
void VectorVectors(const Vector3D& forward, Vector3D& right, Vector3D& up)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Vector3D tmp;
|
|
|
|
if (forward[0] == 0 && forward[1] == 0)
|
|
{
|
|
// pitch 90 degrees up/down from identity
|
|
right[0] = 0;
|
|
right[1] = -1;
|
|
right[2] = 0;
|
|
up[0] = -forward[2];
|
|
up[1] = 0;
|
|
up[2] = 0;
|
|
}
|
|
else
|
|
{
|
|
tmp[0] = 0; tmp[1] = 0; tmp[2] = 1.0;
|
|
CrossProduct(forward, tmp, right);
|
|
VectorNormalize(right);
|
|
CrossProduct(right, forward, up);
|
|
VectorNormalize(up);
|
|
}
|
|
}
|
|
|
|
void VectorMatrix(const Vector3D& forward, matrix3x4_t& matrix)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Vector3D right, up;
|
|
VectorVectors(forward, right, up);
|
|
|
|
MatrixSetColumn(forward, 0, matrix);
|
|
MatrixSetColumn(-right, 1, matrix);
|
|
MatrixSetColumn(up, 2, matrix);
|
|
}
|
|
|
|
|
|
void VectorAngles(const float* forward, float* angles)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
float tmp, yaw, pitch;
|
|
|
|
if (forward[1] == 0 && forward[0] == 0)
|
|
{
|
|
yaw = 0;
|
|
if (forward[2] > 0)
|
|
pitch = 270;
|
|
else
|
|
pitch = 90;
|
|
}
|
|
else
|
|
{
|
|
yaw = (atan2(forward[1], forward[0]) * 180 / M_PI);
|
|
if (yaw < 0)
|
|
yaw += 360;
|
|
|
|
tmp = sqrt(forward[0] * forward[0] + forward[1] * forward[1]);
|
|
pitch = (atan2(-forward[2], tmp) * 180 / M_PI);
|
|
if (pitch < 0)
|
|
pitch += 360;
|
|
}
|
|
|
|
angles[0] = pitch;
|
|
angles[1] = yaw;
|
|
angles[2] = 0;
|
|
}
|
|
|
|
|
|
/*
|
|
================
|
|
R_ConcatRotations
|
|
================
|
|
*/
|
|
void ConcatRotations(const float in1[3][3], const float in2[3][3], float out[3][3])
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Assert(in1 != out);
|
|
Assert(in2 != out);
|
|
out[0][0] = in1[0][0] * in2[0][0] + in1[0][1] * in2[1][0] +
|
|
in1[0][2] * in2[2][0];
|
|
out[0][1] = in1[0][0] * in2[0][1] + in1[0][1] * in2[1][1] +
|
|
in1[0][2] * in2[2][1];
|
|
out[0][2] = in1[0][0] * in2[0][2] + in1[0][1] * in2[1][2] +
|
|
in1[0][2] * in2[2][2];
|
|
out[1][0] = in1[1][0] * in2[0][0] + in1[1][1] * in2[1][0] +
|
|
in1[1][2] * in2[2][0];
|
|
out[1][1] = in1[1][0] * in2[0][1] + in1[1][1] * in2[1][1] +
|
|
in1[1][2] * in2[2][1];
|
|
out[1][2] = in1[1][0] * in2[0][2] + in1[1][1] * in2[1][2] +
|
|
in1[1][2] * in2[2][2];
|
|
out[2][0] = in1[2][0] * in2[0][0] + in1[2][1] * in2[1][0] +
|
|
in1[2][2] * in2[2][0];
|
|
out[2][1] = in1[2][0] * in2[0][1] + in1[2][1] * in2[1][1] +
|
|
in1[2][2] * in2[2][1];
|
|
out[2][2] = in1[2][0] * in2[0][2] + in1[2][1] * in2[1][2] +
|
|
in1[2][2] * in2[2][2];
|
|
}
|
|
|
|
void ConcatTransforms_Aligned(const matrix3x4_t& m0, const matrix3x4_t& m1, matrix3x4_t& out)
|
|
{
|
|
Assert((((size_t)&m0) % 16) == 0);
|
|
Assert((((size_t)&m1) % 16) == 0);
|
|
Assert((((size_t)&out) % 16) == 0);
|
|
|
|
fltx4 lastMask = *(fltx4*)(&g_SIMD_ComponentMask[3]);
|
|
fltx4 rowA0 = LoadAlignedSIMD(m0.m_flMatVal[0]);
|
|
fltx4 rowA1 = LoadAlignedSIMD(m0.m_flMatVal[1]);
|
|
fltx4 rowA2 = LoadAlignedSIMD(m0.m_flMatVal[2]);
|
|
|
|
fltx4 rowB0 = LoadAlignedSIMD(m1.m_flMatVal[0]);
|
|
fltx4 rowB1 = LoadAlignedSIMD(m1.m_flMatVal[1]);
|
|
fltx4 rowB2 = LoadAlignedSIMD(m1.m_flMatVal[2]);
|
|
|
|
// now we have the rows of m0 and the columns of m1
|
|
// first output row
|
|
fltx4 A0 = SplatXSIMD(rowA0);
|
|
fltx4 A1 = SplatYSIMD(rowA0);
|
|
fltx4 A2 = SplatZSIMD(rowA0);
|
|
fltx4 mul00 = MulSIMD(A0, rowB0);
|
|
fltx4 mul01 = MulSIMD(A1, rowB1);
|
|
fltx4 mul02 = MulSIMD(A2, rowB2);
|
|
fltx4 out0 = AddSIMD(mul00, AddSIMD(mul01, mul02));
|
|
|
|
// second output row
|
|
A0 = SplatXSIMD(rowA1);
|
|
A1 = SplatYSIMD(rowA1);
|
|
A2 = SplatZSIMD(rowA1);
|
|
fltx4 mul10 = MulSIMD(A0, rowB0);
|
|
fltx4 mul11 = MulSIMD(A1, rowB1);
|
|
fltx4 mul12 = MulSIMD(A2, rowB2);
|
|
fltx4 out1 = AddSIMD(mul10, AddSIMD(mul11, mul12));
|
|
|
|
// third output row
|
|
A0 = SplatXSIMD(rowA2);
|
|
A1 = SplatYSIMD(rowA2);
|
|
A2 = SplatZSIMD(rowA2);
|
|
fltx4 mul20 = MulSIMD(A0, rowB0);
|
|
fltx4 mul21 = MulSIMD(A1, rowB1);
|
|
fltx4 mul22 = MulSIMD(A2, rowB2);
|
|
fltx4 out2 = AddSIMD(mul20, AddSIMD(mul21, mul22));
|
|
|
|
// add in translation Vector3D
|
|
A0 = AndSIMD(rowA0, lastMask);
|
|
A1 = AndSIMD(rowA1, lastMask);
|
|
A2 = AndSIMD(rowA2, lastMask);
|
|
out0 = AddSIMD(out0, A0);
|
|
out1 = AddSIMD(out1, A1);
|
|
out2 = AddSIMD(out2, A2);
|
|
|
|
StoreAlignedSIMD(out.m_flMatVal[0], out0);
|
|
StoreAlignedSIMD(out.m_flMatVal[1], out1);
|
|
StoreAlignedSIMD(out.m_flMatVal[2], out2);
|
|
}
|
|
|
|
/*
|
|
================
|
|
R_ConcatTransforms
|
|
================
|
|
*/
|
|
|
|
void ConcatTransforms(const matrix3x4_t& in1, const matrix3x4_t& in2, matrix3x4_t& out)
|
|
{
|
|
#if 0
|
|
// test for ones that'll be 2x faster
|
|
if ((((size_t)&in1) % 16) == 0 && (((size_t)&in2) % 16) == 0 && (((size_t)&out) % 16) == 0)
|
|
{
|
|
ConcatTransforms_Aligned(in1, in2, out);
|
|
return;
|
|
}
|
|
#endif
|
|
|
|
fltx4 lastMask = *(fltx4*)(&g_SIMD_ComponentMask[3]);
|
|
fltx4 rowA0 = LoadUnalignedSIMD(in1.m_flMatVal[0]);
|
|
fltx4 rowA1 = LoadUnalignedSIMD(in1.m_flMatVal[1]);
|
|
fltx4 rowA2 = LoadUnalignedSIMD(in1.m_flMatVal[2]);
|
|
|
|
fltx4 rowB0 = LoadUnalignedSIMD(in2.m_flMatVal[0]);
|
|
fltx4 rowB1 = LoadUnalignedSIMD(in2.m_flMatVal[1]);
|
|
fltx4 rowB2 = LoadUnalignedSIMD(in2.m_flMatVal[2]);
|
|
|
|
// now we have the rows of m0 and the columns of m1
|
|
// first output row
|
|
fltx4 A0 = SplatXSIMD(rowA0);
|
|
fltx4 A1 = SplatYSIMD(rowA0);
|
|
fltx4 A2 = SplatZSIMD(rowA0);
|
|
fltx4 mul00 = MulSIMD(A0, rowB0);
|
|
fltx4 mul01 = MulSIMD(A1, rowB1);
|
|
fltx4 mul02 = MulSIMD(A2, rowB2);
|
|
fltx4 out0 = AddSIMD(mul00, AddSIMD(mul01, mul02));
|
|
|
|
// second output row
|
|
A0 = SplatXSIMD(rowA1);
|
|
A1 = SplatYSIMD(rowA1);
|
|
A2 = SplatZSIMD(rowA1);
|
|
fltx4 mul10 = MulSIMD(A0, rowB0);
|
|
fltx4 mul11 = MulSIMD(A1, rowB1);
|
|
fltx4 mul12 = MulSIMD(A2, rowB2);
|
|
fltx4 out1 = AddSIMD(mul10, AddSIMD(mul11, mul12));
|
|
|
|
// third output row
|
|
A0 = SplatXSIMD(rowA2);
|
|
A1 = SplatYSIMD(rowA2);
|
|
A2 = SplatZSIMD(rowA2);
|
|
fltx4 mul20 = MulSIMD(A0, rowB0);
|
|
fltx4 mul21 = MulSIMD(A1, rowB1);
|
|
fltx4 mul22 = MulSIMD(A2, rowB2);
|
|
fltx4 out2 = AddSIMD(mul20, AddSIMD(mul21, mul22));
|
|
|
|
// add in translation Vector3D
|
|
A0 = AndSIMD(rowA0, lastMask);
|
|
A1 = AndSIMD(rowA1, lastMask);
|
|
A2 = AndSIMD(rowA2, lastMask);
|
|
out0 = AddSIMD(out0, A0);
|
|
out1 = AddSIMD(out1, A1);
|
|
out2 = AddSIMD(out2, A2);
|
|
|
|
// write to output
|
|
StoreUnalignedSIMD(out.m_flMatVal[0], out0);
|
|
StoreUnalignedSIMD(out.m_flMatVal[1], out1);
|
|
StoreUnalignedSIMD(out.m_flMatVal[2], out2);
|
|
}
|
|
|
|
|
|
/*
|
|
===================
|
|
FloorDivMod
|
|
|
|
Returns mathematically correct (floor-based) quotient and remainder for
|
|
numer and denom, both of which should contain no fractional part. The
|
|
quotient must fit in 32 bits.
|
|
====================
|
|
*/
|
|
|
|
void FloorDivMod(double numer, double denom, int* quotient,
|
|
int* rem)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
int q, r;
|
|
double x;
|
|
|
|
#ifdef PARANOID
|
|
if (denom <= 0.0)
|
|
Sys_Error("FloorDivMod: bad denominator %d\n", denom);
|
|
|
|
// if ((floor(numer) != numer) || (floor(denom) != denom))
|
|
// Sys_Error ("FloorDivMod: non-integer numer or denom %f %f\n",
|
|
// numer, denom);
|
|
#endif
|
|
|
|
if (numer >= 0.0)
|
|
{
|
|
|
|
x = floor(numer / denom);
|
|
q = (int)x;
|
|
r = Floor2Int(numer - (x * denom));
|
|
}
|
|
else
|
|
{
|
|
//
|
|
// perform operations with positive values, and fix mod to make floor-based
|
|
//
|
|
x = floor(-numer / denom);
|
|
q = -(int)x;
|
|
r = Floor2Int(-numer - (x * denom));
|
|
if (r != 0)
|
|
{
|
|
q--;
|
|
r = (int)denom - r;
|
|
}
|
|
}
|
|
|
|
*quotient = q;
|
|
*rem = r;
|
|
}
|
|
|
|
|
|
/*
|
|
===================
|
|
GreatestCommonDivisor
|
|
====================
|
|
*/
|
|
int GreatestCommonDivisor(int i1, int i2)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
if (i1 > i2)
|
|
{
|
|
if (i2 == 0)
|
|
return (i1);
|
|
return GreatestCommonDivisor(i2, i1 % i2);
|
|
}
|
|
else
|
|
{
|
|
if (i1 == 0)
|
|
return (i2);
|
|
return GreatestCommonDivisor(i1, i2 % i1);
|
|
}
|
|
}
|
|
|
|
|
|
bool IsDenormal(const float& val)
|
|
{
|
|
const int x = *reinterpret_cast <const int*> (&val); // needs 32-bit int
|
|
const int abs_mantissa = x & 0x007FFFFF;
|
|
const int biased_exponent = x & 0x7F800000;
|
|
|
|
return (biased_exponent == 0 && abs_mantissa != 0);
|
|
}
|
|
|
|
int SignbitsForPlane(cplane_t* out)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
int bits, j;
|
|
|
|
// for fast box on planeside test
|
|
|
|
bits = 0;
|
|
for (j = 0; j < 3; j++)
|
|
{
|
|
if (out->normal[j] < 0)
|
|
bits |= 1 << j;
|
|
}
|
|
return bits;
|
|
}
|
|
|
|
/*
|
|
==================
|
|
BoxOnPlaneSide
|
|
|
|
Returns 1, 2, or 1 + 2
|
|
==================
|
|
*/
|
|
int __cdecl BoxOnPlaneSide(const float* emins, const float* emaxs, const cplane_t* p)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
float dist1, dist2;
|
|
int sides;
|
|
|
|
// fast axial cases
|
|
if (p->type < 3)
|
|
{
|
|
if (p->dist <= emins[p->type])
|
|
return 1;
|
|
if (p->dist >= emaxs[p->type])
|
|
return 2;
|
|
return 3;
|
|
}
|
|
|
|
// general case
|
|
switch (p->signbits)
|
|
{
|
|
case 0:
|
|
dist1 = p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] + p->normal[2] * emaxs[2];
|
|
dist2 = p->normal[0] * emins[0] + p->normal[1] * emins[1] + p->normal[2] * emins[2];
|
|
break;
|
|
case 1:
|
|
dist1 = p->normal[0] * emins[0] + p->normal[1] * emaxs[1] + p->normal[2] * emaxs[2];
|
|
dist2 = p->normal[0] * emaxs[0] + p->normal[1] * emins[1] + p->normal[2] * emins[2];
|
|
break;
|
|
case 2:
|
|
dist1 = p->normal[0] * emaxs[0] + p->normal[1] * emins[1] + p->normal[2] * emaxs[2];
|
|
dist2 = p->normal[0] * emins[0] + p->normal[1] * emaxs[1] + p->normal[2] * emins[2];
|
|
break;
|
|
case 3:
|
|
dist1 = p->normal[0] * emins[0] + p->normal[1] * emins[1] + p->normal[2] * emaxs[2];
|
|
dist2 = p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] + p->normal[2] * emins[2];
|
|
break;
|
|
case 4:
|
|
dist1 = p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] + p->normal[2] * emins[2];
|
|
dist2 = p->normal[0] * emins[0] + p->normal[1] * emins[1] + p->normal[2] * emaxs[2];
|
|
break;
|
|
case 5:
|
|
dist1 = p->normal[0] * emins[0] + p->normal[1] * emaxs[1] + p->normal[2] * emins[2];
|
|
dist2 = p->normal[0] * emaxs[0] + p->normal[1] * emins[1] + p->normal[2] * emaxs[2];
|
|
break;
|
|
case 6:
|
|
dist1 = p->normal[0] * emaxs[0] + p->normal[1] * emins[1] + p->normal[2] * emins[2];
|
|
dist2 = p->normal[0] * emins[0] + p->normal[1] * emaxs[1] + p->normal[2] * emaxs[2];
|
|
break;
|
|
case 7:
|
|
dist1 = p->normal[0] * emins[0] + p->normal[1] * emins[1] + p->normal[2] * emins[2];
|
|
dist2 = p->normal[0] * emaxs[0] + p->normal[1] * emaxs[1] + p->normal[2] * emaxs[2];
|
|
break;
|
|
default:
|
|
dist1 = dist2 = 0; // shut up compiler
|
|
Assert(0);
|
|
break;
|
|
}
|
|
|
|
sides = 0;
|
|
if (dist1 >= p->dist)
|
|
sides = 1;
|
|
if (dist2 < p->dist)
|
|
sides |= 2;
|
|
|
|
Assert(sides != 0);
|
|
|
|
return sides;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Euler QAngle -> Basis Vector3Ds
|
|
//-----------------------------------------------------------------------------
|
|
|
|
void AngleVectors(const QAngle& angles, Vector3D* forward)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Assert(forward);
|
|
|
|
float sp, sy, cp, cy;
|
|
|
|
SinCos(DEG2RAD(angles[YAW]), &sy, &cy);
|
|
SinCos(DEG2RAD(angles[PITCH]), &sp, &cp);
|
|
|
|
forward->x = cp * cy;
|
|
forward->y = cp * sy;
|
|
forward->z = -sp;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Euler QAngle -> Basis Vector3Ds. Each Vector3D is optional
|
|
//-----------------------------------------------------------------------------
|
|
void AngleVectors(const QAngle& angles, Vector3D* forward, Vector3D* right, Vector3D* up)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
|
|
float sr, sp, sy, cr, cp, cy;
|
|
|
|
#ifdef _X360
|
|
fltx4 radians, scale, sine, cosine;
|
|
radians = LoadUnaligned3SIMD(angles.Base());
|
|
scale = ReplicateX4(M_PI_F / 180.f);
|
|
radians = MulSIMD(radians, scale);
|
|
SinCos3SIMD(sine, cosine, radians);
|
|
sp = SubFloat(sine, 0); sy = SubFloat(sine, 1); sr = SubFloat(sine, 2);
|
|
cp = SubFloat(cosine, 0); cy = SubFloat(cosine, 1); cr = SubFloat(cosine, 2);
|
|
#else
|
|
SinCos(DEG2RAD(angles[YAW]), &sy, &cy);
|
|
SinCos(DEG2RAD(angles[PITCH]), &sp, &cp);
|
|
SinCos(DEG2RAD(angles[ROLL]), &sr, &cr);
|
|
#endif
|
|
|
|
if (forward)
|
|
{
|
|
forward->x = cp * cy;
|
|
forward->y = cp * sy;
|
|
forward->z = -sp;
|
|
}
|
|
|
|
if (right)
|
|
{
|
|
right->x = (-1 * sr * sp * cy + -1 * cr * -sy);
|
|
right->y = (-1 * sr * sp * sy + -1 * cr * cy);
|
|
right->z = -1 * sr * cp;
|
|
}
|
|
|
|
if (up)
|
|
{
|
|
up->x = (cr * sp * cy + -sr * -sy);
|
|
up->y = (cr * sp * sy + -sr * cy);
|
|
up->z = cr * cp;
|
|
}
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Euler QAngle -> Basis Vector3Ds transposed
|
|
//-----------------------------------------------------------------------------
|
|
|
|
void AngleVectorsTranspose(const QAngle& angles, Vector3D* forward, Vector3D* right, Vector3D* up)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
float sr, sp, sy, cr, cp, cy;
|
|
|
|
SinCos(DEG2RAD(angles[YAW]), &sy, &cy);
|
|
SinCos(DEG2RAD(angles[PITCH]), &sp, &cp);
|
|
SinCos(DEG2RAD(angles[ROLL]), &sr, &cr);
|
|
|
|
if (forward)
|
|
{
|
|
forward->x = cp * cy;
|
|
forward->y = (sr * sp * cy + cr * -sy);
|
|
forward->z = (cr * sp * cy + -sr * -sy);
|
|
}
|
|
|
|
if (right)
|
|
{
|
|
right->x = cp * sy;
|
|
right->y = (sr * sp * sy + cr * cy);
|
|
right->z = (cr * sp * sy + -sr * cy);
|
|
}
|
|
|
|
if (up)
|
|
{
|
|
up->x = -sp;
|
|
up->y = sr * cp;
|
|
up->z = cr * cp;
|
|
}
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Forward direction Vector3D -> Euler angles
|
|
//-----------------------------------------------------------------------------
|
|
|
|
void VectorAngles(const Vector3D& forward, QAngle& angles)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
float tmp, yaw, pitch;
|
|
|
|
if (forward[1] == 0 && forward[0] == 0)
|
|
{
|
|
yaw = 0;
|
|
if (forward[2] > 0)
|
|
pitch = 270;
|
|
else
|
|
pitch = 90;
|
|
}
|
|
else
|
|
{
|
|
yaw = (atan2(forward[1], forward[0]) * 180 / M_PI);
|
|
if (yaw < 0)
|
|
yaw += 360;
|
|
|
|
tmp = FastSqrt(forward[0] * forward[0] + forward[1] * forward[1]);
|
|
pitch = (atan2(-forward[2], tmp) * 180 / M_PI);
|
|
if (pitch < 0)
|
|
pitch += 360;
|
|
}
|
|
|
|
angles[0] = pitch;
|
|
angles[1] = yaw;
|
|
angles[2] = 0;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Forward direction Vector3D with a reference up Vector3D -> Euler angles
|
|
//-----------------------------------------------------------------------------
|
|
|
|
void VectorAngles(const Vector3D& forward, const Vector3D& pseudoup, QAngle& angles)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
|
|
Vector3D left;
|
|
|
|
CrossProduct(pseudoup, forward, left);
|
|
VectorNormalizeFast(left);
|
|
|
|
float xyDist = sqrtf(forward[0] * forward[0] + forward[1] * forward[1]);
|
|
|
|
// enough here to get angles?
|
|
if (xyDist > 0.001f)
|
|
{
|
|
// (yaw) y = ATAN( forward.y, forward.x ); -- in our space, forward is the X axis
|
|
angles[1] = RAD2DEG(atan2f(forward[1], forward[0]));
|
|
|
|
// The engine does pitch inverted from this, but we always end up negating it in the DLL
|
|
// UNDONE: Fix the engine to make it consistent
|
|
// (pitch) x = ATAN( -forward.z, sqrt(forward.x*forward.x+forward.y*forward.y) );
|
|
angles[0] = RAD2DEG(atan2f(-forward[2], xyDist));
|
|
|
|
float up_z = (left[1] * forward[0]) - (left[0] * forward[1]);
|
|
|
|
// (roll) z = ATAN( left.z, up.z );
|
|
angles[2] = RAD2DEG(atan2f(left[2], up_z));
|
|
}
|
|
else // forward is mostly Z, gimbal lock-
|
|
{
|
|
// (yaw) y = ATAN( -left.x, left.y ); -- forward is mostly z, so use right for yaw
|
|
angles[1] = RAD2DEG(atan2f(-left[0], left[1])); //This was originally copied from the "void MatrixAngles( const matrix3x4_t& matrix, float *angles )" code, and it's 180 degrees off, negated the values and it all works now (Dave Kircher)
|
|
|
|
// The engine does pitch inverted from this, but we always end up negating it in the DLL
|
|
// UNDONE: Fix the engine to make it consistent
|
|
// (pitch) x = ATAN( -forward.z, sqrt(forward.x*forward.x+forward.y*forward.y) );
|
|
angles[0] = RAD2DEG(atan2f(-forward[2], xyDist));
|
|
|
|
// Assume no roll in this case as one degree of freedom has been lost (i.e. yaw == roll)
|
|
angles[2] = 0;
|
|
}
|
|
}
|
|
|
|
void SetIdentityMatrix(matrix3x4_t& matrix)
|
|
{
|
|
memset(matrix.Base(), 0, sizeof(float) * 3 * 4);
|
|
matrix[0][0] = 1.0;
|
|
matrix[1][1] = 1.0;
|
|
matrix[2][2] = 1.0;
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Builds a scale matrix
|
|
//-----------------------------------------------------------------------------
|
|
void SetScaleMatrix(float x, float y, float z, matrix3x4_t& dst)
|
|
{
|
|
dst[0][0] = x; dst[0][1] = 0.0f; dst[0][2] = 0.0f; dst[0][3] = 0.0f;
|
|
dst[1][0] = 0.0f; dst[1][1] = y; dst[1][2] = 0.0f; dst[1][3] = 0.0f;
|
|
dst[2][0] = 0.0f; dst[2][1] = 0.0f; dst[2][2] = z; dst[2][3] = 0.0f;
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Purpose: Builds the matrix for a counterclockwise rotation about an arbitrary axis.
|
|
//
|
|
// | ax2 + (1 - ax2)cosQ axay(1 - cosQ) - azsinQ azax(1 - cosQ) + aysinQ |
|
|
// Ra(Q) = | axay(1 - cosQ) + azsinQ ay2 + (1 - ay2)cosQ ayaz(1 - cosQ) - axsinQ |
|
|
// | azax(1 - cosQ) - aysinQ ayaz(1 - cosQ) + axsinQ az2 + (1 - az2)cosQ |
|
|
//
|
|
// Input : mat -
|
|
// vAxisOrRot -
|
|
// angle -
|
|
//-----------------------------------------------------------------------------
|
|
void MatrixBuildRotationAboutAxis(const Vector3D& vAxisOfRot, float angleDegrees, matrix3x4_t& dst)
|
|
{
|
|
float radians;
|
|
float axisXSquared;
|
|
float axisYSquared;
|
|
float axisZSquared;
|
|
float fSin;
|
|
float fCos;
|
|
|
|
radians = angleDegrees * (M_PI / 180.0);
|
|
fSin = sin(radians);
|
|
fCos = cos(radians);
|
|
|
|
axisXSquared = vAxisOfRot[0] * vAxisOfRot[0];
|
|
axisYSquared = vAxisOfRot[1] * vAxisOfRot[1];
|
|
axisZSquared = vAxisOfRot[2] * vAxisOfRot[2];
|
|
|
|
// Column 0:
|
|
dst[0][0] = axisXSquared + (1 - axisXSquared) * fCos;
|
|
dst[1][0] = vAxisOfRot[0] * vAxisOfRot[1] * (1 - fCos) + vAxisOfRot[2] * fSin;
|
|
dst[2][0] = vAxisOfRot[2] * vAxisOfRot[0] * (1 - fCos) - vAxisOfRot[1] * fSin;
|
|
|
|
// Column 1:
|
|
dst[0][1] = vAxisOfRot[0] * vAxisOfRot[1] * (1 - fCos) - vAxisOfRot[2] * fSin;
|
|
dst[1][1] = axisYSquared + (1 - axisYSquared) * fCos;
|
|
dst[2][1] = vAxisOfRot[1] * vAxisOfRot[2] * (1 - fCos) + vAxisOfRot[0] * fSin;
|
|
|
|
// Column 2:
|
|
dst[0][2] = vAxisOfRot[2] * vAxisOfRot[0] * (1 - fCos) + vAxisOfRot[1] * fSin;
|
|
dst[1][2] = vAxisOfRot[1] * vAxisOfRot[2] * (1 - fCos) - vAxisOfRot[0] * fSin;
|
|
dst[2][2] = axisZSquared + (1 - axisZSquared) * fCos;
|
|
|
|
// Column 3:
|
|
dst[0][3] = 0;
|
|
dst[1][3] = 0;
|
|
dst[2][3] = 0;
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Computes the transpose
|
|
//-----------------------------------------------------------------------------
|
|
void MatrixTranspose(matrix3x4_t& mat)
|
|
{
|
|
vec_t tmp;
|
|
tmp = mat[0][1]; mat[0][1] = mat[1][0]; mat[1][0] = tmp;
|
|
tmp = mat[0][2]; mat[0][2] = mat[2][0]; mat[2][0] = tmp;
|
|
tmp = mat[1][2]; mat[1][2] = mat[2][1]; mat[2][1] = tmp;
|
|
}
|
|
|
|
void MatrixTranspose(const matrix3x4_t& src, matrix3x4_t& dst)
|
|
{
|
|
dst[0][0] = src[0][0]; dst[0][1] = src[1][0]; dst[0][2] = src[2][0]; dst[0][3] = 0.0f;
|
|
dst[1][0] = src[0][1]; dst[1][1] = src[1][1]; dst[1][2] = src[2][1]; dst[1][3] = 0.0f;
|
|
dst[2][0] = src[0][2]; dst[2][1] = src[1][2]; dst[2][2] = src[2][2]; dst[2][3] = 0.0f;
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Purpose: converts engine euler angles into a matrix
|
|
// Input : vec3_t angles - PITCH, YAW, ROLL
|
|
// Output : *matrix - left-handed column matrix
|
|
// the basis Vector3Ds for the rotations will be in the columns as follows:
|
|
// matrix[][0] is forward
|
|
// matrix[][1] is left
|
|
// matrix[][2] is up
|
|
//-----------------------------------------------------------------------------
|
|
void AngleMatrix(RadianEuler const& angles, const Vector3D& position, matrix3x4_t& matrix)
|
|
{
|
|
AngleMatrix(angles, matrix);
|
|
MatrixSetColumn(position, 3, matrix);
|
|
}
|
|
|
|
void AngleMatrix(const RadianEuler& angles, matrix3x4_t& matrix)
|
|
{
|
|
QAngle quakeEuler(RAD2DEG(angles.y), RAD2DEG(angles.z), RAD2DEG(angles.x));
|
|
|
|
AngleMatrix(quakeEuler, matrix);
|
|
}
|
|
|
|
|
|
void AngleMatrix(const QAngle& angles, const Vector3D& position, matrix3x4_t& matrix)
|
|
{
|
|
AngleMatrix(angles, matrix);
|
|
MatrixSetColumn(position, 3, matrix);
|
|
}
|
|
|
|
void AngleMatrix(const QAngle& angles, matrix3x4_t& matrix)
|
|
{
|
|
#ifdef _VPROF_MATHLIB
|
|
VPROF_BUDGET("AngleMatrix", "Mathlib");
|
|
#endif
|
|
Assert(s_bMathlibInitialized);
|
|
|
|
float sr, sp, sy, cr, cp, cy;
|
|
|
|
#ifdef _X360
|
|
fltx4 radians, scale, sine, cosine;
|
|
radians = LoadUnaligned3SIMD(angles.Base());
|
|
scale = ReplicateX4(M_PI_F / 180.f);
|
|
radians = MulSIMD(radians, scale);
|
|
SinCos3SIMD(sine, cosine, radians);
|
|
|
|
sp = SubFloat(sine, 0); sy = SubFloat(sine, 1); sr = SubFloat(sine, 2);
|
|
cp = SubFloat(cosine, 0); cy = SubFloat(cosine, 1); cr = SubFloat(cosine, 2);
|
|
#else
|
|
SinCos(DEG2RAD(angles[YAW]), &sy, &cy);
|
|
SinCos(DEG2RAD(angles[PITCH]), &sp, &cp);
|
|
SinCos(DEG2RAD(angles[ROLL]), &sr, &cr);
|
|
#endif
|
|
|
|
// matrix = (YAW * PITCH) * ROLL
|
|
matrix[0][0] = cp * cy;
|
|
matrix[1][0] = cp * sy;
|
|
matrix[2][0] = -sp;
|
|
|
|
float crcy = cr * cy;
|
|
float crsy = cr * sy;
|
|
float srcy = sr * cy;
|
|
float srsy = sr * sy;
|
|
matrix[0][1] = sp * srcy - crsy;
|
|
matrix[1][1] = sp * srsy + crcy;
|
|
matrix[2][1] = sr * cp;
|
|
|
|
matrix[0][2] = (sp * crcy + srsy);
|
|
matrix[1][2] = (sp * crsy - srcy);
|
|
matrix[2][2] = cr * cp;
|
|
|
|
matrix[0][3] = 0.0f;
|
|
matrix[1][3] = 0.0f;
|
|
matrix[2][3] = 0.0f;
|
|
}
|
|
|
|
void AngleIMatrix(const RadianEuler& angles, matrix3x4_t& matrix)
|
|
{
|
|
QAngle quakeEuler(RAD2DEG(angles.y), RAD2DEG(angles.z), RAD2DEG(angles.x));
|
|
|
|
AngleIMatrix(quakeEuler, matrix);
|
|
}
|
|
|
|
void AngleIMatrix(const QAngle& angles, matrix3x4_t& matrix)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
float sr, sp, sy, cr, cp, cy;
|
|
|
|
SinCos(DEG2RAD(angles[YAW]), &sy, &cy);
|
|
SinCos(DEG2RAD(angles[PITCH]), &sp, &cp);
|
|
SinCos(DEG2RAD(angles[ROLL]), &sr, &cr);
|
|
|
|
// matrix = (YAW * PITCH) * ROLL
|
|
matrix[0][0] = cp * cy;
|
|
matrix[0][1] = cp * sy;
|
|
matrix[0][2] = -sp;
|
|
matrix[1][0] = sr * sp * cy + cr * -sy;
|
|
matrix[1][1] = sr * sp * sy + cr * cy;
|
|
matrix[1][2] = sr * cp;
|
|
matrix[2][0] = (cr * sp * cy + -sr * -sy);
|
|
matrix[2][1] = (cr * sp * sy + -sr * cy);
|
|
matrix[2][2] = cr * cp;
|
|
matrix[0][3] = 0.f;
|
|
matrix[1][3] = 0.f;
|
|
matrix[2][3] = 0.f;
|
|
}
|
|
|
|
void AngleIMatrix(const QAngle& angles, const Vector3D& position, matrix3x4_t& mat)
|
|
{
|
|
AngleIMatrix(angles, mat);
|
|
|
|
Vector3D vecTranslation;
|
|
VectorRotate(position, mat, vecTranslation);
|
|
vecTranslation *= -1.0f;
|
|
MatrixSetColumn(vecTranslation, 3, mat);
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Bounding box construction methods
|
|
//-----------------------------------------------------------------------------
|
|
|
|
void ClearBounds(Vector3D& mins, Vector3D& maxs)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
mins[0] = mins[1] = mins[2] = 99999;
|
|
maxs[0] = maxs[1] = maxs[2] = -99999;
|
|
}
|
|
|
|
void AddPointToBounds(const Vector3D& v, Vector3D& mins, Vector3D& maxs)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
int i;
|
|
vec_t val;
|
|
|
|
for (i = 0; i < 3; i++)
|
|
{
|
|
val = v[i];
|
|
if (val < mins[i])
|
|
mins[i] = val;
|
|
if (val > maxs[i])
|
|
maxs[i] = val;
|
|
}
|
|
}
|
|
|
|
// solve a x^2 + b x + c = 0
|
|
bool SolveQuadratic(float a, float b, float c, float& root1, float& root2)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
if (a == 0)
|
|
{
|
|
if (b != 0)
|
|
{
|
|
// no x^2 component, it's a linear system
|
|
root1 = root2 = -c / b;
|
|
return true;
|
|
}
|
|
if (c == 0)
|
|
{
|
|
// all zero's
|
|
root1 = root2 = 0;
|
|
return true;
|
|
}
|
|
return false;
|
|
}
|
|
|
|
float tmp = b * b - 4.0f * a * c;
|
|
|
|
if (tmp < 0)
|
|
{
|
|
// imaginary number, bah, no solution.
|
|
return false;
|
|
}
|
|
|
|
tmp = sqrt(tmp);
|
|
root1 = (-b + tmp) / (2.0f * a);
|
|
root2 = (-b - tmp) / (2.0f * a);
|
|
return true;
|
|
}
|
|
|
|
// solves for "a, b, c" where "a x^2 + b x + c = y", return true if solution exists
|
|
bool SolveInverseQuadratic(float x1, float y1, float x2, float y2, float x3, float y3, float& a, float& b, float& c)
|
|
{
|
|
float det = (x1 - x2) * (x1 - x3) * (x2 - x3);
|
|
|
|
// FIXME: check with some sort of epsilon
|
|
if (det == 0.0)
|
|
return false;
|
|
|
|
a = (x3 * (-y1 + y2) + x2 * (y1 - y3) + x1 * (-y2 + y3)) / det;
|
|
|
|
b = (x3 * x3 * (y1 - y2) + x1 * x1 * (y2 - y3) + x2 * x2 * (-y1 + y3)) / det;
|
|
|
|
c = (x1 * x3 * (-x1 + x3) * y2 + x2 * x2 * (x3 * y1 - x1 * y3) + x2 * (-(x3 * x3 * y1) + x1 * x1 * y3)) / det;
|
|
|
|
return true;
|
|
}
|
|
|
|
bool SolveInverseQuadraticMonotonic(float x1, float y1, float x2, float y2, float x3, float y3,
|
|
float& a, float& b, float& c)
|
|
{
|
|
// use SolveInverseQuadratic, but if the sigm of the derivative at the start point is the wrong
|
|
// sign, displace the mid point
|
|
|
|
// first, sort parameters
|
|
if (x1 > x2)
|
|
{
|
|
V_swap(x1, x2);
|
|
V_swap(y1, y2);
|
|
}
|
|
if (x2 > x3)
|
|
{
|
|
V_swap(x2, x3);
|
|
V_swap(y2, y3);
|
|
}
|
|
if (x1 > x2)
|
|
{
|
|
V_swap(x1, x2);
|
|
V_swap(y1, y2);
|
|
}
|
|
// this code is not fast. what it does is when the curve would be non-monotonic, slowly shifts
|
|
// the center point closer to the linear line between the endpoints. Should anyone need htis
|
|
// function to be actually fast, it would be fairly easy to change it to be so.
|
|
for (float blend_to_linear_factor = 0.0; blend_to_linear_factor <= 1.0; blend_to_linear_factor += 0.05)
|
|
{
|
|
float tempy2 = (1 - blend_to_linear_factor) * y2 + blend_to_linear_factor * FLerp(y1, y3, x1, x3, x2);
|
|
if (!SolveInverseQuadratic(x1, y1, x2, tempy2, x3, y3, a, b, c))
|
|
return false;
|
|
float derivative = 2.0 * a + b;
|
|
if ((y1 < y2) && (y2 < y3)) // monotonically increasing
|
|
{
|
|
if (derivative >= 0.0)
|
|
return true;
|
|
}
|
|
else
|
|
{
|
|
if ((y1 > y2) && (y2 > y3)) // monotonically decreasing
|
|
{
|
|
if (derivative <= 0.0)
|
|
return true;
|
|
}
|
|
else
|
|
return true;
|
|
}
|
|
}
|
|
return true;
|
|
}
|
|
|
|
|
|
// solves for "a, b, c" where "1/(a x^2 + b x + c ) = y", return true if solution exists
|
|
bool SolveInverseReciprocalQuadratic(float x1, float y1, float x2, float y2, float x3, float y3, float& a, float& b, float& c)
|
|
{
|
|
float det = (x1 - x2) * (x1 - x3) * (x2 - x3) * y1 * y2 * y3;
|
|
|
|
// FIXME: check with some sort of epsilon
|
|
if (det == 0.0)
|
|
return false;
|
|
|
|
a = (x1 * y1 * (y2 - y3) + x3 * (y1 - y2) * y3 + x2 * y2 * (-y1 + y3)) / det;
|
|
|
|
b = (x2 * x2 * y2 * (y1 - y3) + x3 * x3 * (-y1 + y2) * y3 + x1 * x1 * y1 * (-y2 + y3)) / det;
|
|
|
|
c = (x2 * (x2 - x3) * x3 * y2 * y3 + x1 * x1 * y1 * (x2 * y2 - x3 * y3) + x1 * (-(x2 * x2 * y1 * y2) + x3 * x3 * y1 * y3)) / det;
|
|
|
|
return true;
|
|
}
|
|
|
|
|
|
// Rotate a Vector3D around the Z axis (YAW)
|
|
void VectorYawRotate(const Vector3D& in, float flYaw, Vector3D& out)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
if (&in == &out)
|
|
{
|
|
Vector3D tmp;
|
|
tmp = in;
|
|
VectorYawRotate(tmp, flYaw, out);
|
|
return;
|
|
}
|
|
|
|
float sy, cy;
|
|
|
|
SinCos(DEG2RAD(flYaw), &sy, &cy);
|
|
|
|
out.x = in.x * cy - in.y * sy;
|
|
out.y = in.x * sy + in.y * cy;
|
|
out.z = in.z;
|
|
}
|
|
|
|
|
|
|
|
float Bias(float x, float biasAmt)
|
|
{
|
|
// WARNING: not thread safe
|
|
static float lastAmt = -1;
|
|
static float lastExponent = 0;
|
|
if (lastAmt != biasAmt)
|
|
{
|
|
lastExponent = log(biasAmt) * -1.4427f; // (-1.4427 = 1 / log(0.5))
|
|
}
|
|
float fRet = pow(x, lastExponent);
|
|
Assert(!IS_NAN(fRet));
|
|
return fRet;
|
|
}
|
|
|
|
|
|
float Gain(float x, float biasAmt)
|
|
{
|
|
// WARNING: not thread safe
|
|
if (x < 0.5)
|
|
return 0.5f * Bias(2 * x, 1 - biasAmt);
|
|
else
|
|
return 1 - 0.5f * Bias(2 - 2 * x, 1 - biasAmt);
|
|
}
|
|
|
|
|
|
float SmoothCurve(float x)
|
|
{
|
|
// Actual smooth curve. Visualization:
|
|
// http://www.wolframalpha.com/input/?i=plot%5B+0.5+*+%281+-+cos%5B2+*+pi+*+x%5D%29+for+x+%3D+%280%2C+1%29+%5D
|
|
return 0.5f * (1 - cos(2.0f * M_PI * x));
|
|
}
|
|
|
|
|
|
inline float MovePeak(float x, float flPeakPos)
|
|
{
|
|
// Todo: make this higher-order?
|
|
if (x < flPeakPos)
|
|
return x * 0.5f / flPeakPos;
|
|
else
|
|
return 0.5 + 0.5 * (x - flPeakPos) / (1 - flPeakPos);
|
|
}
|
|
|
|
|
|
float SmoothCurve_Tweak(float x, float flPeakPos, float flPeakSharpness)
|
|
{
|
|
float flMovedPeak = MovePeak(x, flPeakPos);
|
|
float flSharpened = Gain(flMovedPeak, flPeakSharpness);
|
|
return SmoothCurve(flSharpened);
|
|
}
|
|
|
|
void QuaternionExp(const Quaternion& p, Quaternion& q)
|
|
{
|
|
float r = sqrt(p[0] * p[0] + p[1] * p[1] + p[2] * p[2]);
|
|
float et = exp(p[3]);
|
|
float s = r >= 0.00001f ? et * sin(r) / r : 0.f;
|
|
q.Init(s * p[0], s * p[1], s * p[2], et * cos(r));
|
|
}
|
|
|
|
void QuaternionLn(const Quaternion& p, Quaternion& q)
|
|
{
|
|
float r = sqrt(p[0] * p[0] + p[1] * p[1] + p[2] * p[2]);
|
|
float t = r > 0.00001f ? atan2(r, p[3]) / r : 0.f;
|
|
float norm = p[0] * p[0] + p[1] * p[1] + p[2] * p[2] + p[3] * p[3];
|
|
q.Init(t * p[0], t * p[1], t * p[2], 0.5 * log(norm));
|
|
}
|
|
|
|
// Average using exponential method
|
|
// Qave = exp( 1 / n * log( Q1 ) + ... + 1 / n * log( Qn ) ) where
|
|
// if pflWeights passed in 1/n is replaced by normalized weighting
|
|
void QuaternionAverageExponential(Quaternion& q, int nCount, const Quaternion* pQuaternions, const float* pflWeights /*=NULL*/)
|
|
{
|
|
Assert(nCount >= 1);
|
|
Assert(pQuaternions);
|
|
|
|
// Nothing to do if only one input quaternions
|
|
if (nCount == 1)
|
|
{
|
|
q = pQuaternions[0];
|
|
return;
|
|
}
|
|
|
|
float ooWeightSum = 1.0f;
|
|
float flWeightSum = 0.0f;
|
|
for (int i = 0; i < nCount; ++i)
|
|
{
|
|
if (pflWeights)
|
|
{
|
|
flWeightSum += pflWeights[i];
|
|
}
|
|
else
|
|
{
|
|
flWeightSum += 1.0f;
|
|
}
|
|
}
|
|
|
|
if (flWeightSum > 0.0f)
|
|
{
|
|
ooWeightSum = 1.0f / flWeightSum;
|
|
}
|
|
|
|
Quaternion sum(0, 0, 0, 0);
|
|
// Now sum the ln of the quaternions
|
|
for (int i = 0; i < nCount; ++i)
|
|
{
|
|
float weight = ooWeightSum;
|
|
if (pflWeights)
|
|
{
|
|
weight *= pflWeights[i];
|
|
}
|
|
|
|
// Make sure all quaternions are aligned with the
|
|
// first to avoid blending the wrong direction.
|
|
Quaternion alignedQuat;
|
|
QuaternionAlign(pQuaternions[0], pQuaternions[i], alignedQuat);
|
|
|
|
Quaternion qLn;
|
|
QuaternionLn(alignedQuat, qLn);
|
|
for (int j = 0; j < 4; ++j)
|
|
{
|
|
sum[j] += (qLn[j] * weight);
|
|
}
|
|
}
|
|
|
|
// then exponentiate to get final value
|
|
QuaternionExp(sum, q);
|
|
}
|
|
|
|
// Given a vector and a pseudo-up reference vector, create a quaternion which represents
|
|
// the orientation of the forward vector. Note, will be unstable if vecForward is close
|
|
// to referenceUp
|
|
void QuaternionLookAt(const Vector3D& vecForward, const Vector3D& referenceUp, Quaternion& q)
|
|
{
|
|
Vector3D forward = vecForward;
|
|
forward.NormalizeInPlace();
|
|
float ratio = DotProduct(forward, referenceUp);
|
|
Vector3D up = referenceUp - (forward * ratio);
|
|
up.NormalizeInPlace();
|
|
|
|
Vector3D right = forward.Cross(up);
|
|
right.NormalizeInPlace();
|
|
|
|
const Vector3D& x = right;
|
|
const Vector3D& y = forward;
|
|
const Vector3D& z = up;
|
|
|
|
float tr = x.x + y.y + z.z;
|
|
q.Init(y.z - z.y, z.x - x.z, x.y - y.x, tr + 1.0f);
|
|
QuaternionNormalize(q);
|
|
|
|
/*
|
|
Vector z = vecForward;
|
|
z.NormalizeInPlace();
|
|
Vector x = referenceUp.Cross( z );
|
|
x.NormalizeInPlace();
|
|
Vector y = z.Cross( x );
|
|
y.NormalizeInPlace();
|
|
|
|
float tr = x.x + y.y + z.z;
|
|
q.Init( y.z - z.y , z.x - x.z, x.y - y.x, tr + 1.0f );
|
|
QuaternionNormalize( q );
|
|
*/
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// make sure quaternions are within 180 degrees of one another, if not, reverse q
|
|
//-----------------------------------------------------------------------------
|
|
|
|
void QuaternionAlign(const Quaternion& p, const Quaternion& q, Quaternion& qt)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
|
|
// FIXME: can this be done with a quat dot product?
|
|
|
|
int i;
|
|
// decide if one of the quaternions is backwards
|
|
float a = 0;
|
|
float b = 0;
|
|
for (i = 0; i < 4; i++)
|
|
{
|
|
a += (p[i] - q[i]) * (p[i] - q[i]);
|
|
b += (p[i] + q[i]) * (p[i] + q[i]);
|
|
}
|
|
if (a > b)
|
|
{
|
|
for (i = 0; i < 4; i++)
|
|
{
|
|
qt[i] = -q[i];
|
|
}
|
|
}
|
|
else if (&qt != &q)
|
|
{
|
|
for (i = 0; i < 4; i++)
|
|
{
|
|
qt[i] = q[i];
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Do a piecewise addition of the quaternion elements. This actually makes little
|
|
// mathematical sense, but it's a cheap way to simulate a slerp.
|
|
//-----------------------------------------------------------------------------
|
|
void QuaternionBlend(const Quaternion& p, const Quaternion& q, float t, Quaternion& qt)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
#if ALLOW_SIMD_QUATERNION_MATH
|
|
fltx4 psimd, qsimd, qtsimd;
|
|
psimd = LoadUnalignedSIMD(p.Base());
|
|
qsimd = LoadUnalignedSIMD(q.Base());
|
|
qtsimd = QuaternionBlendSIMD(psimd, qsimd, t);
|
|
StoreUnalignedSIMD(qt.Base(), qtsimd);
|
|
#else
|
|
// decide if one of the quaternions is backwards
|
|
Quaternion q2;
|
|
QuaternionAlign(p, q, q2);
|
|
QuaternionBlendNoAlign(p, q2, t, qt);
|
|
#endif
|
|
}
|
|
|
|
|
|
void QuaternionBlendNoAlign(const Quaternion& p, const Quaternion& q, float t, Quaternion& qt)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
float sclp, sclq;
|
|
int i;
|
|
|
|
// 0.0 returns p, 1.0 return q.
|
|
sclp = 1.0f - t;
|
|
sclq = t;
|
|
for (i = 0; i < 4; i++) {
|
|
qt[i] = sclp * p[i] + sclq * q[i];
|
|
}
|
|
QuaternionNormalize(qt);
|
|
}
|
|
|
|
|
|
|
|
void QuaternionIdentityBlend(const Quaternion& p, float t, Quaternion& qt)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
float sclp;
|
|
|
|
sclp = 1.0f - t;
|
|
|
|
qt.x = p.x * sclp;
|
|
qt.y = p.y * sclp;
|
|
qt.z = p.z * sclp;
|
|
if (qt.w < 0.0)
|
|
{
|
|
qt.w = p.w * sclp - t;
|
|
}
|
|
else
|
|
{
|
|
qt.w = p.w * sclp + t;
|
|
}
|
|
QuaternionNormalize(qt);
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Quaternion sphereical linear interpolation
|
|
//-----------------------------------------------------------------------------
|
|
|
|
void QuaternionSlerp(const Quaternion& p, const Quaternion& q, float t, Quaternion& qt)
|
|
{
|
|
Quaternion q2;
|
|
// 0.0 returns p, 1.0 return q.
|
|
|
|
// decide if one of the quaternions is backwards
|
|
QuaternionAlign(p, q, q2);
|
|
|
|
QuaternionSlerpNoAlign(p, q2, t, qt);
|
|
}
|
|
|
|
|
|
void QuaternionSlerpNoAlign(const Quaternion& p, const Quaternion& q, float t, Quaternion& qt)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
float omega, cosom, sinom, sclp, sclq;
|
|
int i;
|
|
|
|
// 0.0 returns p, 1.0 return q.
|
|
|
|
cosom = p[0] * q[0] + p[1] * q[1] + p[2] * q[2] + p[3] * q[3];
|
|
|
|
if ((1.0f + cosom) > 0.000001f) {
|
|
if ((1.0f - cosom) > 0.000001f) {
|
|
omega = acos(cosom);
|
|
sinom = sin(omega);
|
|
sclp = sin((1.0f - t) * omega) / sinom;
|
|
sclq = sin(t * omega) / sinom;
|
|
}
|
|
else {
|
|
// TODO: add short circuit for cosom == 1.0f?
|
|
sclp = 1.0f - t;
|
|
sclq = t;
|
|
}
|
|
for (i = 0; i < 4; i++) {
|
|
qt[i] = sclp * p[i] + sclq * q[i];
|
|
}
|
|
}
|
|
else {
|
|
Assert(&qt != &q);
|
|
|
|
qt[0] = -q[1];
|
|
qt[1] = q[0];
|
|
qt[2] = -q[3];
|
|
qt[3] = q[2];
|
|
sclp = sin((1.0f - t) * (0.5f * M_PI));
|
|
sclq = sin(t * (0.5f * M_PI));
|
|
for (i = 0; i < 3; i++) {
|
|
qt[i] = sclp * p[i] + sclq * qt[i];
|
|
}
|
|
}
|
|
|
|
Assert(qt.IsValid());
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Purpose: Returns the angular delta between the two normalized quaternions in degrees.
|
|
//-----------------------------------------------------------------------------
|
|
float QuaternionAngleDiff(const Quaternion& p, const Quaternion& q)
|
|
{
|
|
#if 1
|
|
// this code path is here for 2 reasons:
|
|
// 1 - acos maps 1-epsilon to values much larger than epsilon (vs asin, which maps epsilon to itself)
|
|
// this means that in floats, anything below ~0.05 degrees truncates to 0
|
|
// 2 - normalized quaternions are frequently slightly non-normalized due to float precision issues,
|
|
// and the epsilon off of normalized can be several percents of a degree
|
|
Quaternion qInv, diff;
|
|
QuaternionConjugate(q, qInv);
|
|
QuaternionMult(p, qInv, diff);
|
|
|
|
// Note if the quaternion is slightly non-normalized the square root below may be more than 1,
|
|
// the value is clamped to one otherwise it may result in asin() returning an undefined result.
|
|
float sinang = MIN(1.0f, sqrt(diff.x * diff.x + diff.y * diff.y + diff.z * diff.z));
|
|
float angle = RAD2DEG(2 * asin(sinang));
|
|
return angle;
|
|
#else
|
|
Quaternion q2;
|
|
QuaternionAlign(p, q, q2);
|
|
|
|
Assert(s_bMathlibInitialized);
|
|
float cosom = p.x * q2.x + p.y * q2.y + p.z * q2.z + p.w * q2.w;
|
|
|
|
if (cosom > -1.0f)
|
|
{
|
|
if (cosom < 1.0f)
|
|
{
|
|
float omega = 2 * fabs(acos(cosom));
|
|
return RAD2DEG(omega);
|
|
}
|
|
return 0.0f;
|
|
}
|
|
|
|
return 180.0f;
|
|
#endif
|
|
}
|
|
|
|
void QuaternionConjugate(const Quaternion& p, Quaternion& q)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Assert(q.IsValid());
|
|
|
|
q.x = -p.x;
|
|
q.y = -p.y;
|
|
q.z = -p.z;
|
|
q.w = p.w;
|
|
}
|
|
|
|
void QuaternionInvert(const Quaternion& p, Quaternion& q)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Assert(q.IsValid());
|
|
|
|
QuaternionConjugate(p, q);
|
|
|
|
float magnitudeSqr = QuaternionDotProduct(p, p);
|
|
Assert(magnitudeSqr);
|
|
if (magnitudeSqr)
|
|
{
|
|
float inv = 1.0f / magnitudeSqr;
|
|
q.x *= inv;
|
|
q.y *= inv;
|
|
q.z *= inv;
|
|
q.w *= inv;
|
|
}
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Make sure the quaternion is of unit length
|
|
//-----------------------------------------------------------------------------
|
|
float QuaternionNormalize(Quaternion& q)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
float radius, iradius;
|
|
|
|
Assert(q.IsValid());
|
|
|
|
radius = q[0] * q[0] + q[1] * q[1] + q[2] * q[2] + q[3] * q[3];
|
|
|
|
if (radius) // > FLT_EPSILON && ((radius < 1.0f - 4*FLT_EPSILON) || (radius > 1.0f + 4*FLT_EPSILON))
|
|
{
|
|
radius = sqrt(radius);
|
|
iradius = 1.0f / radius;
|
|
q[3] *= iradius;
|
|
q[2] *= iradius;
|
|
q[1] *= iradius;
|
|
q[0] *= iradius;
|
|
}
|
|
return radius;
|
|
}
|
|
|
|
|
|
void QuaternionScale(const Quaternion& p, float t, Quaternion& q)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
|
|
#if 0
|
|
Quaternion p0;
|
|
Quaternion q;
|
|
p0.Init(0.0, 0.0, 0.0, 1.0);
|
|
|
|
// slerp in "reverse order" so that p doesn't get realigned
|
|
QuaternionSlerp(p, p0, 1.0 - fabs(t), q);
|
|
if (t < 0.0)
|
|
{
|
|
q.w = -q.w;
|
|
}
|
|
#else
|
|
float r;
|
|
|
|
// FIXME: nick, this isn't overly sensitive to accuracy, and it may be faster to
|
|
// use the cos part (w) of the quaternion (sin(omega)*N,cos(omega)) to figure the new scale.
|
|
float sinom = sqrt(DotProduct(&p.x, &p.x));
|
|
sinom = min(sinom, 1.f);
|
|
|
|
float sinsom = sin(asin(sinom) * t);
|
|
|
|
t = sinsom / (sinom + FLT_EPSILON);
|
|
VectorScale(&p.x, t, &q.x);
|
|
|
|
// rescale rotation
|
|
r = 1.0f - sinsom * sinsom;
|
|
|
|
// Assert( r >= 0 );
|
|
if (r < 0.0f)
|
|
r = 0.0f;
|
|
r = sqrt(r);
|
|
|
|
// keep sign of rotation
|
|
if (p.w < 0)
|
|
q.w = -r;
|
|
else
|
|
q.w = r;
|
|
#endif
|
|
|
|
Assert(q.IsValid());
|
|
|
|
return;
|
|
}
|
|
|
|
|
|
void QuaternionAdd(const Quaternion& p, const Quaternion& q, Quaternion& qt)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Assert(p.IsValid());
|
|
Assert(q.IsValid());
|
|
|
|
// decide if one of the quaternions is backwards
|
|
Quaternion q2;
|
|
QuaternionAlign(p, q, q2);
|
|
|
|
// is this right???
|
|
qt[0] = p[0] + q2[0];
|
|
qt[1] = p[1] + q2[1];
|
|
qt[2] = p[2] + q2[2];
|
|
qt[3] = p[3] + q2[3];
|
|
|
|
return;
|
|
}
|
|
|
|
|
|
float QuaternionDotProduct(const Quaternion& p, const Quaternion& q)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Assert(p.IsValid());
|
|
Assert(q.IsValid());
|
|
|
|
return p.x * q.x + p.y * q.y + p.z * q.z + p.w * q.w;
|
|
}
|
|
|
|
|
|
// qt = p * q
|
|
void QuaternionMult(const Quaternion& p, const Quaternion& q, Quaternion& qt)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Assert(p.IsValid());
|
|
Assert(q.IsValid());
|
|
|
|
if (&p == &qt)
|
|
{
|
|
Quaternion p2 = p;
|
|
QuaternionMult(p2, q, qt);
|
|
return;
|
|
}
|
|
|
|
// decide if one of the quaternions is backwards
|
|
Quaternion q2;
|
|
QuaternionAlign(p, q, q2);
|
|
|
|
qt.x = p.x * q2.w + p.y * q2.z - p.z * q2.y + p.w * q2.x;
|
|
qt.y = -p.x * q2.z + p.y * q2.w + p.z * q2.x + p.w * q2.y;
|
|
qt.z = p.x * q2.y - p.y * q2.x + p.z * q2.w + p.w * q2.z;
|
|
qt.w = -p.x * q2.x - p.y * q2.y - p.z * q2.z + p.w * q2.w;
|
|
}
|
|
|
|
|
|
void QuaternionMatrix(const Quaternion& q, const Vector3D& pos, matrix3x4_t& matrix)
|
|
{
|
|
if (!HushAsserts())
|
|
{
|
|
Assert(pos.IsValid());
|
|
}
|
|
|
|
QuaternionMatrix(q, matrix);
|
|
|
|
matrix[0][3] = pos.x;
|
|
matrix[1][3] = pos.y;
|
|
matrix[2][3] = pos.z;
|
|
}
|
|
|
|
void QuaternionMatrix(const Quaternion& q, matrix3x4_t& matrix)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
if (!HushAsserts())
|
|
{
|
|
Assert(q.IsValid());
|
|
}
|
|
|
|
#ifdef _VPROF_MATHLIB
|
|
VPROF_BUDGET("QuaternionMatrix", "Mathlib");
|
|
#endif
|
|
|
|
// Original code
|
|
// This should produce the same code as below with optimization, but looking at the assmebly,
|
|
// it doesn't. There are 7 extra multiplies in the release build of this, go figure.
|
|
#if 1
|
|
matrix[0][0] = 1.0 - 2.0 * q.y * q.y - 2.0 * q.z * q.z;
|
|
matrix[1][0] = 2.0 * q.x * q.y + 2.0 * q.w * q.z;
|
|
matrix[2][0] = 2.0 * q.x * q.z - 2.0 * q.w * q.y;
|
|
|
|
matrix[0][1] = 2.0f * q.x * q.y - 2.0f * q.w * q.z;
|
|
matrix[1][1] = 1.0f - 2.0f * q.x * q.x - 2.0f * q.z * q.z;
|
|
matrix[2][1] = 2.0f * q.y * q.z + 2.0f * q.w * q.x;
|
|
|
|
matrix[0][2] = 2.0f * q.x * q.z + 2.0f * q.w * q.y;
|
|
matrix[1][2] = 2.0f * q.y * q.z - 2.0f * q.w * q.x;
|
|
matrix[2][2] = 1.0f - 2.0f * q.x * q.x - 2.0f * q.y * q.y;
|
|
|
|
matrix[0][3] = 0.0f;
|
|
matrix[1][3] = 0.0f;
|
|
matrix[2][3] = 0.0f;
|
|
#else
|
|
float wx, wy, wz, xx, yy, yz, xy, xz, zz, x2, y2, z2;
|
|
|
|
// precalculate common multiplitcations
|
|
x2 = q.x + q.x;
|
|
y2 = q.y + q.y;
|
|
z2 = q.z + q.z;
|
|
xx = q.x * x2;
|
|
xy = q.x * y2;
|
|
xz = q.x * z2;
|
|
yy = q.y * y2;
|
|
yz = q.y * z2;
|
|
zz = q.z * z2;
|
|
wx = q.w * x2;
|
|
wy = q.w * y2;
|
|
wz = q.w * z2;
|
|
|
|
matrix[0][0] = 1.0 - (yy + zz);
|
|
matrix[0][1] = xy - wz;
|
|
matrix[0][2] = xz + wy;
|
|
matrix[0][3] = 0.0f;
|
|
|
|
matrix[1][0] = xy + wz;
|
|
matrix[1][1] = 1.0 - (xx + zz);
|
|
matrix[1][2] = yz - wx;
|
|
matrix[1][3] = 0.0f;
|
|
|
|
matrix[2][0] = xz - wy;
|
|
matrix[2][1] = yz + wx;
|
|
matrix[2][2] = 1.0 - (xx + yy);
|
|
matrix[2][3] = 0.0f;
|
|
#endif
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Purpose: Converts a quaternion into engine angles
|
|
// Input : *quaternion - q3 + q0.i + q1.j + q2.k
|
|
// *outAngles - PITCH, YAW, ROLL
|
|
//-----------------------------------------------------------------------------
|
|
void QuaternionAngles(const Quaternion& q, QAngle& angles)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Assert(q.IsValid());
|
|
|
|
#ifdef _VPROF_MATHLIB
|
|
VPROF_BUDGET("QuaternionAngles", "Mathlib");
|
|
#endif
|
|
|
|
#if 1
|
|
// FIXME: doing it this way calculates too much data, needs to do an optimized version...
|
|
matrix3x4_t matrix;
|
|
QuaternionMatrix(q, matrix);
|
|
MatrixAngles(matrix, angles);
|
|
#else
|
|
float m11, m12, m13, m23, m33;
|
|
|
|
m11 = (2.0f * q.w * q.w) + (2.0f * q.x * q.x) - 1.0f;
|
|
m12 = (2.0f * q.x * q.y) + (2.0f * q.w * q.z);
|
|
m13 = (2.0f * q.x * q.z) - (2.0f * q.w * q.y);
|
|
m23 = (2.0f * q.y * q.z) + (2.0f * q.w * q.x);
|
|
m33 = (2.0f * q.w * q.w) + (2.0f * q.z * q.z) - 1.0f;
|
|
|
|
// FIXME: this code has a singularity near PITCH +-90
|
|
angles[YAW] = RAD2DEG(atan2(m12, m11));
|
|
angles[PITCH] = RAD2DEG(asin(-m13));
|
|
angles[ROLL] = RAD2DEG(atan2(m23, m33));
|
|
#endif
|
|
|
|
Assert(angles.IsValid());
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Purpose: Converts a quaternion to an axis / angle in degrees
|
|
// (exponential map)
|
|
//-----------------------------------------------------------------------------
|
|
void QuaternionAxisAngle(const Quaternion& q, Vector3D& axis, float& angle)
|
|
{
|
|
angle = RAD2DEG(2 * acos(q.w));
|
|
if (angle > 180)
|
|
{
|
|
angle -= 360;
|
|
}
|
|
axis.x = q.x;
|
|
axis.y = q.y;
|
|
axis.z = q.z;
|
|
VectorNormalize(axis);
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Purpose: Converts an exponential map (ang/axis) to a quaternion
|
|
//-----------------------------------------------------------------------------
|
|
void AxisAngleQuaternion(const Vector3D& axis, float angle, Quaternion& q)
|
|
{
|
|
float sa, ca;
|
|
|
|
SinCos(DEG2RAD(angle) * 0.5f, &sa, &ca);
|
|
|
|
q.x = axis.x * sa;
|
|
q.y = axis.y * sa;
|
|
q.z = axis.z * sa;
|
|
q.w = ca;
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Purpose: Converts radian-euler axis aligned angles to a quaternion
|
|
// Input : *pfAngles - Right-handed Euler angles in radians
|
|
// *outQuat - quaternion of form (i,j,k,real)
|
|
//-----------------------------------------------------------------------------
|
|
void AngleQuaternion(const RadianEuler& angles, Quaternion& outQuat)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
// Assert( angles.IsValid() );
|
|
|
|
#ifdef _VPROF_MATHLIB
|
|
VPROF_BUDGET("AngleQuaternion", "Mathlib");
|
|
#endif
|
|
|
|
float sr, sp, sy, cr, cp, cy;
|
|
|
|
#ifdef _X360
|
|
fltx4 radians, scale, sine, cosine;
|
|
radians = LoadUnaligned3SIMD(&angles.x);
|
|
scale = ReplicateX4(0.5f);
|
|
radians = MulSIMD(radians, scale);
|
|
SinCos3SIMD(sine, cosine, radians);
|
|
|
|
// NOTE: The ordering here is *different* from the AngleQuaternion below
|
|
// because p, y, r are not in the same locations in QAngle + RadianEuler. Yay!
|
|
sr = SubFloat(sine, 0); sp = SubFloat(sine, 1); sy = SubFloat(sine, 2);
|
|
cr = SubFloat(cosine, 0); cp = SubFloat(cosine, 1); cy = SubFloat(cosine, 2);
|
|
#else
|
|
SinCos(angles.z * 0.5f, &sy, &cy);
|
|
SinCos(angles.y * 0.5f, &sp, &cp);
|
|
SinCos(angles.x * 0.5f, &sr, &cr);
|
|
#endif
|
|
|
|
// NJS: for some reason VC6 wasn't recognizing the common subexpressions:
|
|
float srXcp = sr * cp, crXsp = cr * sp;
|
|
outQuat.x = srXcp * cy - crXsp * sy; // X
|
|
outQuat.y = crXsp * cy + srXcp * sy; // Y
|
|
|
|
float crXcp = cr * cp, srXsp = sr * sp;
|
|
outQuat.z = crXcp * sy - srXsp * cy; // Z
|
|
outQuat.w = crXcp * cy + srXsp * sy; // W (real component)
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Purpose: Converts engine-format euler angles to a quaternion
|
|
// Input : angles - Right-handed Euler angles in degrees as follows:
|
|
// [0]: PITCH: Clockwise rotation around the Y axis.
|
|
// [1]: YAW: Counterclockwise rotation around the Z axis.
|
|
// [2]: ROLL: Counterclockwise rotation around the X axis.
|
|
// *outQuat - quaternion of form (i,j,k,real)
|
|
//-----------------------------------------------------------------------------
|
|
void AngleQuaternion(const QAngle& angles, Quaternion& outQuat)
|
|
{
|
|
#ifdef _VPROF_MATHLIB
|
|
VPROF_BUDGET("AngleQuaternion", "Mathlib");
|
|
#endif
|
|
|
|
float sr, sp, sy, cr, cp, cy;
|
|
|
|
#ifdef _X360
|
|
fltx4 radians, scale, sine, cosine;
|
|
radians = LoadUnaligned3SIMD(angles.Base());
|
|
scale = ReplicateX4(0.5f * M_PI_F / 180.f);
|
|
radians = MulSIMD(radians, scale);
|
|
SinCos3SIMD(sine, cosine, radians);
|
|
|
|
// NOTE: The ordering here is *different* from the AngleQuaternion above
|
|
// because p, y, r are not in the same locations in QAngle + RadianEuler. Yay!
|
|
sp = SubFloat(sine, 0); sy = SubFloat(sine, 1); sr = SubFloat(sine, 2);
|
|
cp = SubFloat(cosine, 0); cy = SubFloat(cosine, 1); cr = SubFloat(cosine, 2);
|
|
#else
|
|
SinCos(DEG2RAD(angles.y) * 0.5f, &sy, &cy);
|
|
SinCos(DEG2RAD(angles.x) * 0.5f, &sp, &cp);
|
|
SinCos(DEG2RAD(angles.z) * 0.5f, &sr, &cr);
|
|
#endif
|
|
|
|
// NJS: for some reason VC6 wasn't recognizing the common subexpressions:
|
|
float srXcp = sr * cp, crXsp = cr * sp;
|
|
outQuat.x = srXcp * cy - crXsp * sy; // X
|
|
outQuat.y = crXsp * cy + srXcp * sy; // Y
|
|
|
|
float crXcp = cr * cp, srXsp = sr * sp;
|
|
outQuat.z = crXcp * sy - srXsp * cy; // Z
|
|
outQuat.w = crXcp * cy + srXsp * sy; // W (real component)
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Purpose: Converts a basis to a quaternion
|
|
//-----------------------------------------------------------------------------
|
|
void BasisToQuaternion(const Vector3D& vecForward, const Vector3D& vecRight, const Vector3D& vecUp, Quaternion& q)
|
|
{
|
|
Assert(fabs(vecForward.LengthSqr() - 1.0f) < 1e-3);
|
|
Assert(fabs(vecRight.LengthSqr() - 1.0f) < 1e-3);
|
|
Assert(fabs(vecUp.LengthSqr() - 1.0f) < 1e-3);
|
|
|
|
Vector3D vecLeft;
|
|
VectorMultiply(vecRight, -1.0f, vecLeft);
|
|
|
|
// FIXME: Don't know why, but this doesn't match at all with other result
|
|
// so we can't use this super-fast way.
|
|
/*
|
|
// Find the trace of the matrix:
|
|
float flTrace = vecForward.x + vecLeft.y + vecUp.z + 1.0f;
|
|
if ( flTrace > 1e-6 )
|
|
{
|
|
float flSqrtTrace = FastSqrt( flTrace );
|
|
float s = 0.5f / flSqrtTrace;
|
|
q.x = ( vecUp.y - vecLeft.z ) * s;
|
|
q.y = ( vecForward.z - vecUp.x ) * s;
|
|
q.z = ( vecLeft.x - vecForward.y ) * s;
|
|
q.w = 0.5f * flSqrtTrace;
|
|
}
|
|
else
|
|
{
|
|
if (( vecForward.x > vecLeft.y ) && ( vecForward.x > vecUp.z ) )
|
|
{
|
|
float flSqrtTrace = FastSqrt( 1.0f + vecForward.x - vecLeft.y - vecUp.z );
|
|
float s = 0.5f / flSqrtTrace;
|
|
q.x = 0.5f * flSqrtTrace;
|
|
q.y = ( vecForward.y + vecLeft.x ) * s;
|
|
q.z = ( vecUp.x + vecForward.z ) * s;
|
|
q.w = ( vecUp.y - vecLeft.z ) * s;
|
|
}
|
|
else if ( vecLeft.y > vecUp.z )
|
|
{
|
|
float flSqrtTrace = FastSqrt( 1.0f + vecLeft.y - vecForward.x - vecUp.z );
|
|
float s = 0.5f / flSqrtTrace;
|
|
q.x = ( vecForward.y + vecLeft.x ) * s;
|
|
q.y = 0.5f * flSqrtTrace;
|
|
q.z = ( vecUp.y + vecLeft.z ) * s;
|
|
q.w = ( vecForward.z - vecUp.x ) * s;
|
|
}
|
|
else
|
|
{
|
|
float flSqrtTrace = FastSqrt( 1.0 + vecUp.z - vecForward.x - vecLeft.y );
|
|
float s = 0.5f / flSqrtTrace;
|
|
q.x = ( vecUp.x + vecForward.z ) * s;
|
|
q.y = ( vecUp.y + vecLeft.z ) * s;
|
|
q.z = 0.5f * flSqrtTrace;
|
|
q.w = ( vecLeft.x - vecForward.y ) * s;
|
|
}
|
|
}
|
|
QuaternionNormalize( q );
|
|
*/
|
|
|
|
// Version 2: Go through angles
|
|
|
|
matrix3x4_t mat;
|
|
MatrixSetColumn(vecForward, 0, mat);
|
|
MatrixSetColumn(vecLeft, 1, mat);
|
|
MatrixSetColumn(vecUp, 2, mat);
|
|
|
|
QAngle angles;
|
|
MatrixAngles(mat, angles);
|
|
|
|
// Quaternion q2;
|
|
AngleQuaternion(angles, q);
|
|
|
|
// Assert( fabs(q.x - q2.x) < 1e-3 );
|
|
// Assert( fabs(q.y - q2.y) < 1e-3 );
|
|
// Assert( fabs(q.z - q2.z) < 1e-3 );
|
|
// Assert( fabs(q.w - q2.w) < 1e-3 );
|
|
}
|
|
|
|
// FIXME: Optimize!
|
|
void MatrixQuaternion(const matrix3x4_t& mat, Quaternion& q)
|
|
{
|
|
QAngle angles;
|
|
MatrixAngles(mat, angles);
|
|
AngleQuaternion(angles, q);
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Purpose: Converts a quaternion into engine angles
|
|
// Input : *quaternion - q3 + q0.i + q1.j + q2.k
|
|
// *outAngles - PITCH, YAW, ROLL
|
|
//-----------------------------------------------------------------------------
|
|
void QuaternionAngles(const Quaternion& q, RadianEuler& angles)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Assert(q.IsValid());
|
|
|
|
// FIXME: doing it this way calculates too much data, needs to do an optimized version...
|
|
matrix3x4_t matrix;
|
|
QuaternionMatrix(q, matrix);
|
|
MatrixAngles(matrix, angles);
|
|
|
|
Assert(angles.IsValid());
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Purpose: A helper function to normalize p2.x->p1.x and p3.x->p4.x to
|
|
// be the same length as p2.x->p3.x
|
|
// Input : &p2 -
|
|
// &p4 -
|
|
// p4n -
|
|
//-----------------------------------------------------------------------------
|
|
void Spline_Normalize(
|
|
const Vector3D& p1,
|
|
const Vector3D& p2,
|
|
const Vector3D& p3,
|
|
const Vector3D& p4,
|
|
Vector3D& p1n,
|
|
Vector3D& p4n)
|
|
{
|
|
float dt = p3.x - p2.x;
|
|
|
|
p1n = p1;
|
|
p4n = p4;
|
|
|
|
if (dt != 0.0)
|
|
{
|
|
if (p1.x != p2.x)
|
|
{
|
|
// Equivalent to p1n = p2 - (p2 - p1) * (dt / (p2.x - p1.x));
|
|
VectorLerp(p2, p1, dt / (p2.x - p1.x), p1n);
|
|
}
|
|
if (p4.x != p3.x)
|
|
{
|
|
// Equivalent to p4n = p3 + (p4 - p3) * (dt / (p4.x - p3.x));
|
|
VectorLerp(p3, p4, dt / (p4.x - p3.x), p4n);
|
|
}
|
|
}
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Purpose:
|
|
// Input :
|
|
//-----------------------------------------------------------------------------
|
|
|
|
void Catmull_Rom_Spline(
|
|
const Vector3D& p1,
|
|
const Vector3D& p2,
|
|
const Vector3D& p3,
|
|
const Vector3D& p4,
|
|
float t,
|
|
Vector3D& output)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
float tSqr = t * t * 0.5f;
|
|
float tSqrSqr = t * tSqr;
|
|
t *= 0.5f;
|
|
|
|
Assert(&output != &p1);
|
|
Assert(&output != &p2);
|
|
Assert(&output != &p3);
|
|
Assert(&output != &p4);
|
|
|
|
output.Init();
|
|
|
|
Vector3D a, b, c, d;
|
|
|
|
// matrix row 1
|
|
VectorScale(p1, -tSqrSqr, a); // 0.5 t^3 * [ (-1*p1) + ( 3*p2) + (-3*p3) + p4 ]
|
|
VectorScale(p2, tSqrSqr * 3, b);
|
|
VectorScale(p3, tSqrSqr * -3, c);
|
|
VectorScale(p4, tSqrSqr, d);
|
|
|
|
VectorAdd(a, output, output);
|
|
VectorAdd(b, output, output);
|
|
VectorAdd(c, output, output);
|
|
VectorAdd(d, output, output);
|
|
|
|
// matrix row 2
|
|
VectorScale(p1, tSqr * 2, a); // 0.5 t^2 * [ ( 2*p1) + (-5*p2) + ( 4*p3) - p4 ]
|
|
VectorScale(p2, tSqr * -5, b);
|
|
VectorScale(p3, tSqr * 4, c);
|
|
VectorScale(p4, -tSqr, d);
|
|
|
|
VectorAdd(a, output, output);
|
|
VectorAdd(b, output, output);
|
|
VectorAdd(c, output, output);
|
|
VectorAdd(d, output, output);
|
|
|
|
// matrix row 3
|
|
VectorScale(p1, -t, a); // 0.5 t * [ (-1*p1) + p3 ]
|
|
VectorScale(p3, t, b);
|
|
|
|
VectorAdd(a, output, output);
|
|
VectorAdd(b, output, output);
|
|
|
|
// matrix row 4
|
|
VectorAdd(p2, output, output); // p2
|
|
}
|
|
|
|
void Catmull_Rom_Spline_Tangent(
|
|
const Vector3D& p1,
|
|
const Vector3D& p2,
|
|
const Vector3D& p3,
|
|
const Vector3D& p4,
|
|
float t,
|
|
Vector3D& output)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
float tOne = 3 * t * t * 0.5f;
|
|
float tTwo = 2 * t * 0.5f;
|
|
float tThree = 0.5;
|
|
|
|
Assert(&output != &p1);
|
|
Assert(&output != &p2);
|
|
Assert(&output != &p3);
|
|
Assert(&output != &p4);
|
|
|
|
output.Init();
|
|
|
|
Vector3D a, b, c, d;
|
|
|
|
// matrix row 1
|
|
VectorScale(p1, -tOne, a); // 0.5 t^3 * [ (-1*p1) + ( 3*p2) + (-3*p3) + p4 ]
|
|
VectorScale(p2, tOne * 3, b);
|
|
VectorScale(p3, tOne * -3, c);
|
|
VectorScale(p4, tOne, d);
|
|
|
|
VectorAdd(a, output, output);
|
|
VectorAdd(b, output, output);
|
|
VectorAdd(c, output, output);
|
|
VectorAdd(d, output, output);
|
|
|
|
// matrix row 2
|
|
VectorScale(p1, tTwo * 2, a); // 0.5 t^2 * [ ( 2*p1) + (-5*p2) + ( 4*p3) - p4 ]
|
|
VectorScale(p2, tTwo * -5, b);
|
|
VectorScale(p3, tTwo * 4, c);
|
|
VectorScale(p4, -tTwo, d);
|
|
|
|
VectorAdd(a, output, output);
|
|
VectorAdd(b, output, output);
|
|
VectorAdd(c, output, output);
|
|
VectorAdd(d, output, output);
|
|
|
|
// matrix row 3
|
|
VectorScale(p1, -tThree, a); // 0.5 t * [ (-1*p1) + p3 ]
|
|
VectorScale(p3, tThree, b);
|
|
|
|
VectorAdd(a, output, output);
|
|
VectorAdd(b, output, output);
|
|
}
|
|
|
|
// area under the curve [0..t]
|
|
void Catmull_Rom_Spline_Integral(
|
|
const Vector3D& p1,
|
|
const Vector3D& p2,
|
|
const Vector3D& p3,
|
|
const Vector3D& p4,
|
|
float t,
|
|
Vector3D& output)
|
|
{
|
|
output = p2 * t
|
|
- 0.25f * (p1 - p3) * t * t
|
|
+ (1.0f / 6.0f) * (2.0f * p1 - 5.0f * p2 + 4.0f * p3 - p4) * t * t * t
|
|
- 0.125f * (p1 - 3.0f * p2 + 3.0f * p3 - p4) * t * t * t * t;
|
|
}
|
|
|
|
|
|
// area under the curve [0..1]
|
|
void Catmull_Rom_Spline_Integral(
|
|
const Vector3D& p1,
|
|
const Vector3D& p2,
|
|
const Vector3D& p3,
|
|
const Vector3D& p4,
|
|
Vector3D& output)
|
|
{
|
|
output = (-0.25f * p1 + 3.25f * p2 + 3.25f * p3 - 0.25f * p4) * (1.0f / 6.0f);
|
|
}
|
|
|
|
|
|
void Catmull_Rom_Spline_Normalize(
|
|
const Vector3D& p1,
|
|
const Vector3D& p2,
|
|
const Vector3D& p3,
|
|
const Vector3D& p4,
|
|
float t,
|
|
Vector3D& output)
|
|
{
|
|
// Normalize p2->p1 and p3->p4 to be the same length as p2->p3
|
|
float dt = p3.DistTo(p2);
|
|
|
|
Vector3D p1n, p4n;
|
|
VectorSubtract(p1, p2, p1n);
|
|
VectorSubtract(p4, p3, p4n);
|
|
|
|
VectorNormalize(p1n);
|
|
VectorNormalize(p4n);
|
|
|
|
VectorMA(p2, dt, p1n, p1n);
|
|
VectorMA(p3, dt, p4n, p4n);
|
|
|
|
Catmull_Rom_Spline(p1n, p2, p3, p4n, t, output);
|
|
}
|
|
|
|
|
|
void Catmull_Rom_Spline_Integral_Normalize(
|
|
const Vector3D& p1,
|
|
const Vector3D& p2,
|
|
const Vector3D& p3,
|
|
const Vector3D& p4,
|
|
float t,
|
|
Vector3D& output)
|
|
{
|
|
// Normalize p2->p1 and p3->p4 to be the same length as p2->p3
|
|
float dt = p3.DistTo(p2);
|
|
|
|
Vector3D p1n, p4n;
|
|
VectorSubtract(p1, p2, p1n);
|
|
VectorSubtract(p4, p3, p4n);
|
|
|
|
VectorNormalize(p1n);
|
|
VectorNormalize(p4n);
|
|
|
|
VectorMA(p2, dt, p1n, p1n);
|
|
VectorMA(p3, dt, p4n, p4n);
|
|
|
|
Catmull_Rom_Spline_Integral(p1n, p2, p3, p4n, t, output);
|
|
}
|
|
|
|
|
|
void Catmull_Rom_Spline_NormalizeX(
|
|
const Vector3D& p1,
|
|
const Vector3D& p2,
|
|
const Vector3D& p3,
|
|
const Vector3D& p4,
|
|
float t,
|
|
Vector3D& output)
|
|
{
|
|
Vector3D p1n, p4n;
|
|
Spline_Normalize(p1, p2, p3, p4, p1n, p4n);
|
|
Catmull_Rom_Spline(p1n, p2, p3, p4n, t, output);
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Purpose: basic hermite spline. t = 0 returns p1, t = 1 returns p2,
|
|
// d1 and d2 are used to entry and exit slope of curve
|
|
// Input :
|
|
//-----------------------------------------------------------------------------
|
|
|
|
void Hermite_Spline(
|
|
const Vector3D& p1,
|
|
const Vector3D& p2,
|
|
const Vector3D& d1,
|
|
const Vector3D& d2,
|
|
float t,
|
|
Vector3D& output)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
float tSqr = t * t;
|
|
float tCube = t * tSqr;
|
|
|
|
Assert(&output != &p1);
|
|
Assert(&output != &p2);
|
|
Assert(&output != &d1);
|
|
Assert(&output != &d2);
|
|
|
|
float b1 = 2.0f * tCube - 3.0f * tSqr + 1.0f;
|
|
float b2 = 1.0f - b1; // -2*tCube+3*tSqr;
|
|
float b3 = tCube - 2 * tSqr + t;
|
|
float b4 = tCube - tSqr;
|
|
|
|
VectorScale(p1, b1, output);
|
|
VectorMA(output, b2, p2, output);
|
|
VectorMA(output, b3, d1, output);
|
|
VectorMA(output, b4, d2, output);
|
|
}
|
|
|
|
float Hermite_Spline(
|
|
float p1,
|
|
float p2,
|
|
float d1,
|
|
float d2,
|
|
float t)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
float output;
|
|
float tSqr = t * t;
|
|
float tCube = t * tSqr;
|
|
|
|
float b1 = 2.0f * tCube - 3.0f * tSqr + 1.0f;
|
|
float b2 = 1.0f - b1; // -2*tCube+3*tSqr;
|
|
float b3 = tCube - 2 * tSqr + t;
|
|
float b4 = tCube - tSqr;
|
|
|
|
output = p1 * b1;
|
|
output += p2 * b2;
|
|
output += d1 * b3;
|
|
output += d2 * b4;
|
|
|
|
return output;
|
|
}
|
|
|
|
|
|
void Hermite_SplineBasis(float t, float basis[4])
|
|
{
|
|
float tSqr = t * t;
|
|
float tCube = t * tSqr;
|
|
|
|
basis[0] = 2.0f * tCube - 3.0f * tSqr + 1.0f;
|
|
basis[1] = 1.0f - basis[0]; // -2*tCube+3*tSqr;
|
|
basis[2] = tCube - 2 * tSqr + t;
|
|
basis[3] = tCube - tSqr;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Purpose: simple three data point hermite spline.
|
|
// t = 0 returns p1, t = 1 returns p2,
|
|
// slopes are generated from the p0->p1 and p1->p2 segments
|
|
// this is reasonable C1 method when there's no "p3" data yet.
|
|
// Input :
|
|
//-----------------------------------------------------------------------------
|
|
|
|
// BUG: the Vector3DSubtract()'s calls go away if the global optimizer is enabled
|
|
#pragma optimize( "g", off )
|
|
|
|
void Hermite_Spline(const Vector3D& p0, const Vector3D& p1, const Vector3D& p2, float t, Vector3D& output)
|
|
{
|
|
Vector3D e10, e21;
|
|
VectorSubtract(p1, p0, e10);
|
|
VectorSubtract(p2, p1, e21);
|
|
Hermite_Spline(p1, p2, e10, e21, t, output);
|
|
}
|
|
|
|
#pragma optimize( "", on )
|
|
|
|
float Hermite_Spline(float p0, float p1, float p2, float t)
|
|
{
|
|
return Hermite_Spline(p1, p2, p1 - p0, p2 - p1, t);
|
|
}
|
|
|
|
|
|
void Hermite_Spline(const Quaternion& q0, const Quaternion& q1, const Quaternion& q2, float t, Quaternion& output)
|
|
{
|
|
// cheap, hacked version of quaternions
|
|
Quaternion q0a;
|
|
Quaternion q1a;
|
|
|
|
QuaternionAlign(q2, q0, q0a);
|
|
QuaternionAlign(q2, q1, q1a);
|
|
|
|
output.x = Hermite_Spline(q0a.x, q1a.x, q2.x, t);
|
|
output.y = Hermite_Spline(q0a.y, q1a.y, q2.y, t);
|
|
output.z = Hermite_Spline(q0a.z, q1a.z, q2.z, t);
|
|
output.w = Hermite_Spline(q0a.w, q1a.w, q2.w, t);
|
|
|
|
QuaternionNormalize(output);
|
|
}
|
|
|
|
// See http://en.wikipedia.org/wiki/Kochanek-Bartels_curves
|
|
//
|
|
// Tension: -1 = Round -> 1 = Tight
|
|
// Bias: -1 = Pre-shoot (bias left) -> 1 = Post-shoot (bias right)
|
|
// Continuity: -1 = Box corners -> 1 = Inverted corners
|
|
//
|
|
// If T=B=C=0 it's the same matrix as Catmull-Rom.
|
|
// If T=1 & B=C=0 it's the same as Cubic.
|
|
// If T=B=0 & C=-1 it's just linear interpolation
|
|
//
|
|
// See http://news.povray.org/povray.binaries.tutorials/attachment/%3CXns91B880592482seed7@povray.org%3E/Splines.bas.txt
|
|
// for example code and descriptions of various spline types...
|
|
//
|
|
void Kochanek_Bartels_Spline(
|
|
float tension,
|
|
float bias,
|
|
float continuity,
|
|
const Vector3D& p1,
|
|
const Vector3D& p2,
|
|
const Vector3D& p3,
|
|
const Vector3D& p4,
|
|
float t,
|
|
Vector3D& output)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
|
|
float ffa, ffb, ffc, ffd;
|
|
|
|
ffa = (1.0f - tension) * (1.0f + continuity) * (1.0f + bias);
|
|
ffb = (1.0f - tension) * (1.0f - continuity) * (1.0f - bias);
|
|
ffc = (1.0f - tension) * (1.0f - continuity) * (1.0f + bias);
|
|
ffd = (1.0f - tension) * (1.0f + continuity) * (1.0f - bias);
|
|
|
|
float tSqr = t * t * 0.5f;
|
|
float tSqrSqr = t * tSqr;
|
|
t *= 0.5f;
|
|
|
|
Assert(&output != &p1);
|
|
Assert(&output != &p2);
|
|
Assert(&output != &p3);
|
|
Assert(&output != &p4);
|
|
|
|
output.Init();
|
|
|
|
Vector3D a, b, c, d;
|
|
|
|
// matrix row 1
|
|
VectorScale(p1, tSqrSqr * -ffa, a);
|
|
VectorScale(p2, tSqrSqr * (4.0f + ffa - ffb - ffc), b);
|
|
VectorScale(p3, tSqrSqr * (-4.0f + ffb + ffc - ffd), c);
|
|
VectorScale(p4, tSqrSqr * ffd, d);
|
|
|
|
VectorAdd(a, output, output);
|
|
VectorAdd(b, output, output);
|
|
VectorAdd(c, output, output);
|
|
VectorAdd(d, output, output);
|
|
|
|
// matrix row 2
|
|
VectorScale(p1, tSqr * 2 * ffa, a);
|
|
VectorScale(p2, tSqr * (-6 - 2 * ffa + 2 * ffb + ffc), b);
|
|
VectorScale(p3, tSqr * (6 - 2 * ffb - ffc + ffd), c);
|
|
VectorScale(p4, tSqr * -ffd, d);
|
|
|
|
VectorAdd(a, output, output);
|
|
VectorAdd(b, output, output);
|
|
VectorAdd(c, output, output);
|
|
VectorAdd(d, output, output);
|
|
|
|
// matrix row 3
|
|
VectorScale(p1, t * -ffa, a);
|
|
VectorScale(p2, t * (ffa - ffb), b);
|
|
VectorScale(p3, t * ffb, c);
|
|
// p4 unchanged
|
|
|
|
VectorAdd(a, output, output);
|
|
VectorAdd(b, output, output);
|
|
VectorAdd(c, output, output);
|
|
|
|
// matrix row 4
|
|
// p1, p3, p4 unchanged
|
|
// p2 is multiplied by 1 and added, so just added it directly
|
|
|
|
VectorAdd(p2, output, output);
|
|
}
|
|
|
|
void Kochanek_Bartels_Spline_NormalizeX(
|
|
float tension,
|
|
float bias,
|
|
float continuity,
|
|
const Vector3D& p1,
|
|
const Vector3D& p2,
|
|
const Vector3D& p3,
|
|
const Vector3D& p4,
|
|
float t,
|
|
Vector3D& output)
|
|
{
|
|
Vector3D p1n, p4n;
|
|
Spline_Normalize(p1, p2, p3, p4, p1n, p4n);
|
|
Kochanek_Bartels_Spline(tension, bias, continuity, p1n, p2, p3, p4n, t, output);
|
|
}
|
|
|
|
void Cubic_Spline(
|
|
const Vector3D& p1,
|
|
const Vector3D& p2,
|
|
const Vector3D& p3,
|
|
const Vector3D& p4,
|
|
float t,
|
|
Vector3D& output)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
|
|
float tSqr = t * t;
|
|
float tSqrSqr = t * tSqr;
|
|
|
|
Assert(&output != &p1);
|
|
Assert(&output != &p2);
|
|
Assert(&output != &p3);
|
|
Assert(&output != &p4);
|
|
|
|
output.Init();
|
|
|
|
Vector3D a, b, c, d;
|
|
|
|
// matrix row 1
|
|
VectorScale(p2, tSqrSqr * 2, b);
|
|
VectorScale(p3, tSqrSqr * -2, c);
|
|
|
|
VectorAdd(b, output, output);
|
|
VectorAdd(c, output, output);
|
|
|
|
// matrix row 2
|
|
VectorScale(p2, tSqr * -3, b);
|
|
VectorScale(p3, tSqr * 3, c);
|
|
|
|
VectorAdd(b, output, output);
|
|
VectorAdd(c, output, output);
|
|
|
|
// matrix row 3
|
|
// no influence
|
|
// p4 unchanged
|
|
|
|
// matrix row 4
|
|
// p1, p3, p4 unchanged
|
|
VectorAdd(p2, output, output);
|
|
}
|
|
|
|
void Cubic_Spline_NormalizeX(
|
|
const Vector3D& p1,
|
|
const Vector3D& p2,
|
|
const Vector3D& p3,
|
|
const Vector3D& p4,
|
|
float t,
|
|
Vector3D& output)
|
|
{
|
|
Vector3D p1n, p4n;
|
|
Spline_Normalize(p1, p2, p3, p4, p1n, p4n);
|
|
Cubic_Spline(p1n, p2, p3, p4n, t, output);
|
|
}
|
|
|
|
void BSpline(
|
|
const Vector3D& p1,
|
|
const Vector3D& p2,
|
|
const Vector3D& p3,
|
|
const Vector3D& p4,
|
|
float t,
|
|
Vector3D& output)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
|
|
float oneOver6 = 1.0f / 6.0f;
|
|
|
|
float tSqr = t * t * oneOver6;
|
|
float tSqrSqr = t * tSqr;
|
|
t *= oneOver6;
|
|
|
|
Assert(&output != &p1);
|
|
Assert(&output != &p2);
|
|
Assert(&output != &p3);
|
|
Assert(&output != &p4);
|
|
|
|
output.Init();
|
|
|
|
Vector3D a, b, c, d;
|
|
|
|
// matrix row 1
|
|
VectorScale(p1, -tSqrSqr, a);
|
|
VectorScale(p2, tSqrSqr * 3.0f, b);
|
|
VectorScale(p3, tSqrSqr * -3.0f, c);
|
|
VectorScale(p4, tSqrSqr, d);
|
|
|
|
VectorAdd(a, output, output);
|
|
VectorAdd(b, output, output);
|
|
VectorAdd(c, output, output);
|
|
VectorAdd(d, output, output);
|
|
|
|
// matrix row 2
|
|
VectorScale(p1, tSqr * 3.0f, a);
|
|
VectorScale(p2, tSqr * -6.0f, b);
|
|
VectorScale(p3, tSqr * 3.0f, c);
|
|
|
|
VectorAdd(a, output, output);
|
|
VectorAdd(b, output, output);
|
|
VectorAdd(c, output, output);
|
|
|
|
// matrix row 3
|
|
VectorScale(p1, t * -3.0f, a);
|
|
VectorScale(p3, t * 3.0f, c);
|
|
// p4 unchanged
|
|
|
|
VectorAdd(a, output, output);
|
|
VectorAdd(c, output, output);
|
|
|
|
// matrix row 4
|
|
// p1 and p3 scaled by 1.0f, so done below
|
|
VectorScale(p1, oneOver6, a);
|
|
VectorScale(p2, 4.0f * oneOver6, b);
|
|
VectorScale(p3, oneOver6, c);
|
|
|
|
VectorAdd(a, output, output);
|
|
VectorAdd(b, output, output);
|
|
VectorAdd(c, output, output);
|
|
}
|
|
|
|
void BSpline_NormalizeX(
|
|
const Vector3D& p1,
|
|
const Vector3D& p2,
|
|
const Vector3D& p3,
|
|
const Vector3D& p4,
|
|
float t,
|
|
Vector3D& output)
|
|
{
|
|
Vector3D p1n, p4n;
|
|
Spline_Normalize(p1, p2, p3, p4, p1n, p4n);
|
|
BSpline(p1n, p2, p3, p4n, t, output);
|
|
}
|
|
|
|
void Parabolic_Spline(
|
|
const Vector3D& p1,
|
|
const Vector3D& p2,
|
|
const Vector3D& p3,
|
|
const Vector3D& p4,
|
|
float t,
|
|
Vector3D& output)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
|
|
float tSqr = t * t * 0.5f;
|
|
t *= 0.5f;
|
|
|
|
Assert(&output != &p1);
|
|
Assert(&output != &p2);
|
|
Assert(&output != &p3);
|
|
Assert(&output != &p4);
|
|
|
|
output.Init();
|
|
|
|
Vector3D a, b, c, d;
|
|
|
|
// matrix row 1
|
|
// no influence from t cubed
|
|
|
|
// matrix row 2
|
|
VectorScale(p1, tSqr, a);
|
|
VectorScale(p2, tSqr * -2.0f, b);
|
|
VectorScale(p3, tSqr, c);
|
|
|
|
VectorAdd(a, output, output);
|
|
VectorAdd(b, output, output);
|
|
VectorAdd(c, output, output);
|
|
|
|
// matrix row 3
|
|
VectorScale(p1, t * -2.0f, a);
|
|
VectorScale(p2, t * 2.0f, b);
|
|
// p4 unchanged
|
|
|
|
VectorAdd(a, output, output);
|
|
VectorAdd(b, output, output);
|
|
|
|
// matrix row 4
|
|
VectorScale(p1, 0.5f, a);
|
|
VectorScale(p2, 0.5f, b);
|
|
|
|
VectorAdd(a, output, output);
|
|
VectorAdd(b, output, output);
|
|
}
|
|
|
|
void Parabolic_Spline_NormalizeX(
|
|
const Vector3D& p1,
|
|
const Vector3D& p2,
|
|
const Vector3D& p3,
|
|
const Vector3D& p4,
|
|
float t,
|
|
Vector3D& output)
|
|
{
|
|
Vector3D p1n, p4n;
|
|
Spline_Normalize(p1, p2, p3, p4, p1n, p4n);
|
|
Parabolic_Spline(p1n, p2, p3, p4n, t, output);
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Purpose: Compress the input values for a ranged result such that from 75% to 200% smoothly of the range maps
|
|
//-----------------------------------------------------------------------------
|
|
|
|
float RangeCompressor(float flValue, float flMin, float flMax, float flBase)
|
|
{
|
|
// clamp base
|
|
if (flBase < flMin)
|
|
flBase = flMin;
|
|
if (flBase > flMax)
|
|
flBase = flMax;
|
|
|
|
flValue += flBase;
|
|
|
|
// convert to 0 to 1 value
|
|
float flMid = (flValue - flMin) / (flMax - flMin);
|
|
// convert to -1 to 1 value
|
|
float flTarget = flMid * 2 - 1;
|
|
|
|
if (fabs(flTarget) > 0.75)
|
|
{
|
|
float t = (fabs(flTarget) - 0.75) / (1.25);
|
|
if (t < 1.0)
|
|
{
|
|
if (flTarget > 0)
|
|
{
|
|
flTarget = Hermite_Spline(0.75, 1, 0.75, 0, t);
|
|
}
|
|
else
|
|
{
|
|
flTarget = -Hermite_Spline(0.75, 1, 0.75, 0, t);
|
|
}
|
|
}
|
|
else
|
|
{
|
|
flTarget = (flTarget > 0) ? 1.0f : -1.0f;
|
|
}
|
|
}
|
|
|
|
flMid = (flTarget + 1) / 2.0;
|
|
flValue = flMin * (1 - flMid) + flMax * flMid;
|
|
|
|
flValue -= flBase;
|
|
|
|
return flValue;
|
|
}
|
|
|
|
|
|
//#pragma optimize( "", on )
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Transforms a AABB into another space; which will inherently grow the box.
|
|
//-----------------------------------------------------------------------------
|
|
void TransformAABB(const matrix3x4_t& transform, const Vector3D& vecMinsIn, const Vector3D& vecMaxsIn, Vector3D& vecMinsOut, Vector3D& vecMaxsOut)
|
|
{
|
|
Vector3D localCenter;
|
|
VectorAdd(vecMinsIn, vecMaxsIn, localCenter);
|
|
localCenter *= 0.5f;
|
|
|
|
Vector3D localExtents;
|
|
VectorSubtract(vecMaxsIn, localCenter, localExtents);
|
|
|
|
Vector3D worldCenter;
|
|
VectorTransform(localCenter, transform, worldCenter);
|
|
|
|
Vector3D worldExtents;
|
|
worldExtents.x = DotProductAbs(localExtents, transform[0]);
|
|
worldExtents.y = DotProductAbs(localExtents, transform[1]);
|
|
worldExtents.z = DotProductAbs(localExtents, transform[2]);
|
|
|
|
VectorSubtract(worldCenter, worldExtents, vecMinsOut);
|
|
VectorAdd(worldCenter, worldExtents, vecMaxsOut);
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Uses the inverse transform of in1
|
|
//-----------------------------------------------------------------------------
|
|
void ITransformAABB(const matrix3x4_t& transform, const Vector3D& vecMinsIn, const Vector3D& vecMaxsIn, Vector3D& vecMinsOut, Vector3D& vecMaxsOut)
|
|
{
|
|
Vector3D worldCenter;
|
|
VectorAdd(vecMinsIn, vecMaxsIn, worldCenter);
|
|
worldCenter *= 0.5f;
|
|
|
|
Vector3D worldExtents;
|
|
VectorSubtract(vecMaxsIn, worldCenter, worldExtents);
|
|
|
|
Vector3D localCenter;
|
|
VectorITransform(worldCenter, transform, localCenter);
|
|
|
|
Vector3D localExtents;
|
|
localExtents.x = FloatMakePositive(worldExtents.x * transform[0][0]) +
|
|
FloatMakePositive(worldExtents.y * transform[1][0]) +
|
|
FloatMakePositive(worldExtents.z * transform[2][0]);
|
|
localExtents.y = FloatMakePositive(worldExtents.x * transform[0][1]) +
|
|
FloatMakePositive(worldExtents.y * transform[1][1]) +
|
|
FloatMakePositive(worldExtents.z * transform[2][1]);
|
|
localExtents.z = FloatMakePositive(worldExtents.x * transform[0][2]) +
|
|
FloatMakePositive(worldExtents.y * transform[1][2]) +
|
|
FloatMakePositive(worldExtents.z * transform[2][2]);
|
|
|
|
VectorSubtract(localCenter, localExtents, vecMinsOut);
|
|
VectorAdd(localCenter, localExtents, vecMaxsOut);
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Rotates a AABB into another space; which will inherently grow the box.
|
|
// (same as TransformAABB, but doesn't take the translation into account)
|
|
//-----------------------------------------------------------------------------
|
|
void RotateAABB(const matrix3x4_t& transform, const Vector3D& vecMinsIn, const Vector3D& vecMaxsIn, Vector3D& vecMinsOut, Vector3D& vecMaxsOut)
|
|
{
|
|
Vector3D localCenter;
|
|
VectorAdd(vecMinsIn, vecMaxsIn, localCenter);
|
|
localCenter *= 0.5f;
|
|
|
|
Vector3D localExtents;
|
|
VectorSubtract(vecMaxsIn, localCenter, localExtents);
|
|
|
|
Vector3D newCenter;
|
|
VectorRotate(localCenter, transform, newCenter);
|
|
|
|
Vector3D newExtents;
|
|
newExtents.x = DotProductAbs(localExtents, transform[0]);
|
|
newExtents.y = DotProductAbs(localExtents, transform[1]);
|
|
newExtents.z = DotProductAbs(localExtents, transform[2]);
|
|
|
|
VectorSubtract(newCenter, newExtents, vecMinsOut);
|
|
VectorAdd(newCenter, newExtents, vecMaxsOut);
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Uses the inverse transform of in1
|
|
//-----------------------------------------------------------------------------
|
|
void IRotateAABB(const matrix3x4_t& transform, const Vector3D& vecMinsIn, const Vector3D& vecMaxsIn, Vector3D& vecMinsOut, Vector3D& vecMaxsOut)
|
|
{
|
|
Vector3D oldCenter;
|
|
VectorAdd(vecMinsIn, vecMaxsIn, oldCenter);
|
|
oldCenter *= 0.5f;
|
|
|
|
Vector3D oldExtents;
|
|
VectorSubtract(vecMaxsIn, oldCenter, oldExtents);
|
|
|
|
Vector3D newCenter;
|
|
VectorIRotate(oldCenter, transform, newCenter);
|
|
|
|
Vector3D newExtents;
|
|
newExtents.x = FloatMakePositive(oldExtents.x * transform[0][0]) +
|
|
FloatMakePositive(oldExtents.y * transform[1][0]) +
|
|
FloatMakePositive(oldExtents.z * transform[2][0]);
|
|
newExtents.y = FloatMakePositive(oldExtents.x * transform[0][1]) +
|
|
FloatMakePositive(oldExtents.y * transform[1][1]) +
|
|
FloatMakePositive(oldExtents.z * transform[2][1]);
|
|
newExtents.z = FloatMakePositive(oldExtents.x * transform[0][2]) +
|
|
FloatMakePositive(oldExtents.y * transform[1][2]) +
|
|
FloatMakePositive(oldExtents.z * transform[2][2]);
|
|
|
|
VectorSubtract(newCenter, newExtents, vecMinsOut);
|
|
VectorAdd(newCenter, newExtents, vecMaxsOut);
|
|
}
|
|
|
|
|
|
float CalcSqrDistanceToAABB(const Vector3D& mins, const Vector3D& maxs, const Vector3D& point)
|
|
{
|
|
float flDelta;
|
|
float flDistSqr = 0.0f;
|
|
|
|
if (point.x < mins.x)
|
|
{
|
|
flDelta = (mins.x - point.x);
|
|
flDistSqr += flDelta * flDelta;
|
|
}
|
|
else if (point.x > maxs.x)
|
|
{
|
|
flDelta = (point.x - maxs.x);
|
|
flDistSqr += flDelta * flDelta;
|
|
}
|
|
|
|
if (point.y < mins.y)
|
|
{
|
|
flDelta = (mins.y - point.y);
|
|
flDistSqr += flDelta * flDelta;
|
|
}
|
|
else if (point.y > maxs.y)
|
|
{
|
|
flDelta = (point.y - maxs.y);
|
|
flDistSqr += flDelta * flDelta;
|
|
}
|
|
|
|
if (point.z < mins.z)
|
|
{
|
|
flDelta = (mins.z - point.z);
|
|
flDistSqr += flDelta * flDelta;
|
|
}
|
|
else if (point.z > maxs.z)
|
|
{
|
|
flDelta = (point.z - maxs.z);
|
|
flDistSqr += flDelta * flDelta;
|
|
}
|
|
|
|
return flDistSqr;
|
|
}
|
|
|
|
|
|
void CalcClosestPointOnAABB(const Vector3D& mins, const Vector3D& maxs, const Vector3D& point, Vector3D& closestOut)
|
|
{
|
|
closestOut.x = clamp(point.x, mins.x, maxs.x);
|
|
closestOut.y = clamp(point.y, mins.y, maxs.y);
|
|
closestOut.z = clamp(point.z, mins.z, maxs.z);
|
|
}
|
|
|
|
void CalcSqrDistAndClosestPointOnAABB(const Vector3D& mins, const Vector3D& maxs, const Vector3D& point, Vector3D& closestOut, float& distSqrOut)
|
|
{
|
|
distSqrOut = 0.0f;
|
|
for (int i = 0; i < 3; i++)
|
|
{
|
|
if (point[i] < mins[i])
|
|
{
|
|
closestOut[i] = mins[i];
|
|
float flDelta = closestOut[i] - mins[i];
|
|
distSqrOut += flDelta * flDelta;
|
|
}
|
|
else if (point[i] > maxs[i])
|
|
{
|
|
closestOut[i] = maxs[i];
|
|
float flDelta = closestOut[i] - maxs[i];
|
|
distSqrOut += flDelta * flDelta;
|
|
}
|
|
else
|
|
{
|
|
closestOut[i] = point[i];
|
|
}
|
|
}
|
|
|
|
}
|
|
|
|
float CalcClosestPointToLineT(const Vector3D& P, const Vector3D& vLineA, const Vector3D& vLineB, Vector3D& vDir)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
VectorSubtract(vLineB, vLineA, vDir);
|
|
|
|
// D dot [P - (A + D*t)] = 0
|
|
// t = ( DP - DA) / DD
|
|
float div = vDir.Dot(vDir);
|
|
if (div < 0.00001f)
|
|
{
|
|
return 0;
|
|
}
|
|
else
|
|
{
|
|
return (vDir.Dot(P) - vDir.Dot(vLineA)) / div;
|
|
}
|
|
}
|
|
|
|
void CalcClosestPointOnLine(const Vector3D& P, const Vector3D& vLineA, const Vector3D& vLineB, Vector3D& vClosest, float* outT)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Vector3D vDir;
|
|
float t = CalcClosestPointToLineT(P, vLineA, vLineB, vDir);
|
|
if (outT) *outT = t;
|
|
vClosest.MulAdd(vLineA, vDir, t);
|
|
}
|
|
|
|
|
|
float CalcDistanceToLine(const Vector3D& P, const Vector3D& vLineA, const Vector3D& vLineB, float* outT)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Vector3D vClosest;
|
|
CalcClosestPointOnLine(P, vLineA, vLineB, vClosest, outT);
|
|
return P.DistTo(vClosest);
|
|
}
|
|
|
|
float CalcDistanceSqrToLine(const Vector3D& P, const Vector3D& vLineA, const Vector3D& vLineB, float* outT)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Vector3D vClosest;
|
|
CalcClosestPointOnLine(P, vLineA, vLineB, vClosest, outT);
|
|
return P.DistToSqr(vClosest);
|
|
}
|
|
|
|
void CalcClosestPointOnLineSegment(const Vector3D& P, const Vector3D& vLineA, const Vector3D& vLineB, Vector3D& vClosest, float* outT)
|
|
{
|
|
Vector3D vDir;
|
|
float t = CalcClosestPointToLineT(P, vLineA, vLineB, vDir);
|
|
t = clamp(t, 0.f, 1.f);
|
|
if (outT)
|
|
{
|
|
*outT = t;
|
|
}
|
|
vClosest.MulAdd(vLineA, vDir, t);
|
|
}
|
|
|
|
|
|
float CalcDistanceToLineSegment(const Vector3D& P, const Vector3D& vLineA, const Vector3D& vLineB, float* outT)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Vector3D vClosest;
|
|
CalcClosestPointOnLineSegment(P, vLineA, vLineB, vClosest, outT);
|
|
return P.DistTo(vClosest);
|
|
}
|
|
|
|
float CalcDistanceSqrToLineSegment(const Vector3D& P, const Vector3D& vLineA, const Vector3D& vLineB, float* outT)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Vector3D vClosest;
|
|
CalcClosestPointOnLineSegment(P, vLineA, vLineB, vClosest, outT);
|
|
return P.DistToSqr(vClosest);
|
|
}
|
|
|
|
float CalcClosestPointToLineT2D(const Vector2D& P, const Vector2D& vLineA, const Vector2D& vLineB, Vector2D& vDir)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Vector2DSubtract(vLineB, vLineA, vDir);
|
|
|
|
// D dot [P - (A + D*t)] = 0
|
|
// t = (DP - DA) / DD
|
|
float div = vDir.Dot(vDir);
|
|
if (div < 0.00001f)
|
|
{
|
|
return 0;
|
|
}
|
|
else
|
|
{
|
|
return (vDir.Dot(P) - vDir.Dot(vLineA)) / div;
|
|
}
|
|
}
|
|
|
|
void CalcClosestPointOnLine2D(const Vector2D& P, const Vector2D& vLineA, const Vector2D& vLineB, Vector2D& vClosest, float* outT)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Vector2D vDir;
|
|
float t = CalcClosestPointToLineT2D(P, vLineA, vLineB, vDir);
|
|
if (outT) *outT = t;
|
|
vClosest.MulAdd(vLineA, vDir, t);
|
|
}
|
|
|
|
float CalcDistanceToLine2D(const Vector2D& P, const Vector2D& vLineA, const Vector2D& vLineB, float* outT)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Vector2D vClosest;
|
|
CalcClosestPointOnLine2D(P, vLineA, vLineB, vClosest, outT);
|
|
return P.DistTo(vClosest);
|
|
}
|
|
|
|
float CalcDistanceSqrToLine2D(const Vector2D& P, const Vector2D& vLineA, const Vector2D& vLineB, float* outT)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Vector2D vClosest;
|
|
CalcClosestPointOnLine2D(P, vLineA, vLineB, vClosest, outT);
|
|
return P.DistToSqr(vClosest);
|
|
}
|
|
|
|
void CalcClosestPointOnLineSegment2D(const Vector2D& P, const Vector2D& vLineA, const Vector2D& vLineB, Vector2D& vClosest, float* outT)
|
|
{
|
|
Vector2D vDir;
|
|
float t = CalcClosestPointToLineT2D(P, vLineA, vLineB, vDir);
|
|
t = clamp(t, 0.f, 1.f);
|
|
if (outT)
|
|
{
|
|
*outT = t;
|
|
}
|
|
vClosest.MulAdd(vLineA, vDir, t);
|
|
}
|
|
|
|
float CalcDistanceToLineSegment2D(const Vector2D& P, const Vector2D& vLineA, const Vector2D& vLineB, float* outT)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Vector2D vClosest;
|
|
CalcClosestPointOnLineSegment2D(P, vLineA, vLineB, vClosest, outT);
|
|
return P.DistTo(vClosest);
|
|
}
|
|
|
|
float CalcDistanceSqrToLineSegment2D(const Vector2D& P, const Vector2D& vLineA, const Vector2D& vLineB, float* outT)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
Vector2D vClosest;
|
|
CalcClosestPointOnLineSegment2D(P, vLineA, vLineB, vClosest, outT);
|
|
return P.DistToSqr(vClosest);
|
|
}
|
|
|
|
// Do we have another epsilon we could use
|
|
#define LINE_EPS ( 0.000001f )
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Purpose: Given lines p1->p2 and p3->p4, computes a line segment (pa->pb) and returns the parameters 0->1 multipliers
|
|
// along each segment for the returned points
|
|
// Input : p1 -
|
|
// p2 -
|
|
// p3 -
|
|
// p4 -
|
|
// *s1 -
|
|
// *s2 -
|
|
// Output : Returns true on success, false on failure.
|
|
//-----------------------------------------------------------------------------
|
|
bool CalcLineToLineIntersectionSegment(
|
|
const Vector3D& p1, const Vector3D& p2, const Vector3D& p3, const Vector3D& p4, Vector3D* s1, Vector3D* s2,
|
|
float* t1, float* t2)
|
|
{
|
|
Vector3D p13, p43, p21;
|
|
float d1343, d4321, d1321, d4343, d2121;
|
|
float numer, denom;
|
|
|
|
p13.x = p1.x - p3.x;
|
|
p13.y = p1.y - p3.y;
|
|
p13.z = p1.z - p3.z;
|
|
p43.x = p4.x - p3.x;
|
|
p43.y = p4.y - p3.y;
|
|
p43.z = p4.z - p3.z;
|
|
|
|
if (fabs(p43.x) < LINE_EPS && fabs(p43.y) < LINE_EPS && fabs(p43.z) < LINE_EPS)
|
|
return false;
|
|
p21.x = p2.x - p1.x;
|
|
p21.y = p2.y - p1.y;
|
|
p21.z = p2.z - p1.z;
|
|
if (fabs(p21.x) < LINE_EPS && fabs(p21.y) < LINE_EPS && fabs(p21.z) < LINE_EPS)
|
|
return false;
|
|
|
|
d1343 = p13.x * p43.x + p13.y * p43.y + p13.z * p43.z;
|
|
d4321 = p43.x * p21.x + p43.y * p21.y + p43.z * p21.z;
|
|
d1321 = p13.x * p21.x + p13.y * p21.y + p13.z * p21.z;
|
|
d4343 = p43.x * p43.x + p43.y * p43.y + p43.z * p43.z;
|
|
d2121 = p21.x * p21.x + p21.y * p21.y + p21.z * p21.z;
|
|
|
|
denom = d2121 * d4343 - d4321 * d4321;
|
|
if (fabs(denom) < LINE_EPS)
|
|
return false;
|
|
numer = d1343 * d4321 - d1321 * d4343;
|
|
|
|
*t1 = numer / denom;
|
|
*t2 = (d1343 + d4321 * (*t1)) / d4343;
|
|
|
|
s1->x = p1.x + *t1 * p21.x;
|
|
s1->y = p1.y + *t1 * p21.y;
|
|
s1->z = p1.z + *t1 * p21.z;
|
|
s2->x = p3.x + *t2 * p43.x;
|
|
s2->y = p3.y + *t2 * p43.y;
|
|
s2->z = p3.z + *t2 * p43.z;
|
|
|
|
return true;
|
|
}
|
|
|
|
#pragma optimize( "", off )
|
|
|
|
#ifndef EXCEPTION_EXECUTE_HANDLER
|
|
#define EXCEPTION_EXECUTE_HANDLER 1
|
|
#endif
|
|
|
|
#pragma optimize( "", on )
|
|
|
|
static bool s_b3DNowEnabled = false;
|
|
static bool s_bMMXEnabled = false;
|
|
static bool s_bSSEEnabled = false;
|
|
static bool s_bSSE2Enabled = false;
|
|
|
|
void MathLib_Init(float gamma, float texGamma, float brightness, int overbright, bool bAllow3DNow, bool bAllowSSE, bool bAllowSSE2, bool bAllowMMX)
|
|
{
|
|
if (s_bMathlibInitialized)
|
|
return;
|
|
|
|
// FIXME: Hook SSE into Vector3DAligned + Vector3D4DAligned
|
|
|
|
#if !defined( _X360 )
|
|
// Grab the processor information:
|
|
const CPUInformation& pi = GetCPUInformation();
|
|
|
|
// Select the default generic routines.
|
|
pfSqrt = _sqrtf;
|
|
pfRSqrt = _rsqrtf;
|
|
pfRSqrtFast = _rsqrtf;
|
|
pfVectorNormalize = _VectorNormalize;
|
|
pfVectorNormalizeFast = _VectorNormalizeFast;
|
|
pfInvRSquared = _InvRSquared;
|
|
pfFastSinCos = SinCos;
|
|
pfFastCos = cosf;
|
|
|
|
if (bAllowMMX && pi.m_bMMX)
|
|
{
|
|
// Select the MMX specific routines if available
|
|
// (MMX routines were used by SW span fillers - not currently used for HW)
|
|
s_bMMXEnabled = true;
|
|
}
|
|
else
|
|
{
|
|
s_bMMXEnabled = false;
|
|
}
|
|
|
|
// SSE Generally performs better than 3DNow when present, so this is placed
|
|
// first to allow SSE to override these settings.
|
|
#if !defined( OSX ) && !defined( PLATFORM_WINDOWS_PC64 ) && !defined(LINUX)
|
|
if (bAllow3DNow && pi.m_b3DNow)
|
|
{
|
|
s_b3DNowEnabled = true;
|
|
|
|
// Select the 3DNow specific routines if available;
|
|
pfVector3DNormalize = _3DNow_Vector3DNormalize;
|
|
pfVector3DNormalizeFast = _3DNow_Vector3DNormalizeFast;
|
|
pfInvRSquared = _3DNow_InvRSquared;
|
|
pfSqrt = _3DNow_Sqrt;
|
|
pfRSqrt = _3DNow_RSqrt;
|
|
pfRSqrtFast = _3DNow_RSqrt;
|
|
}
|
|
else
|
|
#endif
|
|
{
|
|
s_b3DNowEnabled = false;
|
|
}
|
|
|
|
if (bAllowSSE && pi.m_bSSE)
|
|
{
|
|
s_bSSEEnabled = true;
|
|
|
|
#ifndef PLATFORM_WINDOWS_PC64
|
|
// These are not yet available.
|
|
// Select the SSE specific routines if available
|
|
pfVector3DNormalize = _Vector3DNormalize;
|
|
pfVector3DNormalizeFast = _SSE_Vector3DNormalizeFast;
|
|
pfInvRSquared = _SSE_InvRSquared;
|
|
pfSqrt = _SSE_Sqrt;
|
|
pfRSqrt = _SSE_RSqrtAccurate;
|
|
pfRSqrtFast = _SSE_RSqrtFast;
|
|
#endif
|
|
#ifdef PLATFORM_WINDOWS_PC32
|
|
pfFastSinCos = _SSE_SinCos;
|
|
pfFastCos = _SSE_cos;
|
|
#endif
|
|
}
|
|
else
|
|
{
|
|
s_bSSEEnabled = false;
|
|
}
|
|
|
|
if (bAllowSSE2 && pi.m_bSSE2)
|
|
{
|
|
s_bSSE2Enabled = true;
|
|
#ifdef PLATFORM_WINDOWS_PC32
|
|
pfFastSinCos = _SSE2_SinCos;
|
|
pfFastCos = _SSE2_cos;
|
|
#endif
|
|
}
|
|
else
|
|
{
|
|
s_bSSE2Enabled = false;
|
|
}
|
|
#endif // !_X360
|
|
|
|
s_bMathlibInitialized = true;
|
|
|
|
InitSinCosTable();
|
|
BuildGammaTable(gamma, texGamma, brightness, overbright);
|
|
}
|
|
|
|
bool MathLib_3DNowEnabled(void)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
return s_b3DNowEnabled;
|
|
}
|
|
|
|
bool MathLib_MMXEnabled(void)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
return s_bMMXEnabled;
|
|
}
|
|
|
|
bool MathLib_SSEEnabled(void)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
return s_bSSEEnabled;
|
|
}
|
|
|
|
bool MathLib_SSE2Enabled(void)
|
|
{
|
|
Assert(s_bMathlibInitialized);
|
|
return s_bSSE2Enabled;
|
|
}
|
|
|
|
// BUGBUG: Why doesn't this call angle diff?!?!?
|
|
float ApproachAngle(float target, float value, float speed)
|
|
{
|
|
target = anglemod(target);
|
|
value = anglemod(value);
|
|
|
|
float delta = target - value;
|
|
|
|
// Speed is assumed to be positive
|
|
if (speed < 0)
|
|
speed = -speed;
|
|
|
|
if (delta < -180)
|
|
delta += 360;
|
|
else if (delta > 180)
|
|
delta -= 360;
|
|
|
|
if (delta > speed)
|
|
value += speed;
|
|
else if (delta < -speed)
|
|
value -= speed;
|
|
else
|
|
value = target;
|
|
|
|
return value;
|
|
}
|
|
|
|
|
|
// BUGBUG: Why do we need both of these?
|
|
float AngleDiff(float destAngle, float srcAngle)
|
|
{
|
|
float delta;
|
|
|
|
delta = fmodf(destAngle - srcAngle, 360.0f);
|
|
if (destAngle > srcAngle)
|
|
{
|
|
if (delta >= 180)
|
|
delta -= 360;
|
|
}
|
|
else
|
|
{
|
|
if (delta <= -180)
|
|
delta += 360;
|
|
}
|
|
return delta;
|
|
}
|
|
|
|
|
|
float AngleDistance(float next, float cur)
|
|
{
|
|
float delta = next - cur;
|
|
|
|
if (delta < -180)
|
|
delta += 360;
|
|
else if (delta > 180)
|
|
delta -= 360;
|
|
|
|
return delta;
|
|
}
|
|
|
|
|
|
float AngleNormalize(float angle)
|
|
{
|
|
angle = fmodf(angle, 360.0f);
|
|
if (angle > 180)
|
|
{
|
|
angle -= 360;
|
|
}
|
|
if (angle < -180)
|
|
{
|
|
angle += 360;
|
|
}
|
|
return angle;
|
|
}
|
|
|
|
//--------------------------------------------------------------------------------------------------------------
|
|
// ensure that 0 <= angle <= 360
|
|
float AngleNormalizePositive(float angle)
|
|
{
|
|
angle = fmodf(angle, 360.0f);
|
|
|
|
if (angle < 0.0f)
|
|
{
|
|
angle += 360.0f;
|
|
}
|
|
|
|
return angle;
|
|
}
|
|
|
|
//--------------------------------------------------------------------------------------------------------------
|
|
bool AnglesAreEqual(float a, float b, float tolerance)
|
|
{
|
|
return (fabs(AngleDiff(a, b)) < tolerance);
|
|
}
|
|
|
|
void RotationDeltaAxisAngle(const QAngle& srcAngles, const QAngle& destAngles, Vector3D& deltaAxis, float& deltaAngle)
|
|
{
|
|
Quaternion srcQuat, destQuat, srcQuatInv, out;
|
|
AngleQuaternion(srcAngles, srcQuat);
|
|
AngleQuaternion(destAngles, destQuat);
|
|
QuaternionScale(srcQuat, -1, srcQuatInv);
|
|
QuaternionMult(destQuat, srcQuatInv, out);
|
|
|
|
QuaternionNormalize(out);
|
|
QuaternionAxisAngle(out, deltaAxis, deltaAngle);
|
|
}
|
|
|
|
void RotationDelta(const QAngle& srcAngles, const QAngle& destAngles, QAngle* out)
|
|
{
|
|
matrix3x4_t src, srcInv;
|
|
matrix3x4_t dest;
|
|
AngleMatrix(srcAngles, src);
|
|
AngleMatrix(destAngles, dest);
|
|
// xform = src(-1) * dest
|
|
MatrixInvert(src, srcInv);
|
|
matrix3x4_t xform;
|
|
ConcatTransforms(dest, srcInv, xform);
|
|
QAngle xformAngles;
|
|
MatrixAngles(xform, xformAngles);
|
|
if (out)
|
|
{
|
|
*out = xformAngles;
|
|
}
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Purpose: Computes a triangle normal
|
|
//-----------------------------------------------------------------------------
|
|
void ComputeTrianglePlane(const Vector3D& v1, const Vector3D& v2, const Vector3D& v3, Vector3D& normal, float& intercept)
|
|
{
|
|
Vector3D e1, e2;
|
|
VectorSubtract(v2, v1, e1);
|
|
VectorSubtract(v3, v1, e2);
|
|
CrossProduct(e1, e2, normal);
|
|
VectorNormalize(normal);
|
|
intercept = DotProduct(normal, v1);
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Purpose: This is a clone of BaseWindingForPlane()
|
|
// Input : *outVerts - an array of preallocated verts to build the polygon in
|
|
// normal - the plane normal
|
|
// dist - the plane constant
|
|
// Output : int - vert count (always 4)
|
|
//-----------------------------------------------------------------------------
|
|
int PolyFromPlane(Vector3D* outVerts, const Vector3D& normal, float dist, float fHalfScale)
|
|
{
|
|
int i, x;
|
|
vec_t max, v;
|
|
Vector3D org, vright, vup;
|
|
|
|
// find the major axis
|
|
|
|
max = -16384; //MAX_COORD_INTEGER
|
|
x = -1;
|
|
for (i = 0; i < 3; i++)
|
|
{
|
|
v = fabs(normal[i]);
|
|
if (v > max)
|
|
{
|
|
x = i;
|
|
max = v;
|
|
}
|
|
}
|
|
|
|
if (x == -1)
|
|
return 0;
|
|
|
|
// Build a unit Vector3D along something other than the major axis
|
|
VectorCopy(vec3_origin, vup);
|
|
switch (x)
|
|
{
|
|
case 0:
|
|
case 1:
|
|
vup[2] = 1;
|
|
break;
|
|
case 2:
|
|
vup[0] = 1;
|
|
break;
|
|
}
|
|
|
|
// Remove the component of this Vector3D along the normal
|
|
v = DotProduct(vup, normal);
|
|
VectorMA(vup, -v, normal, vup);
|
|
// Make it a unit (perpendicular)
|
|
VectorNormalize(vup);
|
|
|
|
// Center of the poly is at normal * dist
|
|
VectorScale(normal, dist, org);
|
|
// Calculate the third orthonormal basis Vector3D for our plane space (this one and vup are in the plane)
|
|
CrossProduct(vup, normal, vright);
|
|
|
|
// Make the plane's basis Vector3Ds big (these are the half-sides of the polygon we're making)
|
|
VectorScale(vup, fHalfScale, vup);
|
|
VectorScale(vright, fHalfScale, vright);
|
|
|
|
// Move diagonally away from org to create the corner verts
|
|
VectorSubtract(org, vright, outVerts[0]); // left
|
|
VectorAdd(outVerts[0], vup, outVerts[0]); // up
|
|
|
|
VectorAdd(org, vright, outVerts[1]); // right
|
|
VectorAdd(outVerts[1], vup, outVerts[1]); // up
|
|
|
|
VectorAdd(org, vright, outVerts[2]); // right
|
|
VectorSubtract(outVerts[2], vup, outVerts[2]); // down
|
|
|
|
VectorSubtract(org, vright, outVerts[3]); // left
|
|
VectorSubtract(outVerts[3], vup, outVerts[3]); // down
|
|
|
|
// The four corners form a planar quadrilateral normal to "normal"
|
|
return 4;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Purpose: clip a poly to the plane and return the poly on the front side of the plane
|
|
// Input : *inVerts - input polygon
|
|
// vertCount - # verts in input poly
|
|
// *outVerts - destination poly
|
|
// normal - plane normal
|
|
// dist - plane constant
|
|
// Output : int - # verts in output poly
|
|
//-----------------------------------------------------------------------------
|
|
|
|
int ClipPolyToPlane(Vector3D* inVerts, int vertCount, Vector3D* outVerts, const Vector3D& normal, float dist, float fOnPlaneEpsilon)
|
|
{
|
|
vec_t* dists = (vec_t*)stackalloc(sizeof(vec_t) * vertCount * 4); //4x vertcount should cover all cases
|
|
int* sides = (int*)stackalloc(sizeof(vec_t) * vertCount * 4);
|
|
int counts[3];
|
|
vec_t dot;
|
|
int i, j;
|
|
Vector3D mid = vec3_origin;
|
|
int outCount;
|
|
|
|
counts[0] = counts[1] = counts[2] = 0;
|
|
|
|
// determine sides for each point
|
|
for (i = 0; i < vertCount; i++)
|
|
{
|
|
dot = DotProduct(inVerts[i], normal) - dist;
|
|
dists[i] = dot;
|
|
if (dot > fOnPlaneEpsilon)
|
|
{
|
|
sides[i] = SIDE_FRONT;
|
|
}
|
|
else if (dot < -fOnPlaneEpsilon)
|
|
{
|
|
sides[i] = SIDE_BACK;
|
|
}
|
|
else
|
|
{
|
|
sides[i] = SIDE_ON;
|
|
}
|
|
counts[sides[i]]++;
|
|
}
|
|
sides[i] = sides[0];
|
|
dists[i] = dists[0];
|
|
|
|
if (!counts[0])
|
|
return 0;
|
|
|
|
if (!counts[1])
|
|
{
|
|
// Copy to output verts
|
|
for (i = 0; i < vertCount; i++)
|
|
{
|
|
VectorCopy(inVerts[i], outVerts[i]);
|
|
}
|
|
return vertCount;
|
|
}
|
|
|
|
outCount = 0;
|
|
for (i = 0; i < vertCount; i++)
|
|
{
|
|
Vector3D& p1 = inVerts[i];
|
|
|
|
if (sides[i] == SIDE_ON)
|
|
{
|
|
VectorCopy(p1, outVerts[outCount]);
|
|
outCount++;
|
|
continue;
|
|
}
|
|
|
|
if (sides[i] == SIDE_FRONT)
|
|
{
|
|
VectorCopy(p1, outVerts[outCount]);
|
|
outCount++;
|
|
}
|
|
|
|
if (sides[i + 1] == SIDE_ON || sides[i + 1] == sides[i])
|
|
continue;
|
|
|
|
// generate a split point
|
|
Vector3D& p2 = inVerts[(i + 1) % vertCount];
|
|
|
|
dot = dists[i] / (dists[i] - dists[i + 1]);
|
|
for (j = 0; j < 3; j++)
|
|
{ // avoid round off error when possible
|
|
if (normal[j] == 1)
|
|
mid[j] = dist;
|
|
else if (normal[j] == -1)
|
|
mid[j] = -dist;
|
|
else
|
|
mid[j] = p1[j] + dot * (p2[j] - p1[j]);
|
|
}
|
|
|
|
VectorCopy(mid, outVerts[outCount]);
|
|
outCount++;
|
|
}
|
|
|
|
return outCount;
|
|
}
|
|
|
|
|
|
int ClipPolyToPlane_Precise(double* inVerts, int vertCount, double* outVerts, const double* normal, double dist, double fOnPlaneEpsilon)
|
|
{
|
|
double* dists = (double*)stackalloc(sizeof(double) * vertCount * 4); //4x vertcount should cover all cases
|
|
int* sides = (int*)stackalloc(sizeof(double) * vertCount * 4);
|
|
int counts[3];
|
|
double dot;
|
|
int i, j;
|
|
//Vector3D mid = vec3_origin;
|
|
double mid[3];
|
|
mid[0] = 0.0;
|
|
mid[1] = 0.0;
|
|
mid[2] = 0.0;
|
|
int outCount;
|
|
|
|
counts[0] = counts[1] = counts[2] = 0;
|
|
|
|
// determine sides for each point
|
|
for (i = 0; i < vertCount; i++)
|
|
{
|
|
//dot = DotProduct( inVerts[i], normal) - dist;
|
|
dot = ((inVerts[i * 3 + 0] * normal[0]) + (inVerts[i * 3 + 1] * normal[1]) + (inVerts[i * 3 + 2] * normal[2])) - dist;
|
|
dists[i] = dot;
|
|
if (dot > fOnPlaneEpsilon)
|
|
{
|
|
sides[i] = SIDE_FRONT;
|
|
}
|
|
else if (dot < -fOnPlaneEpsilon)
|
|
{
|
|
sides[i] = SIDE_BACK;
|
|
}
|
|
else
|
|
{
|
|
sides[i] = SIDE_ON;
|
|
}
|
|
counts[sides[i]]++;
|
|
}
|
|
sides[i] = sides[0];
|
|
dists[i] = dists[0];
|
|
|
|
if (!counts[0])
|
|
return 0;
|
|
|
|
if (!counts[1])
|
|
{
|
|
// Copy to output verts
|
|
//for ( i = 0; i < vertCount; i++ )
|
|
for (i = 0; i < vertCount * 3; i++)
|
|
{
|
|
//Vector3DCopy( inVerts[i], outVerts[i] );
|
|
outVerts[i] = inVerts[i];
|
|
}
|
|
return vertCount;
|
|
}
|
|
|
|
outCount = 0;
|
|
for (i = 0; i < vertCount; i++)
|
|
{
|
|
//Vector3D& p1 = inVerts[i];
|
|
double* p1 = &inVerts[i * 3];
|
|
//p1[0] = inVerts[i*3 + 0];
|
|
//p1[1] = inVerts[i*3 + 1];
|
|
//p1[2] = inVerts[i*3 + 2];
|
|
|
|
if (sides[i] == SIDE_ON)
|
|
{
|
|
//Vector3DCopy( p1, outVerts[outCount]);
|
|
outVerts[outCount * 3 + 0] = p1[0];
|
|
outVerts[outCount * 3 + 1] = p1[1];
|
|
outVerts[outCount * 3 + 2] = p1[2];
|
|
outCount++;
|
|
continue;
|
|
}
|
|
|
|
if (sides[i] == SIDE_FRONT)
|
|
{
|
|
//Vector3DCopy( p1, outVerts[outCount]);
|
|
outVerts[outCount * 3 + 0] = p1[0];
|
|
outVerts[outCount * 3 + 1] = p1[1];
|
|
outVerts[outCount * 3 + 2] = p1[2];
|
|
outCount++;
|
|
}
|
|
|
|
if (sides[i + 1] == SIDE_ON || sides[i + 1] == sides[i])
|
|
continue;
|
|
|
|
// generate a split point
|
|
//Vector3D& p2 = inVerts[(i+1)%vertCount];
|
|
int wrappedindex = (i + 1) % vertCount;
|
|
double* p2 = &inVerts[wrappedindex * 3];
|
|
//p2[0] = inVerts[wrappedindex*3 + 0];
|
|
//p2[1] = inVerts[wrappedindex*3 + 1];
|
|
//p2[2] = inVerts[wrappedindex*3 + 2];
|
|
|
|
dot = dists[i] / (dists[i] - dists[i + 1]);
|
|
for (j = 0; j < 3; j++)
|
|
{
|
|
mid[j] = (double)p1[j] + dot * ((double)p2[j] - (double)p1[j]);
|
|
}
|
|
|
|
//Vector3DCopy (mid, outVerts[outCount]);
|
|
outVerts[outCount * 3 + 0] = mid[0];
|
|
outVerts[outCount * 3 + 1] = mid[1];
|
|
outVerts[outCount * 3 + 2] = mid[2];
|
|
outCount++;
|
|
}
|
|
|
|
return outCount;
|
|
}
|
|
|
|
int CeilPow2(int in)
|
|
{
|
|
int retval;
|
|
|
|
retval = 1;
|
|
while (retval < in)
|
|
retval <<= 1;
|
|
return retval;
|
|
}
|
|
|
|
int FloorPow2(int in)
|
|
{
|
|
int retval;
|
|
|
|
retval = 1;
|
|
while (retval < in)
|
|
retval <<= 1;
|
|
return retval >> 1;
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Computes Y fov from an X fov and a screen aspect ratio
|
|
//-----------------------------------------------------------------------------
|
|
float CalcFovY(float flFovX, float flAspect)
|
|
{
|
|
if (flFovX < 1 || flFovX > 179)
|
|
{
|
|
flFovX = 90; // error, set to 90
|
|
}
|
|
|
|
// The long, but illustrative version (more closely matches CShaderAPIDX8::PerspectiveX, which
|
|
// is what it's based on).
|
|
//
|
|
//float width = 2 * zNear * tan( DEG2RAD( fov_x / 2.0 ) );
|
|
//float height = width / screenaspect;
|
|
//float yRadians = atan( (height/2.0) / zNear );
|
|
//return RAD2DEG( yRadians ) * 2;
|
|
|
|
// The short and sweet version.
|
|
float val = atan(tan(DEG2RAD(flFovX) * 0.5f) / flAspect);
|
|
val = RAD2DEG(val) * 2.0f;
|
|
return val;
|
|
}
|
|
|
|
float CalcFovX(float flFovY, float flAspect)
|
|
{
|
|
return RAD2DEG(atan(tan(DEG2RAD(flFovY) * 0.5f) * flAspect)) * 2.0f;
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Generate a frustum based on perspective view parameters
|
|
//-----------------------------------------------------------------------------
|
|
void GeneratePerspectiveFrustum(const Vector3D& origin, const Vector3D& forward,
|
|
const Vector3D& right, const Vector3D& up, float flZNear, float flZFar,
|
|
float flFovX, float flFovY, VPlane* pPlanesOut)
|
|
{
|
|
float flIntercept = DotProduct(origin, forward);
|
|
|
|
// Setup the near and far planes.
|
|
pPlanesOut[FRUSTUM_FARZ].Init(-forward, -flZFar - flIntercept);
|
|
pPlanesOut[FRUSTUM_NEARZ].Init(forward, flZNear + flIntercept);
|
|
|
|
flFovX *= 0.5f;
|
|
flFovY *= 0.5f;
|
|
|
|
float flTanX = tan(DEG2RAD(flFovX));
|
|
float flTanY = tan(DEG2RAD(flFovY));
|
|
|
|
// OPTIMIZE: Normalizing these planes is not necessary for culling
|
|
Vector3D normalPos, normalNeg;
|
|
|
|
VectorMA(right, flTanX, forward, normalPos);
|
|
VectorMA(normalPos, -2.0f, right, normalNeg);
|
|
|
|
VectorNormalize(normalPos);
|
|
VectorNormalize(normalNeg);
|
|
|
|
pPlanesOut[FRUSTUM_LEFT].Init(normalPos, normalPos.Dot(origin));
|
|
pPlanesOut[FRUSTUM_RIGHT].Init(normalNeg, normalNeg.Dot(origin));
|
|
|
|
VectorMA(up, flTanY, forward, normalPos);
|
|
VectorMA(normalPos, -2.0f, up, normalNeg);
|
|
|
|
VectorNormalize(normalPos);
|
|
VectorNormalize(normalNeg);
|
|
|
|
pPlanesOut[FRUSTUM_BOTTOM].Init(normalPos, normalPos.Dot(origin));
|
|
pPlanesOut[FRUSTUM_TOP].Init(normalNeg, normalNeg.Dot(origin));
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Generate a frustum based on orthographic parameters
|
|
//-----------------------------------------------------------------------------
|
|
void GenerateOrthoFrustum(const Vector3D& origin, const Vector3D& forward, const Vector3D& right, const Vector3D& up, float flLeft, float flRight, float flBottom, float flTop, float flZNear, float flZFar, VPlane* pPlanesOut)
|
|
{
|
|
float flIntercept = DotProduct(origin, forward);
|
|
|
|
pPlanesOut[FRUSTUM_NEARZ].Init(forward, flZNear + flIntercept);
|
|
pPlanesOut[FRUSTUM_FARZ].Init(-forward, -flZFar - flIntercept);
|
|
|
|
flIntercept = DotProduct(origin, right);
|
|
|
|
pPlanesOut[FRUSTUM_RIGHT].Init(-right, -flRight - flIntercept);
|
|
pPlanesOut[FRUSTUM_LEFT].Init(right, flLeft + flIntercept);
|
|
|
|
flIntercept = DotProduct(origin, up);
|
|
|
|
pPlanesOut[FRUSTUM_BOTTOM].Init(up, flBottom + flIntercept);
|
|
pPlanesOut[FRUSTUM_TOP].Init(-up, -flTop - flIntercept);
|
|
}
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Generate a frustum based on perspective view parameters
|
|
//-----------------------------------------------------------------------------
|
|
void GeneratePerspectiveFrustum(const Vector3D& origin, const Vector3D& forward,
|
|
const Vector3D& right, const Vector3D& up, float flZNear, float flZFar,
|
|
float flFovX, float flFovY, Frustum_t& frustum)
|
|
{
|
|
float flIntercept = DotProduct(origin, forward);
|
|
|
|
// Setup the near and far planes.
|
|
frustum.SetPlane(FRUSTUM_FARZ, PLANE_ANYZ, -forward, -flZFar - flIntercept);
|
|
frustum.SetPlane(FRUSTUM_NEARZ, PLANE_ANYZ, forward, flZNear + flIntercept);
|
|
|
|
flFovX *= 0.5f;
|
|
flFovY *= 0.5f;
|
|
|
|
float flTanX = tan(DEG2RAD(flFovX));
|
|
float flTanY = tan(DEG2RAD(flFovY));
|
|
|
|
// OPTIMIZE: Normalizing these planes is not necessary for culling
|
|
Vector3D normalPos, normalNeg;
|
|
|
|
VectorMA(right, flTanX, forward, normalPos);
|
|
VectorMA(normalPos, -2.0f, right, normalNeg);
|
|
|
|
VectorNormalize(normalPos);
|
|
VectorNormalize(normalNeg);
|
|
|
|
frustum.SetPlane(FRUSTUM_LEFT, PLANE_ANYZ, normalPos, normalPos.Dot(origin));
|
|
frustum.SetPlane(FRUSTUM_RIGHT, PLANE_ANYZ, normalNeg, normalNeg.Dot(origin));
|
|
|
|
VectorMA(up, flTanY, forward, normalPos);
|
|
VectorMA(normalPos, -2.0f, up, normalNeg);
|
|
|
|
VectorNormalize(normalPos);
|
|
VectorNormalize(normalNeg);
|
|
|
|
frustum.SetPlane(FRUSTUM_BOTTOM, PLANE_ANYZ, normalPos, normalPos.Dot(origin));
|
|
frustum.SetPlane(FRUSTUM_TOP, PLANE_ANYZ, normalNeg, normalNeg.Dot(origin));
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Version that accepts angles instead of Vector3Ds
|
|
//-----------------------------------------------------------------------------
|
|
void GeneratePerspectiveFrustum(const Vector3D& origin, const QAngle& angles, float flZNear, float flZFar, float flFovX, float flAspectRatio, Frustum_t& frustum)
|
|
{
|
|
Vector3D vecForward, vecRight, vecUp;
|
|
AngleVectors(angles, &vecForward, &vecRight, &vecUp);
|
|
float flFovY = CalcFovY(flFovX, flAspectRatio);
|
|
GeneratePerspectiveFrustum(origin, vecForward, vecRight, vecUp, flZNear, flZFar, flFovX, flFovY, frustum);
|
|
}
|
|
|
|
bool R_CullBox(const Vector3D& mins, const Vector3D& maxs, const Frustum_t& frustum)
|
|
{
|
|
return ((BoxOnPlaneSide(mins, maxs, frustum.GetPlane(FRUSTUM_RIGHT)) == 2) ||
|
|
(BoxOnPlaneSide(mins, maxs, frustum.GetPlane(FRUSTUM_LEFT)) == 2) ||
|
|
(BoxOnPlaneSide(mins, maxs, frustum.GetPlane(FRUSTUM_TOP)) == 2) ||
|
|
(BoxOnPlaneSide(mins, maxs, frustum.GetPlane(FRUSTUM_BOTTOM)) == 2) ||
|
|
(BoxOnPlaneSide(mins, maxs, frustum.GetPlane(FRUSTUM_NEARZ)) == 2) ||
|
|
(BoxOnPlaneSide(mins, maxs, frustum.GetPlane(FRUSTUM_FARZ)) == 2));
|
|
}
|
|
|
|
bool R_CullBoxSkipNear(const Vector3D& mins, const Vector3D& maxs, const Frustum_t& frustum)
|
|
{
|
|
return ((BoxOnPlaneSide(mins, maxs, frustum.GetPlane(FRUSTUM_RIGHT)) == 2) ||
|
|
(BoxOnPlaneSide(mins, maxs, frustum.GetPlane(FRUSTUM_LEFT)) == 2) ||
|
|
(BoxOnPlaneSide(mins, maxs, frustum.GetPlane(FRUSTUM_TOP)) == 2) ||
|
|
(BoxOnPlaneSide(mins, maxs, frustum.GetPlane(FRUSTUM_BOTTOM)) == 2) ||
|
|
(BoxOnPlaneSide(mins, maxs, frustum.GetPlane(FRUSTUM_FARZ)) == 2));
|
|
}
|
|
|
|
|
|
// NOTE: This routine was taken (and modified) from NVidia's BlinnReflection demo
|
|
// Creates basis Vector3Ds, based on a vertex and index list.
|
|
// See the NVidia white paper 'GDC2K PerPixel Lighting' for a description
|
|
// of how this computation works
|
|
#define SMALL_FLOAT 1e-12
|
|
|
|
void CalcTriangleTangentSpace(const Vector3D& p0, const Vector3D& p1, const Vector3D& p2,
|
|
const Vector2D& t0, const Vector2D& t1, const Vector2D& t2,
|
|
Vector3D& sVect, Vector3D& tVect)
|
|
{
|
|
/* Compute the partial derivatives of X, Y, and Z with respect to S and T. */
|
|
sVect.Init(0.0f, 0.0f, 0.0f);
|
|
tVect.Init(0.0f, 0.0f, 0.0f);
|
|
|
|
// x, s, t
|
|
Vector3D edge01(p1.x - p0.x, t1.x - t0.x, t1.y - t0.y);
|
|
Vector3D edge02(p2.x - p0.x, t2.x - t0.x, t2.y - t0.y);
|
|
|
|
Vector3D cross;
|
|
CrossProduct(edge01, edge02, cross);
|
|
if (fabs(cross.x) > SMALL_FLOAT)
|
|
{
|
|
sVect.x += -cross.y / cross.x;
|
|
tVect.x += -cross.z / cross.x;
|
|
}
|
|
|
|
// y, s, t
|
|
edge01.Init(p1.y - p0.y, t1.x - t0.x, t1.y - t0.y);
|
|
edge02.Init(p2.y - p0.y, t2.x - t0.x, t2.y - t0.y);
|
|
|
|
CrossProduct(edge01, edge02, cross);
|
|
if (fabs(cross.x) > SMALL_FLOAT)
|
|
{
|
|
sVect.y += -cross.y / cross.x;
|
|
tVect.y += -cross.z / cross.x;
|
|
}
|
|
|
|
// z, s, t
|
|
edge01.Init(p1.z - p0.z, t1.x - t0.x, t1.y - t0.y);
|
|
edge02.Init(p2.z - p0.z, t2.x - t0.x, t2.y - t0.y);
|
|
|
|
CrossProduct(edge01, edge02, cross);
|
|
if (fabs(cross.x) > SMALL_FLOAT)
|
|
{
|
|
sVect.z += -cross.y / cross.x;
|
|
tVect.z += -cross.z / cross.x;
|
|
}
|
|
|
|
// Normalize sVect and tVect
|
|
VectorNormalize(sVect);
|
|
VectorNormalize(tVect);
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Convert RGB to HSV
|
|
//-----------------------------------------------------------------------------
|
|
void RGBtoHSV(const Vector3D& rgb, Vector3D& hsv)
|
|
{
|
|
float flMax = max(rgb.x, rgb.y);
|
|
flMax = max(flMax, rgb.z);
|
|
float flMin = min(rgb.x, rgb.y);
|
|
flMin = min(flMin, rgb.z);
|
|
|
|
// hsv.z is the value
|
|
hsv.z = flMax;
|
|
|
|
// hsv.y is the saturation
|
|
if (flMax != 0.0F)
|
|
{
|
|
hsv.y = (flMax - flMin) / flMax;
|
|
}
|
|
else
|
|
{
|
|
hsv.y = 0.0F;
|
|
}
|
|
|
|
// hsv.x is the hue
|
|
if (hsv.y == 0.0F)
|
|
{
|
|
hsv.x = -1.0f;
|
|
}
|
|
else
|
|
{
|
|
float32 d = flMax - flMin;
|
|
if (rgb.x == flMax)
|
|
{
|
|
hsv.x = (rgb.y - rgb.z) / d;
|
|
}
|
|
else if (rgb.y == flMax)
|
|
{
|
|
hsv.x = 2.0F + (rgb.z - rgb.x) / d;
|
|
}
|
|
else
|
|
{
|
|
hsv.x = 4.0F + (rgb.x - rgb.y) / d;
|
|
}
|
|
hsv.x *= 60.0F;
|
|
if (hsv.x < 0.0F)
|
|
{
|
|
hsv.x += 360.0F;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
//-----------------------------------------------------------------------------
|
|
// Convert HSV to RGB
|
|
//-----------------------------------------------------------------------------
|
|
void HSVtoRGB(const Vector3D& hsv, Vector3D& rgb)
|
|
{
|
|
if (hsv.y == 0.0F)
|
|
{
|
|
rgb.Init(hsv.z, hsv.z, hsv.z);
|
|
return;
|
|
}
|
|
|
|
float32 hue = hsv.x;
|
|
if (hue == 360.0F)
|
|
{
|
|
hue = 0.0F;
|
|
}
|
|
hue /= 60.0F;
|
|
int i = hue; // integer part
|
|
float32 f = hue - i; // fractional part
|
|
float32 p = hsv.z * (1.0F - hsv.y);
|
|
float32 q = hsv.z * (1.0F - hsv.y * f);
|
|
float32 t = hsv.z * (1.0F - hsv.y * (1.0F - f));
|
|
switch (i)
|
|
{
|
|
case 0: rgb.Init(hsv.z, t, p); break;
|
|
case 1: rgb.Init(q, hsv.z, p); break;
|
|
case 2: rgb.Init(p, hsv.z, t); break;
|
|
case 3: rgb.Init(p, q, hsv.z); break;
|
|
case 4: rgb.Init(t, p, hsv.z); break;
|
|
case 5: rgb.Init(hsv.z, p, q); break;
|
|
}
|
|
}
|
|
|
|
|
|
void GetInterpolationData(float const* pKnotPositions,
|
|
float const* pKnotValues,
|
|
int nNumValuesinList,
|
|
int nInterpolationRange,
|
|
float flPositionToInterpolateAt,
|
|
bool bWrap,
|
|
float* pValueA,
|
|
float* pValueB,
|
|
float* pInterpolationValue)
|
|
{
|
|
// first, find the bracketting knots by looking for the first knot >= our index
|
|
|
|
int idx;
|
|
for (idx = 0; idx < nNumValuesinList; idx++)
|
|
{
|
|
if (pKnotPositions[idx] >= flPositionToInterpolateAt)
|
|
break;
|
|
}
|
|
int nKnot1, nKnot2;
|
|
float flOffsetFromStartOfGap, flSizeOfGap;
|
|
if (idx == 0)
|
|
{
|
|
if (bWrap)
|
|
{
|
|
nKnot1 = nNumValuesinList - 1;
|
|
nKnot2 = 0;
|
|
flSizeOfGap =
|
|
(pKnotPositions[nKnot2] + (nInterpolationRange - pKnotPositions[nKnot1]));
|
|
flOffsetFromStartOfGap =
|
|
flPositionToInterpolateAt + (nInterpolationRange - pKnotPositions[nKnot1]);
|
|
}
|
|
else
|
|
{
|
|
*pValueA = *pValueB = pKnotValues[0];
|
|
*pInterpolationValue = 1.0;
|
|
return;
|
|
}
|
|
}
|
|
else if (idx == nNumValuesinList) // ran out of values
|
|
{
|
|
if (bWrap)
|
|
{
|
|
nKnot1 = nNumValuesinList - 1;
|
|
nKnot2 = 0;
|
|
flSizeOfGap = (pKnotPositions[nKnot2] +
|
|
(nInterpolationRange - pKnotPositions[nKnot1]));
|
|
flOffsetFromStartOfGap = flPositionToInterpolateAt - pKnotPositions[nKnot1];
|
|
}
|
|
else
|
|
{
|
|
*pValueA = *pValueB = pKnotValues[nNumValuesinList - 1];
|
|
*pInterpolationValue = 1.0;
|
|
return;
|
|
}
|
|
|
|
}
|
|
else
|
|
{
|
|
nKnot1 = idx - 1;
|
|
nKnot2 = idx;
|
|
flSizeOfGap = pKnotPositions[nKnot2] - pKnotPositions[nKnot1];
|
|
flOffsetFromStartOfGap = flPositionToInterpolateAt - pKnotPositions[nKnot1];
|
|
}
|
|
|
|
*pValueA = pKnotValues[nKnot1];
|
|
*pValueB = pKnotValues[nKnot2];
|
|
*pInterpolationValue = FLerp(0, 1, 0, flSizeOfGap, flOffsetFromStartOfGap);
|
|
return;
|
|
}
|
|
|
|
float RandomVector3DInUnitSphere(Vector3D* pVector3D)
|
|
{
|
|
// Guarantee uniform random distribution within a sphere
|
|
// Graphics gems III contains this algorithm ("Nonuniform random point sets via warping")
|
|
float u = ((float)rand() / VALVE_RAND_MAX);
|
|
float v = ((float)rand() / VALVE_RAND_MAX);
|
|
float w = ((float)rand() / VALVE_RAND_MAX);
|
|
|
|
float flPhi = acos(1 - 2 * u);
|
|
float flTheta = 2 * M_PI * v;
|
|
float flRadius = powf(w, 1.0f / 3.0f);
|
|
|
|
float flSinPhi, flCosPhi;
|
|
float flSinTheta, flCosTheta;
|
|
SinCos(flPhi, &flSinPhi, &flCosPhi);
|
|
SinCos(flTheta, &flSinTheta, &flCosTheta);
|
|
|
|
pVector3D->x = flRadius * flSinPhi * flCosTheta;
|
|
pVector3D->y = flRadius * flSinPhi * flSinTheta;
|
|
pVector3D->z = flRadius * flCosPhi;
|
|
return flRadius;
|
|
}
|
|
|
|
float RandomVector3DInUnitCircle(Vector2D* pVector3D)
|
|
{
|
|
// Guarantee uniform random distribution within a sphere
|
|
// Graphics gems III contains this algorithm ("Nonuniform random point sets via warping")
|
|
float u = ((float)rand() / VALVE_RAND_MAX);
|
|
float v = ((float)rand() / VALVE_RAND_MAX);
|
|
|
|
float flTheta = 2 * M_PI * v;
|
|
float flRadius = powf(u, 1.0f / 2.0f);
|
|
|
|
float flSinTheta, flCosTheta;
|
|
SinCos(flTheta, &flSinTheta, &flCosTheta);
|
|
|
|
pVector3D->x = flRadius * flCosTheta;
|
|
pVector3D->y = flRadius * flSinTheta;
|
|
return flRadius;
|
|
}
|
|
#ifdef FP_EXCEPTIONS_ENABLED
|
|
#include <float.h> // For _clearfp and _controlfp_s
|
|
#endif
|
|
|
|
// FPExceptionDisable and FPExceptionEnabler taken from my blog post
|
|
// at http://www.altdevblogaday.com/2012/04/20/exceptional-floating-point/
|
|
|
|
#ifdef FP_EXCEPTIONS_ENABLED
|
|
// These functions are all inlined NOPs if FP_EXCEPTIONS_ENABLED is not defined.
|
|
FPExceptionDisabler::FPExceptionDisabler()
|
|
{
|
|
// Retrieve the current state of the exception flags. This
|
|
// must be done before changing them. _MCW_EM is a bit
|
|
// mask representing all available exception masks.
|
|
_controlfp_s(&mOldValues, 0, 0);
|
|
// Set all of the exception flags, which suppresses FP
|
|
// exceptions on the x87 and SSE units.
|
|
_controlfp_s(0, _MCW_EM, _MCW_EM);
|
|
}
|
|
|
|
FPExceptionDisabler::~FPExceptionDisabler()
|
|
{
|
|
// Clear any pending FP exceptions. This must be done
|
|
// prior to enabling FP exceptions since otherwise there
|
|
// may be a 'deferred crash' as soon the exceptions are
|
|
// enabled.
|
|
_clearfp();
|
|
|
|
// Reset (possibly enabling) the exception status.
|
|
_controlfp_s(0, mOldValues, _MCW_EM);
|
|
}
|
|
|
|
// Overflow, divide-by-zero, and invalid-operation are the FP
|
|
// exceptions most frequently associated with bugs.
|
|
FPExceptionEnabler::FPExceptionEnabler(unsigned int enableBits /*= _EM_OVERFLOW | _EM_ZERODIVIDE | _EM_INVALID*/)
|
|
{
|
|
// Retrieve the current state of the exception flags. This
|
|
// must be done before changing them. _MCW_EM is a bit
|
|
// mask representing all available exception masks.
|
|
_controlfp_s(&mOldValues, 0, 0);
|
|
|
|
// Make sure no non-exception flags have been specified,
|
|
// to avoid accidental changing of rounding modes, etc.
|
|
enableBits &= _MCW_EM;
|
|
|
|
// Clear any pending FP exceptions. This must be done
|
|
// prior to enabling FP exceptions since otherwise there
|
|
// may be a 'deferred crash' as soon the exceptions are
|
|
// enabled.
|
|
_clearfp();
|
|
|
|
// Zero out the specified bits, leaving other bits alone.
|
|
_controlfp_s(0, ~enableBits, enableBits);
|
|
}
|
|
|
|
FPExceptionEnabler::~FPExceptionEnabler()
|
|
{
|
|
// Reset the exception state.
|
|
_controlfp_s(0, mOldValues, _MCW_EM);
|
|
}
|
|
#endif
|