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r5sdk/r5dev/mathlib/mathlib_base.cpp

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Mathlib implementation SourceSDK mathlib port with light modifications. Renamed Vector to Vector3D (to avoid confusion with std::vector (declared as vector) and Vector2D/Vector4D).
2022-07-06 21:11:32 +02:00
//========= Copyright Valve Corporation, All rights reserved. ============//
//
// Purpose: Math primitives.
//
//===========================================================================//
/// FIXME: As soon as all references to mathlib.c are gone, include it in here
#include "core/stdafx.h"
#include <math.h>
#include <float.h> // Needed for FLT_EPSILON
#include "tier0/basetypes.h"
#include <memory.h>
#include "tier0/dbg.h"
//#define _VPROF_MATHLIB
#pragma warning(disable:4244) // "conversion from 'const int' to 'float', possible loss of data"
#pragma warning(disable:4730) // "mixing _m64 and floating point expressions may result in incorrect code"
#include "mathlib/bits.h"
#include "mathlib/vplane.h"
#include "mathlib/Vector.h"
#include "mathlib/Vector2d.h"
#include "mathlib/mathlib.h"
#include "mathlib/ssemath.h"
#include "mathlib/math_pfns.h"
#include <tier0/cpu.h>
bool s_bMathlibInitialized = false;
#ifdef PARANOID
// User must provide an implementation of Sys_Error()
void Sys_Error(char* error, ...);
#endif
const Vector3D vec3_origin(0, 0, 0);
const QAngle vec3_angle(0, 0, 0);
const Vector3D vec3_invalid(FLT_MAX, FLT_MAX, FLT_MAX);
const int nanmask = 255 << 23;
//-----------------------------------------------------------------------------
// Standard C implementations of optimized routines:
//-----------------------------------------------------------------------------
float _sqrtf(float _X)
{
Assert(s_bMathlibInitialized);
return sqrtf(_X);
}
float _rsqrtf(float x)
{
Assert(s_bMathlibInitialized);
return 1.f / _sqrtf(x);
}
float FASTCALL _VectorNormalize(Vector3D& vec)
{
#ifdef _VPROF_MATHLIB
VPROF_BUDGET("_Vector3Normalize", "Mathlib");
#endif
Assert(s_bMathlibInitialized);
float radius = sqrtf(vec.x * vec.x + vec.y * vec.y + vec.z * vec.z);
// FLT_EPSILON is added to the radius to eliminate the possibility of divide by zero.
float iradius = 1.f / (radius + FLT_EPSILON);
vec.x *= iradius;
vec.y *= iradius;
vec.z *= iradius;
return radius;
}
// TODO: Add fast C VectorNormalizeFast.
// Perhaps use approximate rsqrt trick, if the accuracy isn't too bad.
void FASTCALL _VectorNormalizeFast(Vector3D& vec)
{
Assert(s_bMathlibInitialized);
// FLT_EPSILON is added to the radius to eliminate the possibility of divide by zero.
float iradius = 1.f / (sqrtf(vec.x * vec.x + vec.y * vec.y + vec.z * vec.z) + FLT_EPSILON);
vec.x *= iradius;
vec.y *= iradius;
vec.z *= iradius;
}
float _InvRSquared(const float* v)
{
Assert(s_bMathlibInitialized);
float r2 = DotProduct(v, v);
return r2 < 1.f ? 1.f : 1 / r2;
}
//-----------------------------------------------------------------------------
// Function pointers selecting the appropriate implementation
//-----------------------------------------------------------------------------
float (*pfSqrt)(float x) = _sqrtf;
float (*pfRSqrt)(float x) = _rsqrtf;
float (*pfRSqrtFast)(float x) = _rsqrtf;
float (FASTCALL* pfVectorNormalize)(Vector3D& v) = _VectorNormalize;
void (FASTCALL* pfVectorNormalizeFast)(Vector3D& v) = _VectorNormalizeFast;
float (*pfInvRSquared)(const float* v) = _InvRSquared;
void (*pfFastSinCos)(float x, float* s, float* c) = SinCos;
float (*pfFastCos)(float x) = cosf;
float SinCosTable[SIN_TABLE_SIZE];
void InitSinCosTable()
{
for (int i = 0; i < SIN_TABLE_SIZE; i++)
{
SinCosTable[i] = sin(i * 2.0 * M_PI / SIN_TABLE_SIZE);
}
}
qboolean VectorsEqual(const float* v1, const float* v2)
{
Assert(s_bMathlibInitialized);
return ((v1[0] == v2[0]) &&
(v1[1] == v2[1]) &&
(v1[2] == v2[2]));
}
//-----------------------------------------------------------------------------
// Purpose: Generates Euler angles given a left-handed orientation matrix. The
// columns of the matrix contain the forward, left, and up Vector3s.
// Input : matrix - Left-handed orientation matrix.
// angles[PITCH, YAW, ROLL]. Receives right-handed counterclockwise
// rotations in degrees around Y, Z, and X respectively.
//-----------------------------------------------------------------------------
void MatrixAngles(const matrix3x4_t& matrix, RadianEuler& angles, Vector3D& position)
{
MatrixGetColumn(matrix, 3, position);
MatrixAngles(matrix, angles);
}
void MatrixAngles(const matrix3x4_t& matrix, Quaternion& q, Vector3D& pos)
{
#ifdef _VPROF_MATHLIB
VPROF_BUDGET("MatrixQuaternion", "Mathlib");
#endif
float trace;
trace = matrix[0][0] + matrix[1][1] + matrix[2][2] + 1.0f;
if (trace > 1.0f + FLT_EPSILON)
{
// VPROF_INCREMENT_COUNTER("MatrixQuaternion A",1);
q.x = (matrix[2][1] - matrix[1][2]);
q.y = (matrix[0][2] - matrix[2][0]);
q.z = (matrix[1][0] - matrix[0][1]);
q.w = trace;
}
else if (matrix[0][0] > matrix[1][1] && matrix[0][0] > matrix[2][2])
{
// VPROF_INCREMENT_COUNTER("MatrixQuaternion B",1);
trace = 1.0f + matrix[0][0] - matrix[1][1] - matrix[2][2];
q.x = trace;
q.y = (matrix[1][0] + matrix[0][1]);
q.z = (matrix[0][2] + matrix[2][0]);
q.w = (matrix[2][1] - matrix[1][2]);
}
else if (matrix[1][1] > matrix[2][2])
{
// VPROF_INCREMENT_COUNTER("MatrixQuaternion C",1);
trace = 1.0f + matrix[1][1] - matrix[0][0] - matrix[2][2];
q.x = (matrix[0][1] + matrix[1][0]);
q.y = trace;
q.z = (matrix[2][1] + matrix[1][2]);
q.w = (matrix[0][2] - matrix[2][0]);
}
else
{
// VPROF_INCREMENT_COUNTER("MatrixQuaternion D",1);
trace = 1.0f + matrix[2][2] - matrix[0][0] - matrix[1][1];
q.x = (matrix[0][2] + matrix[2][0]);
q.y = (matrix[2][1] + matrix[1][2]);
q.z = trace;
q.w = (matrix[1][0] - matrix[0][1]);
}
QuaternionNormalize(q);
#if 0
// check against the angle version
RadianEuler ang;
MatrixAngles(matrix, ang);
Quaternion test;
AngleQuaternion(ang, test);
float d = QuaternionDotProduct(q, test);
Assert(fabs(d) > 0.99 && fabs(d) < 1.01);
#endif
MatrixGetColumn(matrix, 3, pos);
}
void MatrixAngles(const matrix3x4_t& matrix, float* angles)
{
#ifdef _VPROF_MATHLIB
VPROF_BUDGET("MatrixAngles", "Mathlib");
#endif
Assert(s_bMathlibInitialized);
float forward[3];
float left[3];
float up[3];
//
// Extract the basis Vector3s from the matrix. Since we only need the Z
// component of the up Vector3, we don't get X and Y.
//
forward[0] = matrix[0][0];
forward[1] = matrix[1][0];
forward[2] = matrix[2][0];
left[0] = matrix[0][1];
left[1] = matrix[1][1];
left[2] = matrix[2][1];
up[2] = matrix[2][2];
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]));
// (pitch) x = ATAN( -forward.z, sqrt(forward.x*forward.x+forward.y*forward.y) );
angles[0] = RAD2DEG(atan2f(-forward[2], xyDist));
// (roll) z = ATAN( left.z, up.z );
angles[2] = RAD2DEG(atan2f(left[2], up[2]));
}
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]));
// (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;
}
}
// transform in1 by the matrix in2
void VectorTransform(const float* in1, const matrix3x4_t& in2, float* out)
{
Assert(s_bMathlibInitialized);
Assert(in1 != out);
out[0] = DotProduct(in1, in2[0]) + in2[0][3];
out[1] = DotProduct(in1, in2[1]) + in2[1][3];
out[2] = DotProduct(in1, in2[2]) + in2[2][3];
}
// assuming the matrix is orthonormal, transform in1 by the transpose (also the inverse in this case) of in2.
void VectorITransform(const float* in1, const matrix3x4_t& in2, float* out)
{
Assert(s_bMathlibInitialized);
float in1t[3];
in1t[0] = in1[0] - in2[0][3];
in1t[1] = in1[1] - in2[1][3];
in1t[2] = in1[2] - in2[2][3];
out[0] = in1t[0] * in2[0][0] + in1t[1] * in2[1][0] + in1t[2] * in2[2][0];
out[1] = in1t[0] * in2[0][1] + in1t[1] * in2[1][1] + in1t[2] * in2[2][1];
out[2] = in1t[0] * in2[0][2] + in1t[1] * in2[1][2] + in1t[2] * in2[2][2];
}
// assume in2 is a rotation and rotate the input Vector3D
void VectorRotate(const float* in1, const matrix3x4_t& in2, float* out)
{
Assert(s_bMathlibInitialized);
Assert(in1 != out);
out[0] = DotProduct(in1, in2[0]);
out[1] = DotProduct(in1, in2[1]);
out[2] = DotProduct(in1, in2[2]);
}
// assume in2 is a rotation and rotate the input Vector3D
void VectorRotate(const Vector3D& in1, const QAngle& in2, Vector3D& out)
{
matrix3x4_t matRotate;
AngleMatrix(in2, matRotate);
VectorRotate(in1, matRotate, out);
}
// assume in2 is a rotation and rotate the input Vector3D
void VectorRotate(const Vector3D& in1, const Quaternion& in2, Vector3D& out)
{
matrix3x4_t matRotate;
QuaternionMatrix(in2, matRotate);
VectorRotate(in1, matRotate, out);
}
// rotate by the inverse of the matrix
void VectorIRotate(const float* in1, const matrix3x4_t& in2, float* out)
{
Assert(s_bMathlibInitialized);
Assert(in1 != out);
out[0] = in1[0] * in2[0][0] + in1[1] * in2[1][0] + in1[2] * in2[2][0];
out[1] = in1[0] * in2[0][1] + in1[1] * in2[1][1] + in1[2] * in2[2][1];
out[2] = in1[0] * in2[0][2] + in1[1] * in2[1][2] + in1[2] * in2[2][2];
}
#ifndef Vector_NO_SLOW_OPERATIONS
// transform a set of angles in the output space of parentMatrix to the input space
QAngle TransformAnglesToLocalSpace(const QAngle& angles, const matrix3x4_t& parentMatrix)
{
matrix3x4_t angToWorld, worldToParent, localMatrix;
MatrixInvert(parentMatrix, worldToParent);
AngleMatrix(angles, angToWorld);
ConcatTransforms(worldToParent, angToWorld, localMatrix);
QAngle out;
MatrixAngles(localMatrix, out);
return out;
}
// transform a set of angles in the input space of parentMatrix to the output space
QAngle TransformAnglesToWorldSpace(const QAngle& angles, const matrix3x4_t& parentMatrix)
{
matrix3x4_t angToParent, angToWorld;
AngleMatrix(angles, angToParent);
ConcatTransforms(parentMatrix, angToParent, angToWorld);
QAngle out;
MatrixAngles(angToWorld, out);
return out;
}
#endif // Vector3D_NO_SLOW_OPERATIONS
void MatrixInitialize(matrix3x4_t& mat, const Vector3D& vecOrigin, const Vector3D& vecXAxis, const Vector3D& vecYAxis, const Vector3D& vecZAxis)
{
MatrixSetColumn(vecXAxis, 0, mat);
MatrixSetColumn(vecYAxis, 1, mat);
MatrixSetColumn(vecZAxis, 2, mat);
MatrixSetColumn(vecOrigin, 3, mat);
}
void MatrixCopy(const matrix3x4_t& in, matrix3x4_t& out)
{
Assert(s_bMathlibInitialized);
memcpy(out.Base(), in.Base(), sizeof(float) * 3 * 4);
}
//-----------------------------------------------------------------------------
// Matrix equality test
//-----------------------------------------------------------------------------
bool MatricesAreEqual(const matrix3x4_t& src1, const matrix3x4_t& src2, float flTolerance)
{
for (int i = 0; i < 3; ++i)
{
for (int j = 0; j < 4; ++j)
{
if (fabs(src1[i][j] - src2[i][j]) > flTolerance)
return false;
}
}
return true;
}
// NOTE: This is just the transpose not a general inverse
void MatrixInvert(const matrix3x4_t& in, matrix3x4_t& out)
{
Assert(s_bMathlibInitialized);
if (&in == &out)
{
V_swap(out[0][1], out[1][0]);
V_swap(out[0][2], out[2][0]);
V_swap(out[1][2], out[2][1]);
}
else
{
// transpose the matrix
out[0][0] = in[0][0];
out[0][1] = in[1][0];
out[0][2] = in[2][0];
out[1][0] = in[0][1];
out[1][1] = in[1][1];
out[1][2] = in[2][1];
out[2][0] = in[0][2];
out[2][1] = in[1][2];
out[2][2] = in[2][2];
}
// now fix up the translation to be in the other space
float tmp[3];
tmp[0] = in[0][3];
tmp[1] = in[1][3];
tmp[2] = in[2][3];
out[0][3] = -DotProduct(tmp, out[0]);
out[1][3] = -DotProduct(tmp, out[1]);
out[2][3] = -DotProduct(tmp, out[2]);
}
void MatrixGetColumn(const matrix3x4_t& in, int column, Vector3D& out)
{
out.x = in[0][column];
out.y = in[1][column];
out.z = in[2][column];
}
void MatrixSetColumn(const Vector3D& in, int column, matrix3x4_t& out)
{
out[0][column] = in.x;
out[1][column] = in.y;
out[2][column] = in.z;
}
void MatrixScaleBy(const float flScale, matrix3x4_t& out)
{
out[0][0] *= flScale;
out[1][0] *= flScale;
out[2][0] *= flScale;
out[0][1] *= flScale;
out[1][1] *= flScale;
out[2][1] *= flScale;
out[0][2] *= flScale;
out[1][2] *= flScale;
out[2][2] *= flScale;
}
void MatrixScaleByZero(matrix3x4_t& out)
{
out[0][0] = 0.0f;
out[1][0] = 0.0f;
out[2][0] = 0.0f;
out[0][1] = 0.0f;
out[1][1] = 0.0f;
out[2][1] = 0.0f;
out[0][2] = 0.0f;
out[1][2] = 0.0f;
out[2][2] = 0.0f;
}
int VectorCompare(const float* v1, const float* v2)
{
Assert(s_bMathlibInitialized);
int i;
for (i = 0; i < 3; i++)
if (v1[i] != v2[i])
return 0;
return 1;
}
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
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