//===== Copyright � 1996-2005, Valve Corporation, All rights reserved. ======//
//
// Purpose:
//
//===========================================================================//
#ifndef MATH_LIB_H
#define MATH_LIB_H
#include "tier0/basetypes.h"
#include "mathlib/vector.h"
#include "mathlib/vector2d.h"
#include "tier0/dbg.h"
#include "mathlib/math_pfns.h"
#include "mathlib/fltx4.h"
#ifndef ALIGN8_POST
#define ALIGN8_POST
#endif
#if defined(_PS3)
#if defined(__SPU__)
#include <spu_intrinsics.h>
#include <vmx2spu.h>
#include <vectormath/c/vectormath_soa.h>
#else
#include <ppu_intrinsics.h>
#include <altivec.h>
#include <vectormath/c/vectormath_soa.h>
#endif
#include <mathlib/ssemath.h>
#endif
// plane_t structure
// !!! if this is changed, it must be changed in asm code too !!!
// FIXME: does the asm code even exist anymore?
// FIXME: this should move to a different file
struct cplane_t
{
Vector3D normal;
float dist;
byte type; // for fast side tests
byte signbits; // signx + (signy<<1) + (signz<<1)
byte pad[2];
#ifdef VECTOR_NO_SLOW_OPERATIONS
cplane_t() {}
private:
// No copy constructors allowed if we're in optimal mode
cplane_t(const cplane_t& vOther);
#endif
};
// structure offset for asm code
#define CPLANE_NORMAL_X 0
#define CPLANE_NORMAL_Y 4
#define CPLANE_NORMAL_Z 8
#define CPLANE_DIST 12
#define CPLANE_TYPE 16
#define CPLANE_SIGNBITS 17
#define CPLANE_PAD0 18
#define CPLANE_PAD1 19
// 0-2 are axial planes
#define PLANE_X 0
#define PLANE_Y 1
#define PLANE_Z 2
// 3-5 are non-axial planes snapped to the nearest
#define PLANE_ANYX 3
#define PLANE_ANYY 4
#define PLANE_ANYZ 5
//-----------------------------------------------------------------------------
// Frustum plane indices.
// WARNING: there is code that depends on these values
//-----------------------------------------------------------------------------
enum
{
FRUSTUM_RIGHT = 0,
FRUSTUM_LEFT = 1,
FRUSTUM_TOP = 2,
FRUSTUM_BOTTOM = 3,
FRUSTUM_NEARZ = 4,
FRUSTUM_FARZ = 5,
FRUSTUM_NUMPLANES = 6
};
extern int SignbitsForPlane(cplane_t* out);
class Frustum_t;
// Computes Y fov from an X fov and a screen aspect ratio + X from Y
float CalcFovY(float flFovX, float flScreenAspect);
float CalcFovX(float flFovY, float flScreenAspect);
// Generate a frustum based on perspective view parameters
// NOTE: FOV is specified in degrees, as the *full* view angle (not half-angle)
class VPlane;
void GeneratePerspectiveFrustum(const Vector3D& origin, const QAngle& angles, float flZNear, float flZFar, float flFovX, float flAspectRatio, Frustum_t& frustum);
void GeneratePerspectiveFrustum(const Vector3D& origin, const Vector3D& forward, const Vector3D& right, const Vector3D& up, float flZNear, float flZFar, float flFovX, float flFovY, VPlane* pPlanesOut);
// Cull the world-space bounding box to the specified frustum.
// bool R_CullBox( const Vector& mins, const Vector& maxs, const Frustum_t &frustum );
// bool R_CullBoxSkipNear( const Vector& mins, const Vector& maxs, const Frustum_t &frustum );
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);
class CTransform;
class matrix3x4a_t;
struct matrix3x4_t
{
matrix3x4_t() {}
matrix3x4_t(
float m00, float m01, float m02, float m03,
float m10, float m11, float m12, float m13,
float m20, float m21, float m22, float m23)
{
m_flMatVal[0][0] = m00; m_flMatVal[0][1] = m01; m_flMatVal[0][2] = m02; m_flMatVal[0][3] = m03;
m_flMatVal[1][0] = m10; m_flMatVal[1][1] = m11; m_flMatVal[1][2] = m12; m_flMatVal[1][3] = m13;
m_flMatVal[2][0] = m20; m_flMatVal[2][1] = m21; m_flMatVal[2][2] = m22; m_flMatVal[2][3] = m23;
}
/// Creates a matrix where the X axis = forward the Y axis = left, and the Z axis = up
void InitXYZ(const Vector3D& xAxis, const Vector3D& yAxis, const Vector3D& zAxis, const Vector3D& vecOrigin)
{
m_flMatVal[0][0] = xAxis.x; m_flMatVal[0][1] = yAxis.x; m_flMatVal[0][2] = zAxis.x; m_flMatVal[0][3] = vecOrigin.x;
m_flMatVal[1][0] = xAxis.y; m_flMatVal[1][1] = yAxis.y; m_flMatVal[1][2] = zAxis.y; m_flMatVal[1][3] = vecOrigin.y;
m_flMatVal[2][0] = xAxis.z; m_flMatVal[2][1] = yAxis.z; m_flMatVal[2][2] = zAxis.z; m_flMatVal[2][3] = vecOrigin.z;
}
//-----------------------------------------------------------------------------
// Creates a matrix where the X axis = forward
// the Y axis = left, and the Z axis = up
//-----------------------------------------------------------------------------
void Init(const Vector3D& xAxis, const Vector3D& yAxis, const Vector3D& zAxis, const Vector3D& vecOrigin)
{
m_flMatVal[0][0] = xAxis.x; m_flMatVal[0][1] = yAxis.x; m_flMatVal[0][2] = zAxis.x; m_flMatVal[0][3] = vecOrigin.x;
m_flMatVal[1][0] = xAxis.y; m_flMatVal[1][1] = yAxis.y; m_flMatVal[1][2] = zAxis.y; m_flMatVal[1][3] = vecOrigin.y;
m_flMatVal[2][0] = xAxis.z; m_flMatVal[2][1] = yAxis.z; m_flMatVal[2][2] = zAxis.z; m_flMatVal[2][3] = vecOrigin.z;
}
//-----------------------------------------------------------------------------
// Creates a matrix where the X axis = forward
// the Y axis = left, and the Z axis = up
//-----------------------------------------------------------------------------
matrix3x4_t(const Vector3D& xAxis, const Vector3D& yAxis, const Vector3D& zAxis, const Vector3D& vecOrigin)
{
Init(xAxis, yAxis, zAxis, vecOrigin);
}
inline void InitFromQAngles(const QAngle& angles, const Vector3D& vPosition);
inline void InitFromQAngles(const QAngle& angles);
inline void InitFromRadianEuler(const RadianEuler& angles, const Vector3D& vPosition);
inline void InitFromRadianEuler(const RadianEuler& angles);
inline void InitFromCTransform(const CTransform& transform);
inline void InitFromQuaternion(const Quaternion& orientation, const Vector3D& vPosition);
inline void InitFromQuaternion(const Quaternion& orientation);
inline void InitFromDiagonal(const Vector3D& vDiagonal);
inline Quaternion ToQuaternion() const;
inline QAngle ToQAngle() const;
inline CTransform ToCTransform() const;
inline void SetToIdentity();
/// multiply the scale/rot part of the matrix by a constant. This doesn't init the matrix ,
/// just scale in place. So if you want to construct a scaling matrix, init to identity and
/// then call this.
FORCEINLINE void ScaleUpper3x3Matrix(float flScale);
/// modify the origin
inline void SetOrigin(Vector3D const& p)
{
m_flMatVal[0][3] = p.x;
m_flMatVal[1][3] = p.y;
m_flMatVal[2][3] = p.z;
}
/// return the origin
inline Vector3D GetOrigin(void) const
{
Vector3D vecRet(m_flMatVal[0][3], m_flMatVal[1][3], m_flMatVal[2][3]);
return vecRet;
}
inline void Invalidate(void)
{
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 4; j++)
{
m_flMatVal[i][j] = VEC_T_NAN;
}
}
}
/// check all components for invalid floating point values
inline bool IsValid(void) const
{
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 4; j++)
{
if (!IsFinite(m_flMatVal[i][j]))
return false;
}
}
return true;
}
bool operator==(const matrix3x4_t& other) const
{
return memcmp(this, &other, sizeof(matrix3x4_t)) == 0;
}
bool operator!=(const matrix3x4_t& other) const
{
return memcmp(this, &other, sizeof(matrix3x4_t)) != 0;
}
inline bool IsEqualTo(const matrix3x4_t& other, float flTolerance = 1e-5f) const;
inline void GetBasisVectorsFLU(Vector3D* pForward, Vector3D* pLeft, Vector3D* pUp) const;
inline Vector3D TransformVector(const Vector3D& v0) const;
inline Vector3D RotateVector(const Vector3D& v0) const;
inline Vector3D TransformVectorByInverse(const Vector3D& v0) const;
inline Vector3D RotateVectorByInverse(const Vector3D& v0) const;
inline Vector3D RotateExtents(const Vector3D& vBoxExtents) const; // these are extents and must remain positive/symmetric after rotation
inline void TransformAABB(const Vector3D& vecMinsIn, const Vector3D& vecMaxsIn, Vector3D& vecMinsOut, Vector3D& vecMaxsOut) const;
inline void TransformAABBByInverse(const Vector3D& vecMinsIn, const Vector3D& vecMaxsIn, Vector3D& vecMinsOut, Vector3D& vecMaxsOut) const;
inline void RotateAABB(const Vector3D& vecMinsIn, const Vector3D& vecMaxsIn, Vector3D& vecMinsOut, Vector3D& vecMaxsOut) const;
inline void RotateAABBByInverse(const Vector3D& vecMinsIn, const Vector3D& vecMaxsIn, Vector3D& vecMinsOut, Vector3D& vecMaxsOut) const;
inline void TransformPlane(const cplane_t& inPlane, cplane_t& outPlane) const;
inline void TransformPlaneByInverse(const cplane_t& inPlane, cplane_t& outPlane) const;
inline float GetOrthogonalityError() const;
inline float GetDeterminant()const;
inline float GetSylvestersCriterion()const; // for symmetrical matrices only: should be >0 iff it's a positive definite matrix
inline Vector3D GetColumn(MatrixAxisType_t nColumn) const;
inline void SetColumn(const Vector3D& vColumn, MatrixAxisType_t nColumn);
inline Vector3D GetForward() const { return GetColumn(FORWARD_AXIS); }
inline Vector3D GetLeft() const { return GetColumn(LEFT_AXIS); }
inline Vector3D GetUp() const { return GetColumn(UP_AXIS); }
inline Vector3D GetRow(int nRow) const { return *(Vector3D*)(m_flMatVal[nRow]); }
inline void SetRow(int nRow, const Vector3D& vRow) { m_flMatVal[nRow][0] = vRow.x; m_flMatVal[nRow][1] = vRow.y; m_flMatVal[nRow][2] = vRow.z; }
inline void InverseTR(matrix3x4_t& out) const;
inline matrix3x4_t InverseTR() const;
float* operator[](int i) { Assert((i >= 0) && (i < 3)); return m_flMatVal[i]; }
const float* operator[](int i) const { Assert((i >= 0) && (i < 3)); return m_flMatVal[i]; }
float* Base() { return &m_flMatVal[0][0]; }
const float* Base() const { return &m_flMatVal[0][0]; }
float m_flMatVal[3][4];
};
class ALIGN16 matrix3x4a_t : public matrix3x4_t
{
public:
/*
matrix3x4a_t() { if (((size_t)Base()) % 16 != 0) { Error( "matrix3x4a_t missaligned" ); } }
*/
matrix3x4a_t(const matrix3x4_t& src) { *this = src; };
matrix3x4a_t& operator=(const matrix3x4_t& src) { memcpy(Base(), src.Base(), sizeof(float) * 3 * 4); return *this; };
matrix3x4a_t(
float m00, float m01, float m02, float m03,
float m10, float m11, float m12, float m13,
float m20, float m21, float m22, float m23)
{
AssertDbg(((size_t)Base() & 0xf) == 0);
m_flMatVal[0][0] = m00; m_flMatVal[0][1] = m01; m_flMatVal[0][2] = m02; m_flMatVal[0][3] = m03;
m_flMatVal[1][0] = m10; m_flMatVal[1][1] = m11; m_flMatVal[1][2] = m12; m_flMatVal[1][3] = m13;
m_flMatVal[2][0] = m20; m_flMatVal[2][1] = m21; m_flMatVal[2][2] = m22; m_flMatVal[2][3] = m23;
}
matrix3x4a_t() {}
static FORCEINLINE bool TypeIsAlignedForSIMD(void) { return true; }
// raw data simd accessor
FORCEINLINE fltx4& SIMDRow(uint nIdx) { AssertDbg(nIdx < 3); return *((fltx4*)(&(m_flMatVal[nIdx]))); }
FORCEINLINE const fltx4& SIMDRow(uint nIdx) const { AssertDbg(nIdx < 3); return *((const fltx4*)(&(m_flMatVal[nIdx]))); }
} ALIGN16_POST;
FORCEINLINE void matrix3x4_t::ScaleUpper3x3Matrix(float flScale)
{
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
m_flMatVal[i][j] *= flScale;
}
}
}
#ifndef M_PI
#define M_PI 3.14159265358979323846 // matches value in gcc v2 math.h
#endif
#ifndef M_PI_F
#define M_PI_F ((float)(M_PI))
#endif
// NJS: Inlined to prevent floats from being autopromoted to doubles, as with the old system.
#ifndef RAD2DEG
#define RAD2DEG( x ) ( (float)(x) * (float)(180.f / M_PI_F) )
#endif
#ifndef DEG2RAD
#define DEG2RAD( x ) ( (float)(x) * (float)(M_PI_F / 180.f) )
#endif
// Used to represent sides of things like planes.
#define SIDE_FRONT 0
#define SIDE_BACK 1
#define SIDE_ON 2
#define SIDE_CROSS -2 // necessary for polylib.c
// Use different side values (1, 2, 4) instead of (0, 1, 2) so we can '|' and '&' them, and quickly determine overall clipping
// without having to maintain counters and read / write memory.
enum Sides
{
OR_SIDE_FRONT = 1,
OR_SIDE_BACK = 2,
OR_SIDE_ON = 4,
};
#define ON_VIS_EPSILON 0.01 // necessary for vvis (flow.c) -- again look into moving later!
#define EQUAL_EPSILON 0.001 // necessary for vbsp (faces.c) -- should look into moving it there?
extern bool s_bMathlibInitialized;
extern const matrix3x4a_t g_MatrixIdentity;
extern const Vector3D vec3_origin;
extern const QAngle vec3_angle;
extern const Quaternion quat_identity;
extern const Vector3D vec3_invalid;
extern const int nanmask;
#define IS_NAN(x) (((*(int *)&x)&nanmask)==nanmask)
FORCEINLINE vec_t DotProduct(const vec_t* v1, const vec_t* v2)
{
return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
}
FORCEINLINE void VectorSubtract(const vec_t* a, const vec_t* b, vec_t* c)
{
c[0] = a[0] - b[0];
c[1] = a[1] - b[1];
c[2] = a[2] - b[2];
}
FORCEINLINE void VectorAdd(const vec_t* a, const vec_t* b, vec_t* c)
{
c[0] = a[0] + b[0];
c[1] = a[1] + b[1];
c[2] = a[2] + b[2];
}
FORCEINLINE void VectorCopy(const vec_t* a, vec_t* b)
{
b[0] = a[0];
b[1] = a[1];
b[2] = a[2];
}
FORCEINLINE void VectorClear(vec_t* a)
{
a[0] = a[1] = a[2] = 0;
}
FORCEINLINE float VectorMaximum(const vec_t* v)
{
return MAX(v[0], MAX(v[1], v[2]));
}
FORCEINLINE float VectorMaximum(const Vector3D& v)
{
return MAX(v.x, MAX(v.y, v.z));
}
FORCEINLINE void VectorScale(const float* in, vec_t scale, float* out)
{
out[0] = in[0] * scale;
out[1] = in[1] * scale;
out[2] = in[2] * scale;
}
// Cannot be forceinline as they have overloads:
inline void VectorFill(vec_t* a, float b)
{
a[0] = a[1] = a[2] = b;
}
inline void VectorNegate(vec_t* a)
{
a[0] = -a[0];
a[1] = -a[1];
a[2] = -a[2];
}
//#define VectorMaximum(a) ( max( (a)[0], max( (a)[1], (a)[2] ) ) )
#define Vector2Clear(x) {(x)[0]=(x)[1]=0;}
#define Vector2Negate(x) {(x)[0]=-((x)[0]);(x)[1]=-((x)[1]);}
#define Vector2Copy(a,b) {(b)[0]=(a)[0];(b)[1]=(a)[1];}
#define Vector2Subtract(a,b,c) {(c)[0]=(a)[0]-(b)[0];(c)[1]=(a)[1]-(b)[1];}
#define Vector2Add(a,b,c) {(c)[0]=(a)[0]+(b)[0];(c)[1]=(a)[1]+(b)[1];}
#define Vector2Scale(a,b,c) {(c)[0]=(b)*(a)[0];(c)[1]=(b)*(a)[1];}
// NJS: Some functions in VBSP still need to use these for dealing with mixing vec4's and shorts with vec_t's.
// remove when no longer needed.
#define VECTOR_COPY( A, B ) do { (B)[0] = (A)[0]; (B)[1] = (A)[1]; (B)[2]=(A)[2]; } while(0)
#define DOT_PRODUCT( A, B ) ( (A)[0]*(B)[0] + (A)[1]*(B)[1] + (A)[2]*(B)[2] )
FORCEINLINE void VectorMAInline(const float* start, float scale, const float* direction, float* dest)
{
dest[0] = start[0] + direction[0] * scale;
dest[1] = start[1] + direction[1] * scale;
dest[2] = start[2] + direction[2] * scale;
}
FORCEINLINE void VectorMAInline(const Vector3D& start, float scale, const Vector3D& direction, Vector3D& dest)
{
dest.x = start.x + direction.x * scale;
dest.y = start.y + direction.y * scale;
dest.z = start.z + direction.z * scale;
}
FORCEINLINE void VectorMA(const Vector3D& start, float scale, const Vector3D& direction, Vector3D& dest)
{
VectorMAInline(start, scale, direction, dest);
}
FORCEINLINE void VectorMA(const float* start, float scale, const float* direction, float* dest)
{
VectorMAInline(start, scale, direction, dest);
}
int VectorCompare(const float* v1, const float* v2);
inline float VectorLength(const float* v)
{
return FastSqrt(v[0] * v[0] + v[1] * v[1] + v[2] * v[2] + FLT_EPSILON);
}
void CrossProduct(const float* v1, const float* v2, float* cross);
inline float CrossProductX(const Vector3D& v1, const Vector3D& v2)
{
return v1.y * v2.z - v1.z * v2.y;
}
inline float CrossProductY(const Vector3D& v1, const Vector3D& v2)
{
return v1.z * v2.x - v1.x * v2.z;
}
inline float CrossProductZ(const Vector3D& v1, const Vector3D& v2)
{
return v1.x * v2.y - v1.y * v2.x;
}
qboolean VectorsEqual(const float* v1, const float* v2);
inline vec_t RoundInt(vec_t in)
{
return floor(in + 0.5f);
}
size_t Q_log2(unsigned int val);
// Math routines done in optimized assembly math package routines
void inline SinCos(float radians, float* RESTRICT sine, float* RESTRICT cosine)
{
#if defined( _X360 )
XMScalarSinCos(sine, cosine, radians);
#elif defined( _PS3 )
#if ( __GNUC__ == 4 ) && ( __GNUC_MINOR__ == 1 ) && ( __GNUC_PATCHLEVEL__ == 1 )
vector_float_union s;
vector_float_union c;
vec_float4 rad = vec_splats(radians);
vec_float4 sin;
vec_float4 cos;
sincosf4(rad, &sin, &cos);
vec_st(sin, 0, s.f);
vec_st(cos, 0, c.f);
*sine = s.f[0];
*cosine = c.f[0];
#else //__GNUC__ == 4 && __GNUC_MINOR__ == 1 && __GNUC_PATCHLEVEL__ == 1
vector_float_union r;
vector_float_union s;
vector_float_union c;
vec_float4 rad;
vec_float4 sin;
vec_float4 cos;
r.f[0] = radians;
rad = vec_ld(0, r.f);
sincosf4(rad, &sin, &cos);
vec_st(sin, 0, s.f);
vec_st(cos, 0, c.f);
*sine = s.f[0];
*cosine = c.f[0];
#endif //__GNUC__ == 4 && __GNUC_MINOR__ == 1 && __GNUC_PATCHLEVEL__ == 1
#elif defined( COMPILER_MSVC32 )
_asm
{
fld DWORD PTR[radians]
fsincos
mov edx, DWORD PTR[cosine]
mov eax, DWORD PTR[sine]
fstp DWORD PTR[edx]
fstp DWORD PTR[eax]
}
#elif defined( GNUC )
register double __cosr, __sinr;
__asm __volatile__("fsincos" : "=t" (__cosr), "=u" (__sinr) : "0" (radians));
*sine = __sinr;
*cosine = __cosr;
#else
* sine = sinf(radians);
*cosine = cosf(radians);
#endif
}
#define SIN_TABLE_SIZE 256
#define FTOIBIAS 12582912.f
extern float SinCosTable[SIN_TABLE_SIZE];
inline float TableCos(float theta)
{
#if defined( LINUX )
return cos(theta); // under the GCC compiler the float-represented-as-an-int causes an internal compiler error
#else
union
{
int i;
float f;
} ftmp;
// ideally, the following should compile down to: theta * constant + constant, changing any of these constants from defines sometimes fubars this.
ftmp.f = theta * (float)(SIN_TABLE_SIZE / (2.0f * M_PI)) + (FTOIBIAS + (SIN_TABLE_SIZE / 4));
return SinCosTable[ftmp.i & (SIN_TABLE_SIZE - 1)];
#endif
}
inline float TableSin(float theta)
{
#if defined( LINUX )
return sin(theta); // under the GCC compiler the float-represented-as-an-int causes an internal compiler error
#else
union
{
int i;
float f;
} ftmp;
// ideally, the following should compile down to: theta * constant + constant
ftmp.f = theta * (float)(SIN_TABLE_SIZE / (2.0f * M_PI)) + FTOIBIAS;
return SinCosTable[ftmp.i & (SIN_TABLE_SIZE - 1)];
#endif
}
template<class T>
FORCEINLINE T Square(T const& a)
{
return a * a;
}
FORCEINLINE bool IsPowerOfTwo(uint x)
{
return (x & (x - 1)) == 0;
}
// return the smallest power of two >= x.
// returns 0 if x == 0 or x > 0x80000000 (ie numbers that would be negative if x was signed)
// NOTE: the old code took an int, and if you pass in an int of 0x80000000 casted to a uint,
// you'll get 0x80000000, which is correct for uints, instead of 0, which was correct for ints
FORCEINLINE uint SmallestPowerOfTwoGreaterOrEqual(uint x)
{
x -= 1;
x |= x >> 1;
x |= x >> 2;
x |= x >> 4;
x |= x >> 8;
x |= x >> 16;
return x + 1;
}
// return the largest power of two <= x. Will return 0 if passed 0
FORCEINLINE uint LargestPowerOfTwoLessThanOrEqual(uint x)
{
if (x >= 0x80000000)
return 0x80000000;
return SmallestPowerOfTwoGreaterOrEqual(x + 1) >> 1;
}
// Math routines for optimizing division
void FloorDivMod(double numer, double denom, int* quotient, int* rem);
int GreatestCommonDivisor(int i1, int i2);
// Test for FPU denormal mode
bool IsDenormal(const float& val);
// MOVEMENT INFO
enum
{
PITCH = 0, // up / down
YAW, // left / right
ROLL // fall over
};
void MatrixVectorsFLU(const matrix3x4_t& matrix, Vector3D* pForward, Vector3D* pLeft, Vector3D* pUp);
void MatrixAngles(const matrix3x4_t& matrix, float* angles); // !!!!
void MatrixVectors(const matrix3x4_t& matrix, Vector3D* pForward, Vector3D* pRight, Vector3D* pUp);
void VectorTransform(const float* RESTRICT in1, const matrix3x4_t& in2, float* RESTRICT out);
void VectorITransform(const float* in1, const matrix3x4_t& in2, float* out);
void VectorRotate(const float* RESTRICT in1, const matrix3x4_t& in2, float* RESTRICT out);
void VectorRotate(const Vector3D& in1, const QAngle& in2, Vector3D& out);
void VectorRotate(const Vector3D& in1, const Quaternion& in2, Vector3D& out);
void VectorIRotate(const float* RESTRICT in1, const matrix3x4_t& in2, float* RESTRICT out);
inline const Vector3D VectorRotate(const Vector3D& vIn1, const Quaternion& qIn2)
{
Vector3D out;
VectorRotate(vIn1, qIn2, out);
return out;
}
#ifndef VECTOR_NO_SLOW_OPERATIONS
QAngle TransformAnglesToLocalSpace(const QAngle& angles, const matrix3x4_t& parentMatrix);
QAngle TransformAnglesToWorldSpace(const QAngle& angles, const matrix3x4_t& parentMatrix);
#endif
void MatrixInitialize(matrix3x4_t& mat, const Vector3D& vecOrigin, const Vector3D& vecXAxis, const Vector3D& vecYAxis, const Vector3D& vecZAxis);
void MatrixCopy(const matrix3x4_t& in, matrix3x4_t& out);
void MatrixInvert(const matrix3x4_t& in, matrix3x4_t& out);
// Matrix equality test
bool MatricesAreEqual(const matrix3x4_t& src1, const matrix3x4_t& src2, float flTolerance = 1e-5);
void MatrixGetColumn(const matrix3x4_t& in, int column, Vector3D& out);
void MatrixSetColumn(const Vector3D& in, int column, matrix3x4_t& out);
//void DecomposeRotation( const matrix3x4_t &mat, float *out );
void ConcatRotations(const matrix3x4_t& in1, const matrix3x4_t& in2, matrix3x4_t& out);
void ConcatTransforms(const matrix3x4_t& in1, const matrix3x4_t& in2, matrix3x4_t& out);
// faster version assumes m0, m1, out are 16-byte aligned addresses
void ConcatTransforms_Aligned(const matrix3x4a_t& m0, const matrix3x4a_t& m1, matrix3x4a_t& out);
// For identical interface w/ VMatrix
inline void MatrixMultiply(const matrix3x4_t& in1, const matrix3x4_t& in2, matrix3x4_t& out)
{
ConcatTransforms(in1, in2, out);
}
void QuaternionExp(const Quaternion& p, Quaternion& q);
void QuaternionLn(const Quaternion& p, Quaternion& q);
void QuaternionAverageExponential(Quaternion& q, int nCount, const Quaternion* pQuaternions, const float* pflWeights = NULL);
void QuaternionLookAt(const Vector3D& vecForward, const Vector3D& referenceUp, Quaternion& q);
void QuaternionSlerp(const Quaternion& p, const Quaternion& q, float t, Quaternion& qt);
void QuaternionSlerpNoAlign(const Quaternion& p, const Quaternion& q, float t, Quaternion& qt);
void QuaternionBlend(const Quaternion& p, const Quaternion& q, float t, Quaternion& qt);
void QuaternionBlendNoAlign(const Quaternion& p, const Quaternion& q, float t, Quaternion& qt);
void QuaternionIdentityBlend(const Quaternion& p, float t, Quaternion& qt);
float QuaternionAngleDiff(const Quaternion& p, const Quaternion& q);
void QuaternionScale(const Quaternion& p, float t, Quaternion& q);
void QuaternionAlign(const Quaternion& p, const Quaternion& q, Quaternion& qt);
float QuaternionDotProduct(const Quaternion& p, const Quaternion& q);
void QuaternionConjugate(const Quaternion& p, Quaternion& q);
void QuaternionInvert(const Quaternion& p, Quaternion& q);
float QuaternionNormalize(Quaternion& q);
void QuaternionMultiply(const Quaternion& q, const Vector3D& v, Vector3D& result);
void QuaternionAdd(const Quaternion& p, const Quaternion& q, Quaternion& qt);
void QuaternionMult(const Quaternion& p, const Quaternion& q, Quaternion& qt);
void QuaternionMatrix(const Quaternion& q, matrix3x4_t& matrix);
void QuaternionMatrix(const Quaternion& q, const Vector3D& pos, matrix3x4_t& matrix);
void QuaternionMatrix(const Quaternion& q, const Vector3D& pos, const Vector3D& vScale, matrix3x4_t& mat);
void QuaternionAngles(const Quaternion& q, QAngle& angles);
void AngleQuaternion(const QAngle& angles, Quaternion& qt);
void QuaternionAngles(const Quaternion& q, RadianEuler& angles);
void QuaternionVectorsFLU(Quaternion const& q, Vector3D* pForward, Vector3D* pLeft, Vector3D* pUp);
void QuaternionVectorsForward(const Quaternion& q, Vector3D* pForward);
void AngleQuaternion(RadianEuler const& angles, Quaternion& qt);
void QuaternionAxisAngle(const Quaternion& q, Vector3D& axis, float& angle);
void AxisAngleQuaternion(const Vector3D& axis, float angle, Quaternion& q);
void BasisToQuaternion(const Vector3D& vecForward, const Vector3D& vecRight, const Vector3D& vecUp, Quaternion& q);
void MatrixQuaternion(const matrix3x4_t& mat, Quaternion& q);
void MatrixQuaternionFast(const matrix3x4_t& mat, Quaternion& q);
void MatrixPosition(const matrix3x4_t& matrix, Vector3D& position);
Vector3D MatrixNormalize(const matrix3x4_t& in, matrix3x4_t& out);
inline void MatrixQuaternion(const matrix3x4_t& mat, Quaternion& q, Vector3D& o)
{
MatrixQuaternion(mat, q);
MatrixPosition(mat, o);
}
float MatrixQuaternionTest(uint);
float MatrixQuaternionTest2(uint);
/// qt = p + s * q
void QuaternionAccumulate(const Quaternion& p, float s, const Quaternion& q, Quaternion& qt);
/// qt = ( s * p ) * q
void QuaternionSM(float s, const Quaternion& p, const Quaternion& q, Quaternion& qt);
/// qt = p * ( s * q )
void QuaternionMA(const Quaternion& p, float s, const Quaternion& q, Quaternion& qt);
/*
//-----------------------------------------------------------------------------
// Quaternion equality with tolerance
//-----------------------------------------------------------------------------
inline bool QuaternionsAreEqualInternal( const Quaternion& src1, const Quaternion& src2, float flTolerance )
{
if ( !FloatsAreEqual( src1.x, src2.x, flTolerance ) )
return false;
if ( !FloatsAreEqual( src1.y, src2.y, flTolerance ) )
return false;
if ( !FloatsAreEqual( src1.z, src2.z, flTolerance ) )
return false;
return FloatsAreEqual( src1.w, src2.w, flTolerance );
}
inline bool QuaternionsAreEqual( const Quaternion& src1, const Quaternion& src2, float flTolerance )
{
if ( QuaternionsAreEqualInternal( src1, src2, flTolerance ) )
return true;
// negated quaternions are also 'equal'
Quaternion src2neg( -src2.x, -src2.y, -src2.z, -src2.w );
return QuaternionsAreEqualInternal( src1, src2neg, flTolerance );
}
*/
inline const Quaternion GetNormalized(const Quaternion& q)
{
float flInv = 1.0f / sqrtf(q.x * q.x + q.y * q.y + q.z * q.z + q.w * q.w);
return Quaternion(q.x * flInv, q.y * flInv, q.z * flInv, q.w * flInv);
}
inline const Quaternion AngleQuaternion(const QAngle& angles)
{
Quaternion qt;
AngleQuaternion(angles, qt);
return qt;
}
inline const Quaternion AngleQuaternion(RadianEuler const& angles)
{
Quaternion qt;
AngleQuaternion(angles, qt);
return qt;
}
inline Quaternion QuaternionFromPitchYawRoll(float flPitch, float flYaw, float flRoll)
{
QAngle ang(flPitch, flYaw, flRoll);
Quaternion q;
AngleQuaternion(ang, q);
return q;
}
inline Quaternion QuaternionAddPitch(const Quaternion& q, float flPitch)
{
// FIXME: I know this can be made *tons* faster, but I just want to get something working quickly
// that matches being able to add to the pitch of a QAngles so I can expose Quats to script/game code
QAngle ang;
QuaternionAngles(q, ang);
ang[PITCH] += flPitch;
Quaternion res;
AngleQuaternion(ang, res);
return res;
}
inline Quaternion QuaternionAddYaw(const Quaternion& q, float flYaw)
{
// FIXME: I know this can be made *tons* faster, but I just want to get something working quickly
// that matches being able to add to the yaw of a QAngles so I can expose Quats to script/game code
QAngle ang;
QuaternionAngles(q, ang);
ang[YAW] += flYaw;
Quaternion res;
AngleQuaternion(ang, res);
return res;
}
inline Quaternion QuaternionAddRoll(const Quaternion& q, float flRoll)
{
// FIXME: I know this can be made *tons* faster, but I just want to get something working quickly
// that matches being able to add to the roll of a QAngles so I can expose Quats to script/game code
QAngle ang;
QuaternionAngles(q, ang);
ang[ROLL] += flRoll;
Quaternion res;
AngleQuaternion(ang, res);
return res;
}
inline const Quaternion MatrixQuaternion(const matrix3x4_t& mat)
{
Quaternion tmp;
MatrixQuaternion(mat, tmp);
return tmp;
}
inline const Quaternion MatrixQuaternionFast(const matrix3x4_t& mat)
{
Quaternion tmp;
MatrixQuaternionFast(mat, tmp);
return tmp;
}
inline const matrix3x4_t QuaternionMatrix(const Quaternion& q)
{
matrix3x4_t mat;
QuaternionMatrix(q, mat);
return mat;
}
inline const matrix3x4_t QuaternionMatrix(const Quaternion& q, const Vector3D& pos)
{
matrix3x4_t mat;
QuaternionMatrix(q, pos, mat);
return mat;
}
//! Shortest-arc quaternion that rotates vector v1 into vector v2
const Quaternion RotateBetween(const Vector3D& v1, const Vector3D& v2);
inline const Quaternion QuaternionConjugate(const Quaternion& p)
{
Quaternion q;
QuaternionConjugate(p, q);
return q;
}
inline const Quaternion QuaternionInvert(const Quaternion& p)
{
Quaternion q;
QuaternionInvert(p, q);
return q;
}
/// Actual quaternion multiplication; NOTE: QuaternionMult aligns quaternions first, so that q *
/// conjugate(q) may be -1 instead of 1!
inline const Quaternion operator * (const Quaternion& p, const Quaternion& q)
{
Quaternion qt;
qt.x = p.x * q.w + p.y * q.z - p.z * q.y + p.w * q.x;
qt.y = -p.x * q.z + p.y * q.w + p.z * q.x + p.w * q.y;
qt.z = p.x * q.y - p.y * q.x + p.z * q.w + p.w * q.z;
qt.w = -p.x * q.x - p.y * q.y - p.z * q.z + p.w * q.w;
return qt;
}
inline Quaternion& operator *= (Quaternion& p, const Quaternion& q)
{
QuaternionMult(p, q, p);
return p;
}
inline const matrix3x4_t ConcatTransforms(const matrix3x4_t& in1, const matrix3x4_t& in2)
{
matrix3x4_t out;
ConcatTransforms(in1, in2, out);
return out;
}
inline const matrix3x4_t operator *(const matrix3x4_t& in1, const matrix3x4_t& in2)
{
matrix3x4_t out;
ConcatTransforms(in1, in2, out);
return out;
}
inline const matrix3x4_t MatrixInvert(const matrix3x4_t& in)
{
matrix3x4_t out;
::MatrixInvert(in, out);
return out;
}
inline const Vector3D MatrixGetColumn(const matrix3x4_t& in, MatrixAxisType_t nColumn)
{
return in.GetColumn(nColumn);
}
// A couple methods to find the dot product of a vector with a matrix row or column...
inline float MatrixRowDotProduct(const matrix3x4_t& in1, int row, const Vector3D& in2)
{
Assert((row >= 0) && (row < 3));
return DotProduct(in1[row], in2.Base());
}
inline float MatrixColumnDotProduct(const matrix3x4_t& in1, int col, const Vector3D& in2)
{
Assert((col >= 0) && (col < 4));
return in1[0][col] * in2[0] + in1[1][col] * in2[1] + in1[2][col] * in2[2];
}
int __cdecl BoxOnPlaneSide(const float* emins, const float* emaxs, const cplane_t* plane);
inline float anglemod(float a)
{
a = (360.f / 65536) * ((int)(a * (65536.f / 360.0f)) & 65535);
return a;
}
//// CLAMP
#if defined(__cplusplus) && defined(PLATFORM_PPC)
#ifdef _X360
#define __fsels __fsel
#endif
template< >
inline double clamp(double const& val, double const& minVal, double const& maxVal)
{
float diffmin = val - minVal;
float diffmax = maxVal - val;
float r;
r = __fsel(diffmin, val, minVal);
r = __fsel(diffmax, r, maxVal);
return r;
}
template< >
inline double clamp(double const& val, float const& minVal, float const& maxVal)
{
// these typecasts are actually free since all FPU regs are 64 bit on PPC anyway
return clamp(val, (double)minVal, (double)maxVal);
}
template< >
inline double clamp(double const& val, float const& minVal, double const& maxVal)
{
return clamp(val, (double)minVal, (double)maxVal);
}
template< >
inline double clamp(double const& val, double const& minVal, float const& maxVal)
{
return clamp(val, (double)minVal, (double)maxVal);
}
template< >
inline float clamp(float const& val, float const& minVal, float const& maxVal)
{
float diffmin = val - minVal;
float diffmax = maxVal - val;
float r;
r = __fsels(diffmin, val, minVal);
r = __fsels(diffmax, r, maxVal);
return r;
}
template< >
inline float clamp(float const& val, double const& minVal, double const& maxVal)
{
float diffmin = val - minVal;
float diffmax = maxVal - val;
float r;
r = __fsels(diffmin, val, minVal);
r = __fsels(diffmax, r, maxVal);
return r;
}
template< >
inline float clamp(float const& val, double const& minVal, float const& maxVal)
{
return clamp(val, (float)minVal, maxVal);
}
template< >
inline float clamp(float const& val, float const& minVal, double const& maxVal)
{
return clamp(val, minVal, (float)maxVal);
}
#endif
// Remap a value in the range [A,B] to [C,D].
inline float RemapVal(float val, float A, float B, float C, float D)
{
if (A == B)
return fsel(val - B, D, C);
return C + (D - C) * (val - A) / (B - A);
}
inline float RemapValClamped(float val, float A, float B, float C, float D)
{
if (A == B)
return fsel(val - B, D, C);
float cVal = (val - A) / (B - A);
cVal = clamp<float>(cVal, 0.0f, 1.0f);
return C + (D - C) * cVal;
}
// Returns A + (B-A)*flPercent.
// float Lerp( float flPercent, float A, float B );
template <class T>
FORCEINLINE T Lerp(float flPercent, T const& A, T const& B)
{
return A + (B - A) * flPercent;
}
FORCEINLINE float Sqr(float f)
{
return f * f;
}
// 5-argument floating point linear interpolation.
// FLerp(f1,f2,i1,i2,x)=
// f1 at x=i1
// f2 at x=i2
// smooth lerp between f1 and f2 at x>i1 and x<i2
// extrapolation for x<i1 or x>i2
//
// If you know a function f(x)'s value (f1) at position i1, and its value (f2) at position i2,
// the function can be linearly interpolated with FLerp(f1,f2,i1,i2,x)
// i2=i1 will cause a divide by zero.
static inline float FLerp(float f1, float f2, float i1, float i2, float x)
{
return f1 + (f2 - f1) * (x - i1) / (i2 - i1);
}
#ifndef VECTOR_NO_SLOW_OPERATIONS
// YWB: Specialization for interpolating euler angles via quaternions...
template<> FORCEINLINE QAngle Lerp<QAngle>(float flPercent, const QAngle& q1, const QAngle& q2)
{
// Avoid precision errors
if (q1 == q2)
return q1;
Quaternion src, dest;
// Convert to quaternions
AngleQuaternion(q1, src);
AngleQuaternion(q2, dest);
Quaternion result;
// Slerp
QuaternionSlerp(src, dest, flPercent, result);
// Convert to euler
QAngle output;
QuaternionAngles(result, output);
return output;
}
#else
#pragma error
// NOTE NOTE: I haven't tested this!! It may not work! Check out interpolatedvar.cpp in the client dll to try it
template<> FORCEINLINE QAngleByValue Lerp<QAngleByValue>(float flPercent, const QAngleByValue& q1, const QAngleByValue& q2)
{
// Avoid precision errors
if (q1 == q2)
return q1;
Quaternion src, dest;
// Convert to quaternions
AngleQuaternion(q1, src);
AngleQuaternion(q2, dest);
Quaternion result;
// Slerp
QuaternionSlerp(src, dest, flPercent, result);
// Convert to euler
QAngleByValue output;
QuaternionAngles(result, output);
return output;
}
#endif // VECTOR_NO_SLOW_OPERATIONS
// Swap two of anything.
template <class T>
FORCEINLINE void V_swap(T& x, T& y)
{
T temp = x;
x = y;
y = temp;
}
template <class T> FORCEINLINE T AVG(T a, T b)
{
return (a + b) / 2;
}
// number of elements in an array of static size
#define NELEMS(x) ((sizeof(x))/sizeof(x[0]))
// XYZ macro, for printf type functions - ex printf("%f %f %f",XYZ(myvector));
#define XYZ(v) (v).x,(v).y,(v).z
inline float Sign(float x)
{
return fsel(x, 1.0f, -1.0f); // x >= 0 ? 1.0f : -1.0f
//return (x <0.0f) ? -1.0f : 1.0f;
}
//
// Clamps the input integer to the given array bounds.
// Equivalent to the following, but without using any branches:
//
// if( n < 0 ) return 0;
// else if ( n > maxindex ) return maxindex;
// else return n;
//
// This is not always a clear performance win, but when you have situations where a clamped
// value is thrashing against a boundary this is a big win. (ie, valid, invalid, valid, invalid, ...)
//
// Note: This code has been run against all possible integers.
//
inline int ClampArrayBounds(int n, unsigned maxindex)
{
// mask is 0 if less than 4096, 0xFFFFFFFF if greater than
unsigned int inrangemask = 0xFFFFFFFF + (((unsigned)n) > maxindex);
unsigned int lessthan0mask = 0xFFFFFFFF + (n >= 0);
// If the result was valid, set the result, (otherwise sets zero)
int result = (inrangemask & n);
// if the result was out of range or zero.
result |= ((~inrangemask) & (~lessthan0mask)) & maxindex;
return result;
}
// Turn a number "inside out".
// See Recording Animation in Binary Order for Progressive Temporal Refinement
// by Paul Heckbert from "Graphics Gems".
//
// If you want to iterate something from 0 to n, you can use this to iterate non-sequentially, in
// such a way that you will start with widely separated values and then refine the gaps between
// them, as you would for progressive refinement. This works with non-power of two ranges.
int InsideOut(int nTotal, int nCounter);
#define BOX_ON_PLANE_SIDE(emins, emaxs, p) \
(((p)->type < 3)? \
( \
((p)->dist <= (emins)[(p)->type])? \
1 \
: \
( \
((p)->dist >= (emaxs)[(p)->type])?\
2 \
: \
3 \
) \
) \
: \
BoxOnPlaneSide( (emins), (emaxs), (p)))
//-----------------------------------------------------------------------------
// FIXME: Vector versions.... the float versions will go away hopefully soon!
//-----------------------------------------------------------------------------
void AngleCompose(const QAngle& a1, const QAngle& a2, QAngle& out);
void AngleLerp(const QAngle& a1, const QAngle& a2, float t, QAngle& out);
void AngleInverse(const QAngle& angles, QAngle& out);
void AngleVectors(const QAngle& angles, Vector3D* forward);
void AngleVectors(const QAngle& angles, Vector3D* forward, Vector3D* right, Vector3D* up);
void AngleVectorsTranspose(const QAngle& angles, Vector3D* forward, Vector3D* right, Vector3D* up);
void AngleVectorsFLU(const QAngle& angles, Vector3D* pForward, Vector3D* pLeft, Vector3D* pUp);
void AngleMatrix(const QAngle& angles, matrix3x4_t& mat);
void AngleMatrix(const QAngle& angles, const Vector3D& position, matrix3x4_t& mat);
void AngleMatrix(const RadianEuler& angles, matrix3x4_t& mat);
void AngleMatrix(RadianEuler const& angles, const Vector3D& position, matrix3x4_t& mat);
void AngleIMatrix(const QAngle& angles, matrix3x4_t& mat);
void AngleIMatrix(const QAngle& angles, const Vector3D& position, matrix3x4_t& mat);
void AngleIMatrix(const RadianEuler& angles, matrix3x4_t& mat);
void VectorAngles(const Vector3D& forward, QAngle& angles);
void VectorAngles(const Vector3D& forward, const Vector3D& pseudoup, QAngle& angles);
void VectorMatrix(const Vector3D& forward, matrix3x4_t& mat);
void VectorVectors(const Vector3D& forward, Vector3D& right, Vector3D& up);
void SetIdentityMatrix(matrix3x4_t& mat);
void SetScaleMatrix(float x, float y, float z, matrix3x4_t& dst);
void MatrixBuildRotationAboutAxis(const Vector3D& vAxisOfRot, float angleDegrees, matrix3x4_t& dst);
inline bool MatrixIsIdentity(const matrix3x4_t& m)
{
return
m.m_flMatVal[0][0] == 1.0f && m.m_flMatVal[0][1] == 0.0f && m.m_flMatVal[0][2] == 0.0f && m.m_flMatVal[0][3] == 0.0f &&
m.m_flMatVal[1][0] == 0.0f && m.m_flMatVal[1][1] == 1.0f && m.m_flMatVal[1][2] == 0.0f && m.m_flMatVal[1][3] == 0.0f &&
m.m_flMatVal[2][0] == 0.0f && m.m_flMatVal[2][1] == 0.0f && m.m_flMatVal[2][2] == 1.0f && m.m_flMatVal[2][3] == 0.0f;
}
inline void SetScaleMatrix(float flScale, matrix3x4_t& dst)
{
SetScaleMatrix(flScale, flScale, flScale, dst);
}
inline void SetScaleMatrix(const Vector3D& scale, matrix3x4_t& dst)
{
SetScaleMatrix(scale.x, scale.y, scale.z, dst);
}
// Computes the inverse transpose
void MatrixTranspose(matrix3x4_t& mat);
void MatrixTranspose(const matrix3x4_t& src, matrix3x4_t& dst);
void MatrixInverseTranspose(const matrix3x4_t& src, matrix3x4_t& dst);
inline void PositionMatrix(const Vector3D& position, matrix3x4_t& mat)
{
MatrixSetColumn(position, 3, mat);
}
inline void MatrixPosition(const matrix3x4_t& matrix, Vector3D& position)
{
position[0] = matrix[0][3];
position[1] = matrix[1][3];
position[2] = matrix[2][3];
}
inline void VectorRotate(const Vector3D& in1, const matrix3x4_t& in2, Vector3D& out)
{
VectorRotate(&in1.x, in2, &out.x);
}
inline void VectorIRotate(const Vector3D& in1, const matrix3x4_t& in2, Vector3D& out)
{
VectorIRotate(&in1.x, in2, &out.x);
}
inline void MatrixAngles(const matrix3x4_t& matrix, QAngle& angles)
{
MatrixAngles(matrix, &angles.x);
}
inline void MatrixAngles(const matrix3x4_t& matrix, QAngle& angles, Vector3D& position)
{
MatrixAngles(matrix, angles);
MatrixPosition(matrix, position);
}
inline void MatrixAngles(const matrix3x4_t& matrix, RadianEuler& angles)
{
MatrixAngles(matrix, &angles.x);
angles.Init(DEG2RAD(angles.z), DEG2RAD(angles.x), DEG2RAD(angles.y));
}
void MatrixAngles(const matrix3x4_t& mat, RadianEuler& angles, Vector3D& position);
void MatrixAngles(const matrix3x4_t& mat, Quaternion& q, Vector3D& position);
inline int VectorCompare(const Vector3D& v1, const Vector3D& v2)
{
return v1 == v2;
}
inline void VectorTransform(const Vector3D& in1, const matrix3x4_t& in2, Vector3D& out)
{
VectorTransform(&in1.x, in2, &out.x);
}
// MSVC folds the return value nicely and creates no temporaries on the stack,
// we need more experiments with different compilers and in different circumstances
inline const Vector3D VectorTransform(const Vector3D& in1, const matrix3x4_t& in2)
{
Vector3D out;
VectorTransform(in1, in2, out);
return out;
}
inline const Vector3D VectorRotate(const Vector3D& in1, const matrix3x4_t& in2)
{
Vector3D out;
VectorRotate(in1, in2, out);
return out;
}
inline void VectorITransform(const Vector3D& in1, const matrix3x4_t& in2, Vector3D& out)
{
VectorITransform(&in1.x, in2, &out.x);
}
inline const Vector3D VectorITransform(const Vector3D& in1, const matrix3x4_t& in2)
{
Vector3D out;
VectorITransform(in1, in2, out);
return out;
}
/*
inline void DecomposeRotation( const matrix3x4_t &mat, Vector &out )
{
DecomposeRotation( mat, &out.x );
}
*/
inline int BoxOnPlaneSide(const Vector3D& emins, const Vector3D& emaxs, const cplane_t* plane)
{
return BoxOnPlaneSide(&emins.x, &emaxs.x, plane);
}
inline void VectorFill(Vector3D& a, float b)
{
a[0] = a[1] = a[2] = b;
}
inline void VectorNegate(Vector3D& a)
{
a[0] = -a[0];
a[1] = -a[1];
a[2] = -a[2];
}
inline vec_t VectorAvg(Vector3D& a)
{
return (a[0] + a[1] + a[2]) / 3;
}
//-----------------------------------------------------------------------------
// Box/plane test (slow version)
//-----------------------------------------------------------------------------
inline int FASTCALL BoxOnPlaneSide2(const Vector3D& emins, const Vector3D& emaxs, const cplane_t* p, float tolerance = 0.f)
{
Vector3D corners[2];
if (p->normal[0] < 0)
{
corners[0][0] = emins[0];
corners[1][0] = emaxs[0];
}
else
{
corners[1][0] = emins[0];
corners[0][0] = emaxs[0];
}
if (p->normal[1] < 0)
{
corners[0][1] = emins[1];
corners[1][1] = emaxs[1];
}
else
{
corners[1][1] = emins[1];
corners[0][1] = emaxs[1];
}
if (p->normal[2] < 0)
{
corners[0][2] = emins[2];
corners[1][2] = emaxs[2];
}
else
{
corners[1][2] = emins[2];
corners[0][2] = emaxs[2];
}
int sides = 0;
float dist1 = DotProduct(p->normal, corners[0]) - p->dist;
if (dist1 >= tolerance)
sides = 1;
float dist2 = DotProduct(p->normal, corners[1]) - p->dist;
if (dist2 < -tolerance)
sides |= 2;
return sides;
}
//-----------------------------------------------------------------------------
// Helpers for bounding box construction
//-----------------------------------------------------------------------------
void ClearBounds(Vector3D& mins, Vector3D& maxs);
void AddPointToBounds(const Vector3D& v, Vector3D& mins, Vector3D& maxs);
//-----------------------------------------------------------------------------
// Ensures that the min and max bounds values are valid.
// (ClearBounds() sets min > max, which is clearly invalid.)
//-----------------------------------------------------------------------------
bool AreBoundsValid(const Vector3D& vMin, const Vector3D& vMax);
//-----------------------------------------------------------------------------
// Returns true if the provided point is in the AABB defined by vMin
// at the lower corner and vMax at the upper corner.
//-----------------------------------------------------------------------------
bool IsPointInBounds(const Vector3D& vPoint, const Vector3D& vMin, const Vector3D& vMax);
//
// COLORSPACE/GAMMA CONVERSION STUFF
//
void BuildGammaTable(float gamma, float texGamma, float brightness, int overbright);
// convert texture to linear 0..1 value
inline float TexLightToLinear(int c, int exponent)
{
// On VS 2013 LTCG builds it is required that the array declaration be annotated with
// the same alignment requirements as the array definition.
extern ALIGN128 float power2_n[256];
Assert(exponent >= -128 && exponent <= 127);
return (float)c * power2_n[exponent + 128];
}
// convert texture to linear 0..1 value
int LinearToTexture(float f);
// converts 0..1 linear value to screen gamma (0..255)
int LinearToScreenGamma(float f);
float TextureToLinear(int c);
// compressed color format
struct ColorRGBExp32
{
byte r, g, b;
signed char exponent;
};
void ColorRGBExp32ToVector(const ColorRGBExp32& in, Vector3D& out);
void VectorToColorRGBExp32(const Vector3D& v, ColorRGBExp32& c);
// solve for "x" where "a x^2 + b x + c = 0", return true if solution exists
bool SolveQuadratic(float a, float b, float c, float& root1, float& root2);
// 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);
// solves for a,b,c specified as above, except that it always creates a monotonically increasing or
// decreasing curve if the data is monotonically increasing or decreasing. In order to enforce the
// monoticity condition, it is possible that the resulting quadratic will only approximate the data
// instead of interpolating it. This code is not especially fast.
bool SolveInverseQuadraticMonotonic(float x1, float y1, float x2, float y2,
float x3, float y3, float& a, float& b, float& c);
// 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);
// rotate a vector around the Z axis (YAW)
void VectorYawRotate(const Vector3D& in, float flYaw, Vector3D& out);
// Bias takes an X value between 0 and 1 and returns another value between 0 and 1
// The curve is biased towards 0 or 1 based on biasAmt, which is between 0 and 1.
// Lower values of biasAmt bias the curve towards 0 and higher values bias it towards 1.
//
// For example, with biasAmt = 0.2, the curve looks like this:
//
// 1
// | *
// | *
// | *
// | **
// | **
// | ****
// |*********
// |___________________
// 0 1
//
//
// With biasAmt = 0.8, the curve looks like this:
//
// 1
// | **************
// | **
// | *
// | *
// |*
// |*
// |*
// |___________________
// 0 1
//
// With a biasAmt of 0.5, Bias returns X.
float Bias(float x, float biasAmt);
// Gain is similar to Bias, but biasAmt biases towards or away from 0.5.
// Lower bias values bias towards 0.5 and higher bias values bias away from it.
//
// For example, with biasAmt = 0.2, the curve looks like this:
//
// 1
// | *
// | *
// | **
// | ***************
// | **
// | *
// |*
// |___________________
// 0 1
//
//
// With biasAmt = 0.8, the curve looks like this:
//
// 1
// | *****
// | ***
// | *
// | *
// | *
// | ***
// |*****
// |___________________
// 0 1
float Gain(float x, float biasAmt);
// SmoothCurve maps a 0-1 value into another 0-1 value based on a cosine wave
// where the derivatives of the function at 0 and 1 (and 0.5) are 0. This is useful for
// any fadein/fadeout effect where it should start and end smoothly.
//
// The curve looks like this:
//
// 1
// | **
// | * *
// | * *
// | * *
// | * *
// | ** **
// |*** ***
// |___________________
// 0 1
//
float SmoothCurve(float x);
// This works like SmoothCurve, with two changes:
//
// 1. Instead of the curve peaking at 0.5, it will peak at flPeakPos.
// (So if you specify flPeakPos=0.2, then the peak will slide to the left).
//
// 2. flPeakSharpness is a 0-1 value controlling the sharpness of the peak.
// Low values blunt the peak and high values sharpen the peak.
float SmoothCurve_Tweak(float x, float flPeakPos = 0.5, float flPeakSharpness = 0.5);
//float ExponentialDecay( float halflife, float dt );
//float ExponentialDecay( float decayTo, float decayTime, float dt );
// halflife is time for value to reach 50%
inline float ExponentialDecay(float halflife, float dt)
{
// log(0.5) == -0.69314718055994530941723212145818
return expf(-0.69314718f / halflife * dt);
}
// decayTo is factor the value should decay to in decayTime
inline float ExponentialDecay(float decayTo, float decayTime, float dt)
{
return expf(logf(decayTo) / decayTime * dt);
}
// Get the integrated distanced traveled
// decayTo is factor the value should decay to in decayTime
// dt is the time relative to the last velocity update
inline float ExponentialDecayIntegral(float decayTo, float decayTime, float dt)
{
return (powf(decayTo, dt / decayTime) * decayTime - decayTime) / logf(decayTo);
}
// hermite basis function for smooth interpolation
// Similar to Gain() above, but very cheap to call
// value should be between 0 & 1 inclusive
inline float SimpleSpline(float value)
{
float valueSquared = value * value;
// Nice little ease-in, ease-out spline-like curve
return (3 * valueSquared - 2 * valueSquared * value);
}
// remaps a value in [startInterval, startInterval+rangeInterval] from linear to
// spline using SimpleSpline
inline float SimpleSplineRemapVal(float val, float A, float B, float C, float D)
{
if (A == B)
return val >= B ? D : C;
float cVal = (val - A) / (B - A);
return C + (D - C) * SimpleSpline(cVal);
}
// remaps a value in [startInterval, startInterval+rangeInterval] from linear to
// spline using SimpleSpline
inline float SimpleSplineRemapValClamped(float val, float A, float B, float C, float D)
{
if (A == B)
return val >= B ? D : C;
float cVal = (val - A) / (B - A);
cVal = clamp(cVal, 0.0f, 1.0f);
return C + (D - C) * SimpleSpline(cVal);
}
FORCEINLINE int RoundFloatToInt(float f)
{
#if defined( _X360 )
#ifdef Assert
Assert(IsFPUControlWordSet());
#endif
union
{
double flResult;
int pResult[2];
};
flResult = __fctiw(f);
return pResult[1];
#elif defined ( _PS3 )
#if defined(__SPU__)
int nResult;
nResult = static_cast<int>(f);
return nResult;
#else
return __fctiw(f);
#endif
#else // !X360
int nResult;
#if defined( COMPILER_MSVC32 )
__asm
{
fld f
fistp nResult
}
#elif GNUC
__asm __volatile__(
"fistpl %0;": "=m" (nResult) : "t" (f) : "st"
);
#else
nResult = static_cast<int>(f);
#endif
return nResult;
#endif
}
FORCEINLINE unsigned char RoundFloatToByte(float f)
{
#if defined( _X360 )
#ifdef Assert
Assert(IsFPUControlWordSet());
#endif
union
{
double flResult;
int pIntResult[2];
unsigned char pResult[8];
};
flResult = __fctiw(f);
#ifdef Assert
Assert(pIntResult[1] >= 0 && pIntResult[1] <= 255);
#endif
return pResult[7];
#elif defined ( _PS3 )
#if defined(__SPU__)
int nResult;
nResult = static_cast<unsigned int> (f) & 0xff;
return nResult;
#else
return __fctiw(f);
#endif
#else // !X360
int nResult;
#if defined( COMPILER_MSVC32 )
__asm
{
fld f
fistp nResult
}
#elif GNUC
__asm __volatile__(
"fistpl %0;": "=m" (nResult) : "t" (f) : "st"
);
#else
nResult = static_cast<unsigned int> (f) & 0xff;
#endif
#ifdef Assert
Assert(nResult >= 0 && nResult <= 255);
#endif
return (unsigned char)nResult;
#endif
}
FORCEINLINE unsigned long RoundFloatToUnsignedLong(float f)
{
#if defined( _X360 )
#ifdef Assert
Assert(IsFPUControlWordSet());
#endif
union
{
double flResult;
int pIntResult[2];
unsigned long pResult[2];
};
flResult = __fctiw(f);
Assert(pIntResult[1] >= 0);
return pResult[1];
#elif defined ( _PS3 )
#if defined(__SPU__)
return static_cast<unsigned long>(f);
#else
return __fctiw(f);
#endif
#else // !X360
#if defined( COMPILER_MSVC32 )
unsigned char nResult[8];
__asm
{
fld f
fistp qword ptr nResult
}
return *((unsigned long*)nResult);
#elif defined( COMPILER_GCC )
unsigned char nResult[8];
__asm __volatile__(
"fistpl %0;": "=m" (nResult) : "t" (f) : "st"
);
return *((unsigned long*)nResult);
#else
return static_cast<unsigned long>(f);
#endif
#endif
}
FORCEINLINE bool IsIntegralValue(float flValue, float flTolerance = 0.001f)
{
return fabs(RoundFloatToInt(flValue) - flValue) < flTolerance;
}
// Fast, accurate ftol:
FORCEINLINE int Float2Int(float a)
{
#if defined( _X360 )
union
{
double flResult;
int pResult[2];
};
flResult = __fctiwz(a);
return pResult[1];
#elif defined ( _PS3 )
#if defined(__SPU__)
int RetVal;
RetVal = static_cast<int>(a);
return RetVal;
#else
return __fctiwz(a);
#endif
#else // !X360
int RetVal;
#if defined( COMPILER_MSVC32 )
int CtrlwdHolder;
int CtrlwdSetter;
__asm
{
fld a // push 'a' onto the FP stack
fnstcw CtrlwdHolder // store FPU control word
movzx eax, CtrlwdHolder // move and zero extend word into eax
and eax, 0xFFFFF3FF // set all bits except rounding bits to 1
or eax, 0x00000C00 // set rounding mode bits to round towards zero
mov CtrlwdSetter, eax // Prepare to set the rounding mode -- prepare to enter plaid!
fldcw CtrlwdSetter // Entering plaid!
fistp RetVal // Store and converted (to int) result
fldcw CtrlwdHolder // Restore control word
}
#else
RetVal = static_cast<int>(a);
#endif
return RetVal;
#endif
}
// Over 15x faster than: (int)floor(value)
inline int Floor2Int(float a)
{
int RetVal;
#if defined( PLATFORM_PPC )
RetVal = (int)floor(a);
#elif defined( COMPILER_MSVC32 )
int CtrlwdHolder;
int CtrlwdSetter;
__asm
{
fld a // push 'a' onto the FP stack
fnstcw CtrlwdHolder // store FPU control word
movzx eax, CtrlwdHolder // move and zero extend word into eax
and eax, 0xFFFFF3FF // set all bits except rounding bits to 1
or eax, 0x00000400 // set rounding mode bits to round down
mov CtrlwdSetter, eax // Prepare to set the rounding mode -- prepare to enter plaid!
fldcw CtrlwdSetter // Entering plaid!
fistp RetVal // Store floored and converted (to int) result
fldcw CtrlwdHolder // Restore control word
}
#else
RetVal = static_cast<int>(floor(a));
#endif
return RetVal;
}
//-----------------------------------------------------------------------------
// Fast color conversion from float to unsigned char
//-----------------------------------------------------------------------------
FORCEINLINE unsigned char FastFToC(float c)
{
volatile float dc;
// ieee trick
dc = c * 255.0f + (float)(1 << 23);
// return the lsb
#if defined( _X360 ) || defined( _PS3 )
return ((unsigned char*)&dc)[3];
#else
return *(unsigned char*)&dc;
#endif
}
//-----------------------------------------------------------------------------
// Purpose: Bound input float to .001 (millisecond) boundary
// Input : in -
// Output : inline float
//-----------------------------------------------------------------------------
inline float ClampToMsec(float in)
{
int msec = Floor2Int(in * 1000.0f + 0.5f);
return msec / 1000.0f;
}
// Over 15x faster than: (int)ceil(value)
inline int Ceil2Int(float a)
{
int RetVal;
#if defined( PLATFORM_PPC )
RetVal = (int)ceil(a);
#elif defined( COMPILER_MSVC32 )
int CtrlwdHolder;
int CtrlwdSetter;
__asm
{
fld a // push 'a' onto the FP stack
fnstcw CtrlwdHolder // store FPU control word
movzx eax, CtrlwdHolder // move and zero extend word into eax
and eax, 0xFFFFF3FF // set all bits except rounding bits to 1
or eax, 0x00000800 // set rounding mode bits to round down
mov CtrlwdSetter, eax // Prepare to set the rounding mode -- prepare to enter plaid!
fldcw CtrlwdSetter // Entering plaid!
fistp RetVal // Store floored and converted (to int) result
fldcw CtrlwdHolder // Restore control word
}
#else
RetVal = static_cast<int>(ceil(a));
#endif
return RetVal;
}
// Regular signed area of triangle
#define TriArea2D( A, B, C ) \
( 0.5f * ( ( B.x - A.x ) * ( C.y - A.y ) - ( B.y - A.y ) * ( C.x - A.x ) ) )
// This version doesn't premultiply by 0.5f, so it's the area of the rectangle instead
#define TriArea2DTimesTwo( A, B, C ) \
( ( ( B.x - A.x ) * ( C.y - A.y ) - ( B.y - A.y ) * ( C.x - A.x ) ) )
// Get the barycentric coordinates of "pt" in triangle [A,B,C].
inline void GetBarycentricCoords2D(
Vector2D const& A,
Vector2D const& B,
Vector2D const& C,
Vector2D const& pt,
float bcCoords[3])
{
// Note, because to top and bottom are both x2, the issue washes out in the composite
float invTriArea = 1.0f / TriArea2DTimesTwo(A, B, C);
// NOTE: We assume here that the lightmap coordinate vertices go counterclockwise.
// If not, TriArea2D() is negated so this works out right.
bcCoords[0] = TriArea2DTimesTwo(B, C, pt) * invTriArea;
bcCoords[1] = TriArea2DTimesTwo(C, A, pt) * invTriArea;
bcCoords[2] = TriArea2DTimesTwo(A, B, pt) * invTriArea;
}
// Return true of the sphere might touch the box (the sphere is actually treated
// like a box itself, so this may return true if the sphere's bounding box touches
// a corner of the box but the sphere itself doesn't).
inline bool QuickBoxSphereTest(
const Vector3D& vOrigin,
float flRadius,
const Vector3D& bbMin,
const Vector3D& bbMax)
{
return vOrigin.x - flRadius < bbMax.x&& vOrigin.x + flRadius > bbMin.x &&
vOrigin.y - flRadius < bbMax.y&& vOrigin.y + flRadius > bbMin.y &&
vOrigin.z - flRadius < bbMax.z&& vOrigin.z + flRadius > bbMin.z;
}
// Return true of the boxes intersect (but not if they just touch).
inline bool QuickBoxIntersectTest(
const Vector3D& vBox1Min,
const Vector3D& vBox1Max,
const Vector3D& vBox2Min,
const Vector3D& vBox2Max)
{
return
vBox1Min.x < vBox2Max.x&& vBox1Max.x > vBox2Min.x &&
vBox1Min.y < vBox2Max.y&& vBox1Max.y > vBox2Min.y &&
vBox1Min.z < vBox2Max.z&& vBox1Max.z > vBox2Min.z;
}
extern float GammaToLinearFullRange(float gamma);
extern float LinearToGammaFullRange(float linear);
extern float GammaToLinear(float gamma);
extern float LinearToGamma(float linear);
extern float SrgbGammaToLinear(float flSrgbGammaValue);
extern float SrgbLinearToGamma(float flLinearValue);
extern float X360GammaToLinear(float fl360GammaValue);
extern float X360LinearToGamma(float flLinearValue);
extern float SrgbGammaTo360Gamma(float flSrgbGammaValue);
// linear (0..4) to screen corrected vertex space (0..1?)
FORCEINLINE float LinearToVertexLight(float f)
{
extern float lineartovertex[4096];
// Gotta clamp before the multiply; could overflow...
// assume 0..4 range
int i = RoundFloatToInt(f * 1024.f);
// Presumably the common case will be not to clamp, so check that first:
if ((unsigned)i > 4095)
{
if (i < 0)
i = 0; // Compare to zero instead of 4095 to save 4 bytes in the instruction stream
else
i = 4095;
}
return lineartovertex[i];
}
FORCEINLINE unsigned char LinearToLightmap(float f)
{
extern unsigned char lineartolightmap[4096];
// Gotta clamp before the multiply; could overflow...
int i = RoundFloatToInt(f * 1024.f); // assume 0..4 range
// Presumably the common case will be not to clamp, so check that first:
if ((unsigned)i > 4095)
{
if (i < 0)
i = 0; // Compare to zero instead of 4095 to save 4 bytes in the instruction stream
else
i = 4095;
}
return lineartolightmap[i];
}
FORCEINLINE void ColorClamp(Vector3D& color)
{
float maxc = MAX(color.x, MAX(color.y, color.z));
if (maxc > 1.0f)
{
float ooMax = 1.0f / maxc;
color.x *= ooMax;
color.y *= ooMax;
color.z *= ooMax;
}
if (color[0] < 0.f) color[0] = 0.f;
if (color[1] < 0.f) color[1] = 0.f;
if (color[2] < 0.f) color[2] = 0.f;
}
inline void ColorClampTruncate(Vector3D& color)
{
if (color[0] > 1.0f) color[0] = 1.0f; else if (color[0] < 0.0f) color[0] = 0.0f;
if (color[1] > 1.0f) color[1] = 1.0f; else if (color[1] < 0.0f) color[1] = 0.0f;
if (color[2] > 1.0f) color[2] = 1.0f; else if (color[2] < 0.0f) color[2] = 0.0f;
}
// Interpolate a Catmull-Rom spline.
// t is a [0,1] value and interpolates a curve between p2 and p3.
void Catmull_Rom_Spline(
const Vector3D& p1,
const Vector3D& p2,
const Vector3D& p3,
const Vector3D& p4,
float t,
Vector3D& output);
// Interpolate a Catmull-Rom spline.
// Returns the tangent of the point at t of the spline
void Catmull_Rom_Spline_Tangent(
const Vector3D& p1,
const Vector3D& p2,
const Vector3D& p3,
const Vector3D& p4,
float t,
Vector3D& 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);
// 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);
// Interpolate a Catmull-Rom spline.
// Normalize p2->p1 and p3->p4 to be the same length as p2->p3
void Catmull_Rom_Spline_Normalize(
const Vector3D& p1,
const Vector3D& p2,
const Vector3D& p3,
const Vector3D& p4,
float t,
Vector3D& output);
// area under the curve [0..t]
// Normalize p2->p1 and p3->p4 to be the same length as p2->p3
void Catmull_Rom_Spline_Integral_Normalize(
const Vector3D& p1,
const Vector3D& p2,
const Vector3D& p3,
const Vector3D& p4,
float t,
Vector3D& output);
// Interpolate a Catmull-Rom spline.
// Normalize p2.x->p1.x and p3.x->p4.x to be the same length as p2.x->p3.x
void Catmull_Rom_Spline_NormalizeX(
const Vector3D& p1,
const Vector3D& p2,
const Vector3D& p3,
const Vector3D& p4,
float t,
Vector3D& output);
// area under the curve [0..t]
void Catmull_Rom_Spline_NormalizeX(
const Vector3D& p1,
const Vector3D& p2,
const Vector3D& p3,
const Vector3D& p4,
float t,
Vector3D& output);
// Interpolate a Hermite spline.
// t is a [0,1] value and interpolates a curve between p1 and p2 with the deltas d1 and d2.
void Hermite_Spline(
const Vector3D& p1,
const Vector3D& p2,
const Vector3D& d1,
const Vector3D& d2,
float t,
Vector3D& output);
float Hermite_Spline(
float p1,
float p2,
float d1,
float d2,
float t);
// t is a [0,1] value and interpolates a curve between p1 and p2 with the slopes p0->p1 and p1->p2
void Hermite_Spline(
const Vector3D& p0,
const Vector3D& p1,
const Vector3D& p2,
float t,
Vector3D& output);
float Hermite_Spline(
float p0,
float p1,
float p2,
float t);
void Hermite_SplineBasis(float t, float basis[4]);
void Hermite_Spline(
const Quaternion& q0,
const Quaternion& q1,
const Quaternion& q2,
float t,
Quaternion& 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);
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);
// See link at Kochanek_Bartels_Spline for info on the basis matrix used
void Cubic_Spline(
const Vector3D& p1,
const Vector3D& p2,
const Vector3D& p3,
const Vector3D& p4,
float t,
Vector3D& output);
void Cubic_Spline_NormalizeX(
const Vector3D& p1,
const Vector3D& p2,
const Vector3D& p3,
const Vector3D& p4,
float t,
Vector3D& output);
// See link at Kochanek_Bartels_Spline for info on the basis matrix used
void BSpline(
const Vector3D& p1,
const Vector3D& p2,
const Vector3D& p3,
const Vector3D& p4,
float t,
Vector3D& output);
void BSpline_NormalizeX(
const Vector3D& p1,
const Vector3D& p2,
const Vector3D& p3,
const Vector3D& p4,
float t,
Vector3D& output);
// See link at Kochanek_Bartels_Spline for info on the basis matrix used
void Parabolic_Spline(
const Vector3D& p1,
const Vector3D& p2,
const Vector3D& p3,
const Vector3D& p4,
float t,
Vector3D& output);
void Parabolic_Spline_NormalizeX(
const Vector3D& p1,
const Vector3D& p2,
const Vector3D& p3,
const Vector3D& p4,
float t,
Vector3D& output);
// Evaluate the cubic Bernstein basis for the input parametric coordinate.
// Output is the coefficient for that basis polynomial.
float CubicBasis0(float t);
float CubicBasis1(float t);
float CubicBasis2(float t);
float CubicBasis3(float t);
// quintic interpolating polynomial from Perlin.
// 0->0, 1->1, smooth-in between with smooth tangents
inline float QuinticInterpolatingPolynomial(float t)
{
// 6t^5-15t^4+10t^3
return t * t * t * (t * (t * 6.0f - 15.0f) + 10.0f);
}
// given a table of sorted tabulated positions, return the two indices and blendfactor to linear
// interpolate. Does a search. Can be used to find the blend value to interpolate between
// keyframes.
void GetInterpolationData(float const* pKnotPositions,
float const* pKnotValues,
int nNumValuesinList,
int nInterpolationRange,
float flPositionToInterpolateAt,
bool bWrap,
float* pValueA,
float* pValueB,
float* pInterpolationValue);
float RangeCompressor(float flValue, float flMin, float flMax, float flBase);
// Get the minimum distance from vOrigin to the bounding box defined by [mins,maxs]
// using voronoi regions.
// 0 is returned if the origin is inside the box.
float CalcSqrDistanceToAABB(const Vector3D& mins, const Vector3D& maxs, const Vector3D& point);
void CalcClosestPointOnAABB(const Vector3D& mins, const Vector3D& maxs, const Vector3D& point, Vector3D& closestOut);
void CalcSqrDistAndClosestPointOnAABB(const Vector3D& mins, const Vector3D& maxs, const Vector3D& point, Vector3D& closestOut, float& distSqrOut);
inline float CalcDistanceToAABB(const Vector3D& mins, const Vector3D& maxs, const Vector3D& point)
{
float flDistSqr = CalcSqrDistanceToAABB(mins, maxs, point);
return sqrt(flDistSqr);
}
// Get the closest point from P to the (infinite) line through vLineA and vLineB and
// calculate the shortest distance from P to the line.
// If you pass in a value for t, it will tell you the t for (A + (B-A)t) to get the closest point.
// If the closest point lies on the segment between A and B, then 0 <= t <= 1.
void CalcClosestPointOnLine(const Vector3D& P, const Vector3D& vLineA, const Vector3D& vLineB, Vector3D& vClosest, float* t = 0);
float CalcDistanceToLine(const Vector3D& P, const Vector3D& vLineA, const Vector3D& vLineB, float* t = 0);
float CalcDistanceSqrToLine(const Vector3D& P, const Vector3D& vLineA, const Vector3D& vLineB, float* t = 0);
// The same three functions as above, except now the line is closed between A and B.
void CalcClosestPointOnLineSegment(const Vector3D& P, const Vector3D& vLineA, const Vector3D& vLineB, Vector3D& vClosest, float* t = 0);
float CalcDistanceToLineSegment(const Vector3D& P, const Vector3D& vLineA, const Vector3D& vLineB, float* t = 0);
float CalcDistanceSqrToLineSegment(const Vector3D& P, const Vector3D& vLineA, const Vector3D& vLineB, float* t = 0);
// A function to compute the closes line segment connection two lines (or false if the lines are parallel, etc.)
bool CalcLineToLineIntersectionSegment(
const Vector3D& p1, const Vector3D& p2, const Vector3D& p3, const Vector3D& p4, Vector3D* s1, Vector3D* s2,
float* t1, float* t2);
// The above functions in 2D
void CalcClosestPointOnLine2D(Vector2D const& P, Vector2D const& vLineA, Vector2D const& vLineB, Vector2D& vClosest, float* t = 0);
float CalcDistanceToLine2D(Vector2D const& P, Vector2D const& vLineA, Vector2D const& vLineB, float* t = 0);
float CalcDistanceSqrToLine2D(Vector2D const& P, Vector2D const& vLineA, Vector2D const& vLineB, float* t = 0);
void CalcClosestPointOnLineSegment2D(Vector2D const& P, Vector2D const& vLineA, Vector2D const& vLineB, Vector2D& vClosest, float* t = 0);
float CalcDistanceToLineSegment2D(Vector2D const& P, Vector2D const& vLineA, Vector2D const& vLineB, float* t = 0);
float CalcDistanceSqrToLineSegment2D(Vector2D const& P, Vector2D const& vLineA, Vector2D const& vLineB, float* t = 0);
// Init the mathlib
void MathLib_Init(float gamma = 2.2f, float texGamma = 2.2f, float brightness = 0.0f, int overbright = 2.0f);
bool MathLib_MMXEnabled(void);
bool MathLib_SSEEnabled(void);
bool MathLib_SSE2Enabled(void);
inline float Approach(float target, float value, float speed);
float ApproachAngle(float target, float value, float speed);
float AngleDiff(float destAngle, float srcAngle);
float AngleDistance(float next, float cur);
float AngleNormalize(float angle);
// ensure that 0 <= angle <= 360
float AngleNormalizePositive(float angle);
bool AnglesAreEqual(float a, float b, float tolerance = 0.0f);
void RotationDeltaAxisAngle(const QAngle& srcAngles, const QAngle& destAngles, Vector3D& deltaAxis, float& deltaAngle);
void RotationDelta(const QAngle& srcAngles, const QAngle& destAngles, QAngle* out);
//-----------------------------------------------------------------------------
// Clips a line segment such that only the portion in the positive half-space
// of the plane remains. If the segment is entirely clipped, the vectors
// are set to vec3_invalid (all components are FLT_MAX).
//
// flBias is added to the dot product with the normal. A positive bias
// results in a more inclusive positive half-space, while a negative bias
// results in a more exclusive positive half-space.
//-----------------------------------------------------------------------------
void ClipLineSegmentToPlane(const Vector3D& vNormal, const Vector3D& vPlanePoint, Vector3D* p1, Vector3D* p2, float flBias = 0.0f);
void ComputeTrianglePlane(const Vector3D& v1, const Vector3D& v2, const Vector3D& v3, Vector3D& normal, float& intercept);
int PolyFromPlane(Vector3D* pOutVerts, const Vector3D& normal, float dist, float fHalfScale = 9000.0f);
void PolyFromPlane_SIMD(fltx4* pOutVerts, const fltx4& plane, float fHalfScale = 9000.0f);
int ClipPolyToPlane(Vector3D* inVerts, int vertCount, Vector3D* outVerts, const Vector3D& normal, float dist, float fOnPlaneEpsilon = 0.1f);
int ClipPolyToPlane_SIMD(fltx4* pInVerts, int vertCount, fltx4* pOutVerts, const fltx4& plane, float fOnPlaneEpsilon = 0.1f);
int ClipPolyToPlane_Precise(double* inVerts, int vertCount, double* outVerts, const double* normal, double dist, double fOnPlaneEpsilon = 0.1);
float TetrahedronVolume(const Vector3D& p0, const Vector3D& p1, const Vector3D& p2, const Vector3D& p3);
float TriangleArea(const Vector3D& p0, const Vector3D& p1, const Vector3D& p2);
/// return surface area of an AABB
FORCEINLINE float BoxSurfaceArea(Vector3D const& vecBoxMin, Vector3D const& vecBoxMax)
{
Vector3D boxdim = vecBoxMax - vecBoxMin;
return 2.0f * ((boxdim[0] * boxdim[2]) + (boxdim[0] * boxdim[1]) + (boxdim[1] * boxdim[2]));
}
//-----------------------------------------------------------------------------
// Computes a reasonable tangent space for a triangle
//-----------------------------------------------------------------------------
void CalcTriangleTangentSpace(const Vector3D& p0, const Vector3D& p1, const Vector3D& p2,
const Vector2D& t0, const Vector2D& t1, const Vector2D& t2,
Vector3D& sVect, Vector3D& tVect);
//-----------------------------------------------------------------------------
// Transforms a AABB into another space; which will inherently grow the box.
//-----------------------------------------------------------------------------
void TransformAABB(const matrix3x4_t& in1, const Vector3D& vecMinsIn, const Vector3D& vecMaxsIn, Vector3D& vecMinsOut, Vector3D& vecMaxsOut);
//-----------------------------------------------------------------------------
// Uses the inverse transform of in1
//-----------------------------------------------------------------------------
void ITransformAABB(const matrix3x4_t& in1, const Vector3D& vecMinsIn, const Vector3D& vecMaxsIn, Vector3D& vecMinsOut, Vector3D& 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& in1, const Vector3D& vecMinsIn, const Vector3D& vecMaxsIn, Vector3D& vecMinsOut, Vector3D& vecMaxsOut);
//-----------------------------------------------------------------------------
// Uses the inverse transform of in1
//-----------------------------------------------------------------------------
void IRotateAABB(const matrix3x4_t& in1, const Vector3D& vecMinsIn, const Vector3D& vecMaxsIn, Vector3D& vecMinsOut, Vector3D& vecMaxsOut);
//-----------------------------------------------------------------------------
// Transform a plane
//-----------------------------------------------------------------------------
inline void MatrixTransformPlane(const matrix3x4_t& src, const cplane_t& inPlane, cplane_t& outPlane)
{
// What we want to do is the following:
// 1) transform the normal into the new space.
// 2) Determine a point on the old plane given by plane dist * plane normal
// 3) Transform that point into the new space
// 4) Plane dist = DotProduct( new normal, new point )
// An optimized version, which works if the plane is orthogonal.
// 1) Transform the normal into the new space
// 2) Realize that transforming the old plane point into the new space
// is given by [ d * n'x + Tx, d * n'y + Ty, d * n'z + Tz ]
// where d = old plane dist, n' = transformed normal, Tn = translational component of transform
// 3) Compute the new plane dist using the dot product of the normal result of #2
// For a correct result, this should be an inverse-transpose matrix
// but that only matters if there are nonuniform scale or skew factors in this matrix.
VectorRotate(inPlane.normal, src, outPlane.normal);
outPlane.dist = inPlane.dist * DotProduct(outPlane.normal, outPlane.normal);
outPlane.dist += outPlane.normal.x * src[0][3] + outPlane.normal.y * src[1][3] + outPlane.normal.z * src[2][3];
}
inline void MatrixITransformPlane(const matrix3x4_t& src, const cplane_t& inPlane, cplane_t& outPlane)
{
// The trick here is that Tn = translational component of transform,
// but for an inverse transform, Tn = - R^-1 * T
Vector3D vecTranslation;
MatrixGetColumn(src, 3, vecTranslation);
Vector3D vecInvTranslation;
VectorIRotate(vecTranslation, src, vecInvTranslation);
VectorIRotate(inPlane.normal, src, outPlane.normal);
outPlane.dist = inPlane.dist * DotProduct(outPlane.normal, outPlane.normal);
outPlane.dist -= outPlane.normal.x * vecInvTranslation[0] + outPlane.normal.y * vecInvTranslation[1] + outPlane.normal.z * vecInvTranslation[2];
}
int CeilPow2(int in);
int FloorPow2(int in);
FORCEINLINE float* UnpackNormal_HEND3N(const unsigned int* pPackedNormal, float* pNormal)
{
int temp[3];
temp[0] = ((*pPackedNormal >> 0L) & 0x7ff);
if (temp[0] & 0x400)
{
temp[0] = 2048 - temp[0];
}
temp[1] = ((*pPackedNormal >> 11L) & 0x7ff);
if (temp[1] & 0x400)
{
temp[1] = 2048 - temp[1];
}
temp[2] = ((*pPackedNormal >> 22L) & 0x3ff);
if (temp[2] & 0x200)
{
temp[2] = 1024 - temp[2];
}
pNormal[0] = (float)temp[0] * 1.0f / 1023.0f;
pNormal[1] = (float)temp[1] * 1.0f / 1023.0f;
pNormal[2] = (float)temp[2] * 1.0f / 511.0f;
return pNormal;
}
FORCEINLINE unsigned int* PackNormal_HEND3N(const float* pNormal, unsigned int* pPackedNormal)
{
int temp[3];
temp[0] = Float2Int(pNormal[0] * 1023.0f);
temp[1] = Float2Int(pNormal[1] * 1023.0f);
temp[2] = Float2Int(pNormal[2] * 511.0f);
// the normal is out of bounds, determine the source and fix
// clamping would be even more of a slowdown here
Assert(temp[0] >= -1023 && temp[0] <= 1023);
Assert(temp[1] >= -1023 && temp[1] <= 1023);
Assert(temp[2] >= -511 && temp[2] <= 511);
*pPackedNormal = ((temp[2] & 0x3ff) << 22L) |
((temp[1] & 0x7ff) << 11L) |
((temp[0] & 0x7ff) << 0L);
return pPackedNormal;
}
FORCEINLINE unsigned int* PackNormal_HEND3N(float nx, float ny, float nz, unsigned int* pPackedNormal)
{
int temp[3];
temp[0] = Float2Int(nx * 1023.0f);
temp[1] = Float2Int(ny * 1023.0f);
temp[2] = Float2Int(nz * 511.0f);
// the normal is out of bounds, determine the source and fix
// clamping would be even more of a slowdown here
Assert(temp[0] >= -1023 && temp[0] <= 1023);
Assert(temp[1] >= -1023 && temp[1] <= 1023);
Assert(temp[2] >= -511 && temp[2] <= 511);
*pPackedNormal = ((temp[2] & 0x3ff) << 22L) |
((temp[1] & 0x7ff) << 11L) |
((temp[0] & 0x7ff) << 0L);
return pPackedNormal;
}
FORCEINLINE float* UnpackNormal_SHORT2(const unsigned int* pPackedNormal, float* pNormal, bool bIsTangent = FALSE)
{
// Unpacks from Jason's 2-short format (fills in a 4th binormal-sign (+1/-1) value, if this is a tangent vector)
// FIXME: short math is slow on 360 - use ints here instead (bit-twiddle to deal w/ the sign bits)
short iX = (*pPackedNormal & 0x0000FFFF);
short iY = (*pPackedNormal & 0xFFFF0000) >> 16;
float zSign = +1;
if (iX < 0)
{
zSign = -1;
iX = -iX;
}
float tSign = +1;
if (iY < 0)
{
tSign = -1;
iY = -iY;
}
pNormal[0] = (iX - 16384.0f) / 16384.0f;
pNormal[1] = (iY - 16384.0f) / 16384.0f;
float mag = (pNormal[0] * pNormal[0] + pNormal[1] * pNormal[1]);
if (mag > 1.0f)
{
mag = 1.0f;
}
pNormal[2] = zSign * sqrtf(1.0f - mag);
if (bIsTangent)
{
pNormal[3] = tSign;
}
return pNormal;
}
FORCEINLINE unsigned int* PackNormal_SHORT2(float nx, float ny, float nz, unsigned int* pPackedNormal, float binormalSign = +1.0f)
{
// Pack a vector (ASSUMED TO BE NORMALIZED) into Jason's 4-byte (SHORT2) format.
// This simply reconstructs Z from X & Y. It uses the sign bits of the X & Y coords
// to reconstruct the sign of Z and, if this is a tangent vector, the sign of the
// binormal (this is needed because tangent/binormal vectors are supposed to follow
// UV gradients, but shaders reconstruct the binormal from the tangent and normal
// assuming that they form a right-handed basis).
nx += 1; // [-1,+1] -> [0,2]
ny += 1;
nx *= 16384.0f; // [ 0, 2] -> [0,32768]
ny *= 16384.0f;
// '0' and '32768' values are invalid encodings
nx = MAX(nx, 1.0f); // Make sure there are no zero values
ny = MAX(ny, 1.0f);
nx = MIN(nx, 32767.0f); // Make sure there are no 32768 values
ny = MIN(ny, 32767.0f);
if (nz < 0.0f)
nx = -nx; // Set the sign bit for z
ny *= binormalSign; // Set the sign bit for the binormal (use when encoding a tangent vector)
// FIXME: short math is slow on 360 - use ints here instead (bit-twiddle to deal w/ the sign bits), also use Float2Int()
short sX = (short)nx; // signed short [1,32767]
short sY = (short)ny;
*pPackedNormal = (sX & 0x0000FFFF) | (sY << 16); // NOTE: The mask is necessary (if sX is negative and cast to an int...)
return pPackedNormal;
}
FORCEINLINE unsigned int* PackNormal_SHORT2(const float* pNormal, unsigned int* pPackedNormal, float binormalSign = +1.0f)
{
return PackNormal_SHORT2(pNormal[0], pNormal[1], pNormal[2], pPackedNormal, binormalSign);
}
// Unpacks a UBYTE4 normal (for a tangent, the result's fourth component receives the binormal 'sign')
FORCEINLINE float* UnpackNormal_UBYTE4(const unsigned int* pPackedNormal, float* pNormal, bool bIsTangent = FALSE)
{
unsigned char cX, cY;
if (bIsTangent)
{
cX = (*pPackedNormal >> 16) & UINT8_MAX; // Unpack Z
cY = (*pPackedNormal >> 24) & UINT8_MAX; // Unpack W
}
else
{
cX = (*pPackedNormal >> 0) & UINT8_MAX; // Unpack X
cY = (*pPackedNormal >> 8) & UINT8_MAX; // Unpack Y
}
float x = cX - 128.0f;
float y = cY - 128.0f;
float z;
float zSignBit = x < 0 ? 1.0f : 0.0f; // z and t negative bits (like slt asm instruction)
float tSignBit = y < 0 ? 1.0f : 0.0f;
float zSign = -(2 * zSignBit - 1); // z and t signs
float tSign = -(2 * tSignBit - 1);
x = x * zSign - zSignBit; // 0..127
y = y * tSign - tSignBit;
x = x - 64; // -64..63
y = y - 64;
float xSignBit = x < 0 ? 1.0f : 0.0f; // x and y negative bits (like slt asm instruction)
float ySignBit = y < 0 ? 1.0f : 0.0f;
float xSign = -(2 * xSignBit - 1); // x and y signs
float ySign = -(2 * ySignBit - 1);
x = (x * xSign - xSignBit) / 63.0f; // 0..1 range
y = (y * ySign - ySignBit) / 63.0f;
z = 1.0f - x - y;
float oolen = 1.0f / sqrt(x * x + y * y + z * z); // Normalize and
x *= oolen * xSign; // Recover signs
y *= oolen * ySign;
z *= oolen * zSign;
pNormal[0] = x;
pNormal[1] = y;
pNormal[2] = z;
if (bIsTangent)
{
pNormal[3] = tSign;
}
return pNormal;
}
//////////////////////////////////////////////////////////////////////////////
// See: http://www.oroboro.com/rafael/docserv.php/index/programming/article/unitv2
//
// UBYTE4 encoding, using per-octant projection onto x+y+z=1
// Assume input vector is already unit length
//
// binormalSign specifies 'sign' of binormal, stored in t sign bit of tangent
// (lets the shader know whether norm/tan/bin form a right-handed basis)
//
// bIsTangent is used to specify which WORD of the output to store the data
// The expected usage is to call once with the normal and once with
// the tangent and binormal sign flag, bitwise OR'ing the returned DWORDs
FORCEINLINE unsigned int* PackNormal_UBYTE4(float nx, float ny, float nz, unsigned int* pPackedNormal, bool bIsTangent = false, float binormalSign = +1.0f)
{
float xSign = nx < 0.0f ? -1.0f : 1.0f; // -1 or 1 sign
float ySign = ny < 0.0f ? -1.0f : 1.0f;
float zSign = nz < 0.0f ? -1.0f : 1.0f;
float tSign = binormalSign;
Assert((binormalSign == +1.0f) || (binormalSign == -1.0f));
float xSignBit = 0.5f * (1 - xSign); // [-1,+1] -> [1,0]
float ySignBit = 0.5f * (1 - ySign); // 1 is negative bit (like slt instruction)
float zSignBit = 0.5f * (1 - zSign);
float tSignBit = 0.5f * (1 - binormalSign);
float absX = xSign * nx; // 0..1 range (abs)
float absY = ySign * ny;
float absZ = zSign * nz;
float xbits = absX / (absX + absY + absZ); // Project onto x+y+z=1 plane
float ybits = absY / (absX + absY + absZ);
xbits *= 63; // 0..63
ybits *= 63;
xbits = xbits * xSign - xSignBit; // -64..63 range
ybits = ybits * ySign - ySignBit;
xbits += 64.0f; // 0..127 range
ybits += 64.0f;
xbits = xbits * zSign - zSignBit; // Negate based on z and t
ybits = ybits * tSign - tSignBit; // -128..127 range
xbits += 128.0f; // 0..255 range
ybits += 128.0f;
unsigned char cX = (unsigned char)xbits;
unsigned char cY = (unsigned char)ybits;
if (!bIsTangent)
*pPackedNormal = (cX << 0) | (cY << 8); // xy for normal
else
*pPackedNormal = (cX << 16) | (cY << 24); // zw for tangent
return pPackedNormal;
}
FORCEINLINE unsigned int* PackNormal_UBYTE4(const float* pNormal, unsigned int* pPackedNormal, bool bIsTangent = false, float binormalSign = +1.0f)
{
return PackNormal_UBYTE4(pNormal[0], pNormal[1], pNormal[2], pPackedNormal, bIsTangent, binormalSign);
}
FORCEINLINE void RGB2YUV(int& nR, int& nG, int& nB, float& fY, float& fU, float& fV, bool bApplySaturationCurve)
{
// YUV conversion:
// |Y| | 0.299f 0.587f 0.114f | |R|
// |U| = | -0.14713f -0.28886f 0.436f | x |G|
// |V| | 0.615f -0.51499f -0.10001f | |B|
//
// The coefficients in the first row sum to one, whereas the 2nd and 3rd rows each sum to zero (UV (0,0) means greyscale).
// Ranges are Y [0,1], U [-0.436,+0.436] and V [-0.615,+0.615].
// We scale and offset to [0,1] and allow the caller to round as they please.
fY = (0.29900f * nR + 0.58700f * nG + 0.11400f * nB) / 255;
fU = (-0.14713f * nR + -0.28886f * nG + 0.43600f * nB) * (0.5f / 0.436f) / 255 + 0.5f;
fV = (0.61500f * nR + -0.51499f * nG + -0.10001f * nB) * (0.5f / 0.615f) / 255 + 0.5f;
if (bApplySaturationCurve)
{
// Apply a curve to saturation, and snap-to-grey for low saturations
const float SNAP_TO_GREY = 0;//0.0125f; Disabled, saturation curve seems sufficient
float dX, dY, sat, scale;
dX = 2 * (fU - 0.5f);
dY = 2 * (fV - 0.5f);
sat = sqrtf(dX * dX + dY * dY);
sat = clamp((sat * (1 + SNAP_TO_GREY) - SNAP_TO_GREY), 0.f, 1.f);
scale = (sat == 0) ? 0 : MIN((sqrtf(sat) / sat), 4.0f);
fU = 0.5f + scale * (fU - 0.5f);
fV = 0.5f + scale * (fV - 0.5f);
}
}
#ifdef _X360
// Used for direct CPU access to VB data on 360 (used by shaderapi, studiorender and engine)
struct VBCPU_AccessInfo_t
{
// Points to the GPU data pointer in the CVertexBuffer struct (VB data can be relocated during level transitions)
const byte** ppBaseAddress;
// pBaseAddress should be computed from ppBaseAddress immediately before use
const byte* pBaseAddress;
int nStride;
int nPositionOffset;
int nTexCoord0_Offset;
int nNormalOffset;
int nBoneIndexOffset;
int nBoneWeightOffset;
int nCompressionType;
// TODO: if needed, add colour and tangents
};
#endif
//-----------------------------------------------------------------------------
// Convert RGB to HSV
//-----------------------------------------------------------------------------
void RGBtoHSV(const Vector3D& rgb, Vector3D& hsv);
//-----------------------------------------------------------------------------
// Convert HSV to RGB
//-----------------------------------------------------------------------------
void HSVtoRGB(const Vector3D& hsv, Vector3D& rgb);
//-----------------------------------------------------------------------------
// Fast version of pow and log
//-----------------------------------------------------------------------------
#ifndef _PS3 // these actually aren't fast (or correct) on the PS3
float FastLog2(float i); // log2( i )
float FastPow2(float i); // 2^i
float FastPow(float a, float b); // a^b
float FastPow10(float i); // 10^i
#else
inline float FastLog2(float i) { return logbf(i); } // log2( i )
inline float FastPow2(float i) { return exp2f(i); } // 2^i
inline float FastPow(float a, float b) { return powf(a, b); } // a^b
#define LOGBASE2OF10 3.3219280948873623478703194294893901758648313930
inline float FastPow10(float i) { return exp2f(i * LOGBASE2OF10); } // 10^i, transform to base two, so log2(10^y) = y log2(10) . log2(10) = 3.3219280948873623478703194294893901758648313930
#endif
//-----------------------------------------------------------------------------
// For testing float equality
//-----------------------------------------------------------------------------
inline bool CloseEnough(float a, float b, float epsilon = EQUAL_EPSILON)
{
return fabs(a - b) <= epsilon;
}
inline bool CloseEnough(const Vector3D& a, const Vector3D& b, float epsilon = EQUAL_EPSILON)
{
return fabs(a.x - b.x) <= epsilon &&
fabs(a.y - b.y) <= epsilon &&
fabs(a.z - b.z) <= epsilon;
}
// Fast compare
// maxUlps is the maximum error in terms of Units in the Last Place. This
// specifies how big an error we are willing to accept in terms of the value
// of the least significant digit of the floating point number�s
// representation. maxUlps can also be interpreted in terms of how many
// representable floats we are willing to accept between A and B.
// This function will allow maxUlps-1 floats between A and B.
bool AlmostEqual(float a, float b, int maxUlps = 10);
inline bool AlmostEqual(const Vector3D& a, const Vector3D& b, int maxUlps = 10)
{
return AlmostEqual(a.x, b.x, maxUlps) &&
AlmostEqual(a.y, b.y, maxUlps) &&
AlmostEqual(a.z, b.z, maxUlps);
}
inline Vector3D Approach(Vector3D target, Vector3D value, float speed)
{
Vector3D diff = (target - value);
float delta = diff.Length();
if (delta > speed)
value += diff.Normalized() * speed;
else if (delta < -speed)
value -= diff.Normalized() * speed;
else
value = target;
return value;
}
inline float Approach(float target, float value, float speed)
{
float delta = target - value;
#if defined(_X360) || defined( _PS3 ) // use conditional move for speed on 360
return fsel(delta - speed, // delta >= speed ?
value + speed, // if delta == speed, then value + speed == value + delta == target
fsel((-speed) - delta, // delta <= -speed
value - speed,
target)
); // delta < speed && delta > -speed
#else
if (delta > speed)
value += speed;
else if (delta < -speed)
value -= speed;
else
value = target;
return value;
#endif
}
// return a 0..1 value based on the position of x between edge0 and edge1
inline float smoothstep_bounds(float edge0, float edge1, float x)
{
x = static_cast<float>(clamp(static_cast<int>((x - edge0) / (edge1 - edge0)), 0, 1));
return x * x * (3 - 2 * x);
}
// return a value between edge0 and edge1 based on the 0..1 value of x
inline float interpstep(float edge0, float edge1, float x)
{
return edge0 + (x * (edge1 - edge0));
}
// on PPC we can do this truncate without converting to int
#if defined(_X360) || defined(_PS3)
inline double TruncateFloatToIntAsFloat(double flVal)
{
#if defined(_X360)
double flIntFormat = __fctiwz(flVal);
return __fcfid(flIntFormat);
#elif defined(_PS3)
#if defined(__SPU__)
int iVal = int(flVal);
return static_cast<double>(iVal);
#else
double flIntFormat = __builtin_fctiwz(flVal);
return __builtin_fcfid(flIntFormat);
#endif
#endif
}
#endif
inline double SubtractIntegerPart(double flVal)
{
#if defined(_X360) || defined(_PS3)
return flVal - TruncateFloatToIntAsFloat(flVal);
#else
return flVal - int(flVal);
#endif
}
inline void matrix3x4_t::InitFromQAngles(const QAngle& angles, const Vector3D& vPosition)
{
AngleMatrix(angles, vPosition, *this);
}
inline void matrix3x4_t::InitFromQAngles(const QAngle& angles) { InitFromQAngles(angles, vec3_origin); }
inline void matrix3x4_t::InitFromRadianEuler(const RadianEuler& angles, const Vector3D& vPosition)
{
AngleMatrix(angles, vPosition, *this);
}
inline void matrix3x4_t::InitFromRadianEuler(const RadianEuler& angles) { InitFromRadianEuler(angles, vec3_origin); }
inline void matrix3x4_t::InitFromQuaternion(const Quaternion& orientation, const Vector3D& vPosition)
{
QuaternionMatrix(orientation, vPosition, *this);
}
inline void matrix3x4_t::InitFromDiagonal(const Vector3D& vDiagonal)
{
SetToIdentity();
m_flMatVal[0][0] = vDiagonal.x;
m_flMatVal[1][1] = vDiagonal.y;
m_flMatVal[2][2] = vDiagonal.z;
}
inline void matrix3x4_t::InitFromQuaternion(const Quaternion& orientation) { InitFromQuaternion(orientation, vec3_origin); }
inline Quaternion matrix3x4_t::ToQuaternion() const
{
return MatrixQuaternion(*this);
}
inline QAngle matrix3x4_t::ToQAngle() const
{
QAngle tmp;
MatrixAngles(*this, tmp);
return tmp;
}
inline void matrix3x4_t::SetToIdentity()
{
SetIdentityMatrix(*this);
}
inline bool matrix3x4_t::IsEqualTo(const matrix3x4_t& other, float flTolerance) const
{
return MatricesAreEqual(*this, other, flTolerance);
}
inline void matrix3x4_t::GetBasisVectorsFLU(Vector3D* pForward, Vector3D* pLeft, Vector3D* pUp) const
{
return MatrixVectorsFLU(*this, pForward, pLeft, pUp);
}
inline Vector3D matrix3x4_t::TransformVector(const Vector3D& v0) const
{
return VectorTransform(v0, *this);
}
inline Vector3D matrix3x4_t::RotateVector(const Vector3D& v0) const
{
return VectorRotate(v0, *this);
}
inline Vector3D matrix3x4_t::TransformVectorByInverse(const Vector3D& v0) const
{
return VectorITransform(v0, *this);
}
inline Vector3D matrix3x4_t::RotateVectorByInverse(const Vector3D& v0) const
{
Vector3D tmp;
VectorIRotate(v0, *this, tmp);
return tmp;
}
inline Vector3D matrix3x4_t::RotateExtents(const Vector3D& vBoxExtents) const
{
return Vector3D(DotProductAbs(vBoxExtents, m_flMatVal[0]), DotProductAbs(vBoxExtents, m_flMatVal[1]), DotProductAbs(vBoxExtents, m_flMatVal[2]));
}
inline Vector3D matrix3x4_t::GetColumn(MatrixAxisType_t nColumn) const
{
return Vector3D(m_flMatVal[0][nColumn], m_flMatVal[1][nColumn], m_flMatVal[2][nColumn]);
}
inline void matrix3x4_t::SetColumn(const Vector3D& vColumn, MatrixAxisType_t nColumn)
{
m_flMatVal[0][nColumn] = vColumn.x;
m_flMatVal[1][nColumn] = vColumn.y;
m_flMatVal[2][nColumn] = vColumn.z;
}
inline void matrix3x4_t::InverseTR(matrix3x4_t& out) const
{
::MatrixInvert(*this, out);
}
inline matrix3x4_t matrix3x4_t::InverseTR() const
{
matrix3x4_t out;
::MatrixInvert(*this, out);
return out;
}
inline void matrix3x4_t::TransformAABB(const Vector3D& vecMinsIn, const Vector3D& vecMaxsIn, Vector3D& vecMinsOut, Vector3D& vecMaxsOut) const
{
::TransformAABB(*this, vecMinsIn, vecMaxsIn, vecMinsOut, vecMaxsOut);
}
inline void matrix3x4_t::TransformAABBByInverse(const Vector3D& vecMinsIn, const Vector3D& vecMaxsIn, Vector3D& vecMinsOut, Vector3D& vecMaxsOut) const
{
::ITransformAABB(*this, vecMinsIn, vecMaxsIn, vecMinsOut, vecMaxsOut);
}
inline void matrix3x4_t::RotateAABB(const Vector3D& vecMinsIn, const Vector3D& vecMaxsIn, Vector3D& vecMinsOut, Vector3D& vecMaxsOut) const
{
::RotateAABB(*this, vecMinsIn, vecMaxsIn, vecMinsOut, vecMaxsOut);
}
inline void matrix3x4_t::RotateAABBByInverse(const Vector3D& vecMinsIn, const Vector3D& vecMaxsIn, Vector3D& vecMinsOut, Vector3D& vecMaxsOut) const
{
::IRotateAABB(*this, vecMinsIn, vecMaxsIn, vecMinsOut, vecMaxsOut);
}
inline void matrix3x4_t::TransformPlane(const cplane_t& inPlane, cplane_t& outPlane) const
{
::MatrixTransformPlane(*this, inPlane, outPlane);
}
inline void matrix3x4_t::TransformPlaneByInverse(const cplane_t& inPlane, cplane_t& outPlane) const
{
::MatrixITransformPlane(*this, inPlane, outPlane);
}
inline float matrix3x4_t::GetOrthogonalityError() const
{
return
fabsf(m_flMatVal[0][0] * m_flMatVal[0][1] + m_flMatVal[1][0] * m_flMatVal[1][1] + m_flMatVal[2][0] * m_flMatVal[2][1]) +
fabsf(m_flMatVal[0][1] * m_flMatVal[0][2] + m_flMatVal[1][1] * m_flMatVal[1][2] + m_flMatVal[2][1] * m_flMatVal[2][2]) +
fabsf(m_flMatVal[0][2] * m_flMatVal[0][0] + m_flMatVal[1][2] * m_flMatVal[1][0] + m_flMatVal[2][2] * m_flMatVal[2][0]);
}
inline matrix3x4_t Quaternion::ToMatrix() const
{
matrix3x4_t mat;
mat.InitFromQuaternion(*this);
return mat;
}
inline matrix3x4_t QAngle::ToMatrix() const
{
matrix3x4_t mat;
AngleMatrix(*this, mat);
return mat;
}
inline Quaternion QAngle::ToQuaternion() const
{
return AngleQuaternion(*this);
}
inline float matrix3x4_t::GetDeterminant() const
{
return
m_flMatVal[0][0] * (m_flMatVal[1][1] * m_flMatVal[2][2] - m_flMatVal[2][1] * m_flMatVal[1][2])
- m_flMatVal[0][1] * (m_flMatVal[1][0] * m_flMatVal[2][2] - m_flMatVal[1][2] * m_flMatVal[2][0])
+ m_flMatVal[0][2] * (m_flMatVal[1][0] * m_flMatVal[2][1] - m_flMatVal[1][1] * m_flMatVal[2][0]);
}
inline float GetRelativeDifferenceSqr(const Vector3D& a, const Vector3D& b)
{
return (a - b).LengthSqr() / Max(1.0f, Max(a.LengthSqr(), b.LengthSqr()));
}
inline float GetRelativeDifference(const Vector3D& a, const Vector3D& b)
{
return sqrtf(GetRelativeDifferenceSqr(a, b));
}
// a good measure of relative error between two TR matrices, perhaps with a reasonable scale
inline float GetRelativeDifference(const matrix3x4_t& a, const matrix3x4_t& b)
{
return sqrtf(Max(Max(GetRelativeDifferenceSqr(a.GetColumn(X_AXIS), b.GetColumn(X_AXIS)),
GetRelativeDifferenceSqr(a.GetColumn(Y_AXIS), b.GetColumn(Y_AXIS))),
Max(GetRelativeDifferenceSqr(a.GetColumn(Z_AXIS), b.GetColumn(Z_AXIS)),
GetRelativeDifferenceSqr(a.GetOrigin(), b.GetOrigin()))
)
);
}
inline float matrix3x4_t::GetSylvestersCriterion()const
{
// http://en.wikipedia.org/wiki/Sylvester%27s_criterion
float flDet1 = m_flMatVal[0][0];
float flDet2 = m_flMatVal[0][0] * m_flMatVal[1][1] - m_flMatVal[1][0] * m_flMatVal[0][1];
float flDet3 = GetDeterminant();
return MIN(MIN(flDet1, flDet2), flDet3);
}
// Generate the corner points of a box:
// +y _+z
// ^ /|
// | /
// | 3---7
// /| /|
// / | / |
// 2---6 |
// | 1|--5
// | / | /
// |/ |/
// 0---4 --> +x
void PointsFromBox(const Vector3D& mins, const Vector3D& maxs, Vector3D* points);
void BuildTransformedBox(Vector3D* v2, Vector3D const& bbmin, Vector3D const& bbmax, const matrix3x4_t& m);
// generate the corner points of a angled box:
// +y*r _+z*u
// ^ /|
// | /
// | 3---7
// /| /|
// / | / |
// 2---6 |
// | 1|--5
// | / | /
// |/ |/
// 0---4 --> +x*f
void PointsFromAngledBox(const QAngle& angles, const Vector3D& mins, const Vector3D& maxs, Vector3D* points);
void BuildTransformedAngledBox(Vector3D* v2, const QAngle& a, Vector3D const& bbmin, Vector3D const& bbmax, const matrix3x4_t& m);
#endif // MATH_BASE_H