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Modified source engine (2017) developed by valve and leaked in 2020. Not for commercial purporses
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source-engine/external/vpc/public/mathlib/mathlib.h

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//===== Copyright © 1996-2005, Valve Corporation, All rights reserved. ======//
//
// Purpose:
//
//===========================================================================//
#ifndef MATH_LIB_H
#define MATH_LIB_H
#include <math.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)
#include <ppu_intrinsics.h>
#include <altivec.h>
#include <vectormath/c/vectormath_soa.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
{
Vector 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 Vector& origin, const QAngle &angles, float flZNear, float flZFar, float flFovX, float flAspectRatio, Frustum_t &frustum );
void GeneratePerspectiveFrustum( const Vector& origin, const Vector &forward, const Vector &right, const Vector &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 Vector &origin, const Vector &forward, const Vector &right, const Vector &up, float flLeft, float flRight, float flBottom, float flTop, float flZNear, float flZFar, VPlane *pPlanesOut );
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 Init( const Vector& xAxis, const Vector& yAxis, const Vector& zAxis, const Vector &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 Vector& xAxis, const Vector& yAxis, const Vector& zAxis, const Vector &vecOrigin )
{
Init( xAxis, yAxis, zAxis, vecOrigin );
}
inline void SetOrigin( Vector const & p )
{
m_flMatVal[0][3] = p.x;
m_flMatVal[1][3] = p.y;
m_flMatVal[2][3] = p.z;
}
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;
}
}
}
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& operator=( const matrix3x4_t& src ) { memcpy( Base(), src.Base(), sizeof( float ) * 3 * 4 ); return *this; };
} ALIGN16_POST;
#ifndef M_PI
#define M_PI 3.14159265358979323846 // matches value in gcc v2 math.h
#endif
#define M_PI_F ((float)(M_PI)) // Shouldn't collide with anything.
// 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 Vector vec3_origin;
extern const QAngle vec3_angle;
extern const Quaternion quat_identity;
extern const Vector 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 Vector& 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 Vector& start, float scale, const Vector& direction, Vector& 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 Vector& start, float scale, const Vector& direction, Vector& 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);
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 )
{
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 ) ];
}
inline float TableSin( float theta )
{
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 ) ];
}
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 MatrixAngles( const matrix3x4_t & matrix, float *angles ); // !!!!
void MatrixVectors( const matrix3x4_t &matrix, Vector* pForward, Vector *pRight, Vector *pUp );
void VectorTransform (const float *in1, const matrix3x4_t & in2, float *out);
void VectorITransform (const float *in1, const matrix3x4_t & in2, float *out);
void VectorRotate( const float *in1, const matrix3x4_t & in2, float *out);
void VectorRotate( const Vector &in1, const QAngle &in2, Vector &out );
void VectorRotate( const Vector &in1, const Quaternion &in2, Vector &out );
void VectorIRotate( const float *in1, const matrix3x4_t & in2, float *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 Vector &vecOrigin, const Vector &vecXAxis, const Vector &vecYAxis, const Vector &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, Vector &out );
void MatrixSetColumn( const Vector &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 Vector &vecForward, const Vector &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 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 Vector &pos, matrix3x4_t &matrix );
void QuaternionAngles( const Quaternion &q, QAngle &angles );
void AngleQuaternion( const QAngle& angles, Quaternion &qt );
void QuaternionAngles( const Quaternion &q, RadianEuler &angles );
void AngleQuaternion( RadianEuler const &angles, Quaternion &qt );
void QuaternionAxisAngle( const Quaternion &q, Vector &axis, float &angle );
void AxisAngleQuaternion( const Vector &axis, float angle, Quaternion &q );
void BasisToQuaternion( const Vector &vecForward, const Vector &vecRight, const Vector &vecUp, Quaternion &q );
void MatrixQuaternion( const matrix3x4_t &mat, Quaternion &q );
// 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 Vector& in2 )
{
Assert( (row >= 0) && (row < 3) );
return DotProduct( in1[row], in2.Base() );
}
inline float MatrixColumnDotProduct( const matrix3x4_t &in1, int col, const Vector& 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 AngleVectors (const QAngle& angles, Vector *forward);
void AngleVectors (const QAngle& angles, Vector *forward, Vector *right, Vector *up);
void AngleVectorsTranspose (const QAngle& angles, Vector *forward, Vector *right, Vector *up);
void AngleMatrix (const QAngle &angles, matrix3x4_t &mat );
void AngleMatrix( const QAngle &angles, const Vector &position, matrix3x4_t &mat );
void AngleMatrix (const RadianEuler &angles, matrix3x4_t &mat );
void AngleMatrix( RadianEuler const &angles, const Vector &position, matrix3x4_t &mat );
void AngleIMatrix (const QAngle &angles, matrix3x4_t &mat );
void AngleIMatrix (const QAngle &angles, const Vector &position, matrix3x4_t &mat );
void AngleIMatrix (const RadianEuler &angles, matrix3x4_t &mat );
void VectorAngles( const Vector &forward, QAngle &angles );
void VectorAngles( const Vector &forward, const Vector &pseudoup, QAngle &angles );
void VectorMatrix( const Vector &forward, matrix3x4_t &mat );
void VectorVectors( const Vector &forward, Vector &right, Vector &up );
void SetIdentityMatrix( matrix3x4_t &mat );
void SetScaleMatrix( float x, float y, float z, matrix3x4_t &dst );
void MatrixBuildRotationAboutAxis( const Vector &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 Vector& 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 Vector &position, matrix3x4_t &mat )
{
MatrixSetColumn( position, 3, mat );
}
inline void MatrixPosition( const matrix3x4_t &matrix, Vector &position )
{
position[0] = matrix[0][3];
position[1] = matrix[1][3];
position[2] = matrix[2][3];
}
inline void VectorRotate( const Vector& in1, const matrix3x4_t &in2, Vector &out)
{
VectorRotate( &in1.x, in2, &out.x );
}
inline void VectorIRotate( const Vector& in1, const matrix3x4_t &in2, Vector &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, Vector &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, Vector &position );
void MatrixAngles( const matrix3x4_t &mat, Quaternion &q, Vector &position );
inline int VectorCompare (const Vector& v1, const Vector& v2)
{
return v1 == v2;
}
inline void VectorTransform (const Vector& in1, const matrix3x4_t &in2, Vector &out)
{
VectorTransform( &in1.x, in2, &out.x );
}
inline void VectorITransform (const Vector& in1, const matrix3x4_t &in2, Vector &out)
{
VectorITransform( &in1.x, in2, &out.x );
}
/*
inline void DecomposeRotation( const matrix3x4_t &mat, Vector &out )
{
DecomposeRotation( mat, &out.x );
}
*/
inline int BoxOnPlaneSide (const Vector& emins, const Vector& emaxs, const cplane_t *plane )
{
return BoxOnPlaneSide( &emins.x, &emaxs.x, plane );
}
inline void VectorFill(Vector& a, float b)
{
a[0]=a[1]=a[2]=b;
}
inline void VectorNegate(Vector& a)
{
a[0] = -a[0];
a[1] = -a[1];
a[2] = -a[2];
}
inline vec_t VectorAvg(Vector& a)
{
return ( a[0] + a[1] + a[2] ) / 3;
}
//-----------------------------------------------------------------------------
// Box/plane test (slow version)
//-----------------------------------------------------------------------------
inline int FASTCALL BoxOnPlaneSide2 (const Vector& emins, const Vector& emaxs, const cplane_t *p, float tolerance = 0.f )
{
Vector 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 (Vector& mins, Vector& maxs);
void AddPointToBounds (const Vector& v, Vector& mins, Vector& maxs);
//-----------------------------------------------------------------------------
// Ensures that the min and max bounds values are valid.
// (ClearBounds() sets min > max, which is clearly invalid.)
//-----------------------------------------------------------------------------
bool AreBoundsValid( const Vector &vMin, const Vector &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 Vector &vPoint, const Vector &vMin, const Vector &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 )
{
extern 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, Vector& out );
void VectorToColorRGBExp32( const Vector& 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 Vector& in, float flYaw, Vector &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 )
return __fctiw( f );
#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 )
return __fctiw( f );
#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 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 )
return __fctiw( f );
#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 )
return __fctiwz( a );
#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 Vector& vOrigin,
float flRadius,
const Vector& bbMin,
const Vector& 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 Vector& vBox1Min,
const Vector& vBox1Max,
const Vector& vBox2Min,
const Vector& 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 comman 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 comman 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( Vector& 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( Vector& 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 Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector &output );
// Interpolate a Catmull-Rom spline.
// Returns the tangent of the point at t of the spline
void Catmull_Rom_Spline_Tangent(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector &output );
// area under the curve [0..t]
void Catmull_Rom_Spline_Integral(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output );
// area under the curve [0..1]
void Catmull_Rom_Spline_Integral(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
Vector& 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 Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector &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 Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& 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 Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector &output );
// area under the curve [0..t]
void Catmull_Rom_Spline_NormalizeX(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& 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 Vector &p1,
const Vector &p2,
const Vector &d1,
const Vector &d2,
float t,
Vector& 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 Vector &p0,
const Vector &p1,
const Vector &p2,
float t,
Vector& output );
float Hermite_Spline(
float p0,
float p1,
float p2,
float t );
void Hermite_SplineBasis( float t, float basis[] );
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 Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output );
void Kochanek_Bartels_Spline_NormalizeX(
float tension,
float bias,
float continuity,
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output );
// See link at Kochanek_Bartels_Spline for info on the basis matrix used
void Cubic_Spline(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output );
void Cubic_Spline_NormalizeX(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output );
// See link at Kochanek_Bartels_Spline for info on the basis matrix used
void BSpline(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output );
void BSpline_NormalizeX(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output );
// See link at Kochanek_Bartels_Spline for info on the basis matrix used
void Parabolic_Spline(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& output );
void Parabolic_Spline_NormalizeX(
const Vector &p1,
const Vector &p2,
const Vector &p3,
const Vector &p4,
float t,
Vector& 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
FORCEINLINE float QuinticInterpolatingPolynomial(float t)
{
// 6t^5-15t^4+10t^3
return t * t * t *( t * ( t* 6.0 - 15.0 ) + 10.0 );
}
// 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 Vector &mins, const Vector &maxs, const Vector &point );
void CalcClosestPointOnAABB( const Vector &mins, const Vector &maxs, const Vector &point, Vector &closestOut );
void CalcSqrDistAndClosestPointOnAABB( const Vector &mins, const Vector &maxs, const Vector &point, Vector &closestOut, float &distSqrOut );
inline float CalcDistanceToAABB( const Vector &mins, const Vector &maxs, const Vector &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 Vector &P, const Vector &vLineA, const Vector &vLineB, Vector &vClosest, float *t=0 );
float CalcDistanceToLine( const Vector &P, const Vector &vLineA, const Vector &vLineB, float *t=0 );
float CalcDistanceSqrToLine( const Vector &P, const Vector &vLineA, const Vector &vLineB, float *t=0 );
// The same three functions as above, except now the line is closed between A and B.
void CalcClosestPointOnLineSegment( const Vector &P, const Vector &vLineA, const Vector &vLineB, Vector &vClosest, float *t=0 );
float CalcDistanceToLineSegment( const Vector &P, const Vector &vLineA, const Vector &vLineB, float *t=0 );
float CalcDistanceSqrToLineSegment( const Vector &P, const Vector &vLineA, const Vector &vLineB, float *t=0 );
// A function to compute the closes line segment connnection two lines (or false if the lines are parallel, etc.)
bool CalcLineToLineIntersectionSegment(
const Vector& p1,const Vector& p2,const Vector& p3,const Vector& p4,Vector *s1,Vector *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 bAllow3DNow = true, bool bAllowSSE = true, bool bAllowSSE2 = true, bool bAllowMMX = true );
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, Vector &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 Vector &vNormal, const Vector &vPlanePoint, Vector *p1, Vector *p2, float flBias = 0.0f );
void ComputeTrianglePlane( const Vector& v1, const Vector& v2, const Vector& v3, Vector& normal, float& intercept );
int PolyFromPlane( Vector *pOutVerts, const Vector& normal, float dist, float fHalfScale = 9000.0f );
void PolyFromPlane_SIMD( fltx4 *pOutVerts, const fltx4 & plane, float fHalfScale = 9000.0f );
int ClipPolyToPlane( Vector *inVerts, int vertCount, Vector *outVerts, const Vector& 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 Vector &p0, const Vector &p1, const Vector &p2, const Vector &p3 );
float TriangleArea( const Vector &p0, const Vector &p1, const Vector &p2 );
//-----------------------------------------------------------------------------
// Computes a reasonable tangent space for a triangle
//-----------------------------------------------------------------------------
void CalcTriangleTangentSpace( const Vector &p0, const Vector &p1, const Vector &p2,
const Vector2D &t0, const Vector2D &t1, const Vector2D& t2,
Vector &sVect, Vector &tVect );
//-----------------------------------------------------------------------------
// Transforms a AABB into another space; which will inherently grow the box.
//-----------------------------------------------------------------------------
void TransformAABB( const matrix3x4_t &in1, const Vector &vecMinsIn, const Vector &vecMaxsIn, Vector &vecMinsOut, Vector &vecMaxsOut );
//-----------------------------------------------------------------------------
// Uses the inverse transform of in1
//-----------------------------------------------------------------------------
void ITransformAABB( const matrix3x4_t &in1, const Vector &vecMinsIn, const Vector &vecMaxsIn, Vector &vecMinsOut, Vector &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 Vector &vecMinsIn, const Vector &vecMaxsIn, Vector &vecMinsOut, Vector &vecMaxsOut );
//-----------------------------------------------------------------------------
// Uses the inverse transform of in1
//-----------------------------------------------------------------------------
void IRotateAABB( const matrix3x4_t &in1, const Vector &vecMinsIn, const Vector &vecMaxsIn, Vector &vecMinsOut, Vector &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
Vector vecTranslation;
MatrixGetColumn( src, 3, vecTranslation );
Vector 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; // Unpack Z
cY = *pPackedNormal >> 24; // Unpack W
}
else
{
cX = *pPackedNormal >> 0; // Unpack X
cY = *pPackedNormal >> 8; // 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, 1 );
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 Vector &rgb, Vector &hsv );
//-----------------------------------------------------------------------------
// Convert HSV to RGB
//-----------------------------------------------------------------------------
void HSVtoRGB( const Vector &hsv, Vector &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 Vector &a, const Vector &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 Vector &a, const Vector &b, int maxUlps = 10)
{
return AlmostEqual( a.x, b.x, maxUlps ) &&
AlmostEqual( a.y, b.y, maxUlps ) &&
AlmostEqual( a.z, b.z, maxUlps );
}
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
}
// 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)
double flIntFormat = __builtin_fctiwz( flVal );
return __builtin_fcfid( flIntFormat );
#endif
}
#endif
inline double SubtractIntegerPart( double flVal )
{
#if defined(_X360) || defined(_PS3)
return flVal - TruncateFloatToIntAsFloat(flVal);
#else
return flVal - int(flVal);
#endif
}
#endif // MATH_BASE_H