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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/public/mathlib/mathlib.h

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//========= Copyright Valve Corporation, All rights reserved. ============//
//
// Purpose:
//
//===========================================================================//
#ifndef MATH_LIB_H
#define MATH_LIB_H
#include <math.h>
#include "minmax.h"
#include "tier0/basetypes.h"
#include "tier0/commonmacros.h"
#include "mathlib/vector.h"
#include "mathlib/vector2d.h"
#include "tier0/dbg.h"
#include "mathlib/math_pfns.h"
#if defined(__i386__) || defined(_M_IX86)
// For MMX intrinsics
#include <xmmintrin.h>
#endif
// XXX remove me
#undef clamp
// Uncomment this to enable FP exceptions in parts of the code.
// This can help track down FP bugs. However the code is not
// FP exception clean so this not a turnkey operation.
//#define FP_EXCEPTIONS_ENABLED
#ifdef FP_EXCEPTIONS_ENABLED
#include <float.h> // For _clearfp and _controlfp_s
#endif
// FPExceptionDisabler and FPExceptionEnabler taken from my blog post
// at http://www.altdevblogaday.com/2012/04/20/exceptional-floating-point/
// Declare an object of this type in a scope in order to suppress
// all floating-point exceptions temporarily. The old exception
// state will be reset at the end.
class FPExceptionDisabler
{
public:
#ifdef FP_EXCEPTIONS_ENABLED
FPExceptionDisabler();
~FPExceptionDisabler();
private:
unsigned int mOldValues;
#else
FPExceptionDisabler() {}
~FPExceptionDisabler() {}
#endif
private:
// Make the copy constructor and assignment operator private
// and unimplemented to prohibit copying.
FPExceptionDisabler(const FPExceptionDisabler&);
FPExceptionDisabler& operator=(const FPExceptionDisabler&);
};
// Declare an object of this type in a scope in order to enable a
// specified set of floating-point exceptions temporarily. The old
// exception state will be reset at the end.
// This class can be nested.
class FPExceptionEnabler
{
public:
// Overflow, divide-by-zero, and invalid-operation are the FP
// exceptions most frequently associated with bugs.
#ifdef FP_EXCEPTIONS_ENABLED
FPExceptionEnabler(unsigned int enableBits = _EM_OVERFLOW | _EM_ZERODIVIDE | _EM_INVALID);
~FPExceptionEnabler();
private:
unsigned int mOldValues;
#else
FPExceptionEnabler(unsigned int enableBits = 0)
{
}
~FPExceptionEnabler()
{
}
#endif
private:
// Make the copy constructor and assignment operator private
// and unimplemented to prohibit copying.
FPExceptionEnabler(const FPExceptionEnabler&);
FPExceptionEnabler& operator=(const FPExceptionEnabler&);
};
#ifdef DEBUG // stop crashing edit-and-continue
FORCEINLINE float clamp( float val, float minVal, float maxVal )
{
if ( maxVal < minVal )
return maxVal;
else if( val < minVal )
return minVal;
else if( val > maxVal )
return maxVal;
else
return val;
}
#else // DEBUG
FORCEINLINE float clamp( float val, float minVal, float maxVal )
{
#if defined(__i386__) || defined(_M_IX86)
_mm_store_ss( &val,
_mm_min_ss(
_mm_max_ss(
_mm_load_ss(&val),
_mm_load_ss(&minVal) ),
_mm_load_ss(&maxVal) ) );
#else
val = fpmax(minVal, val);
val = fpmin(maxVal, val);
#endif
return val;
}
#endif // DEBUG
//
// Returns a clamped value in the range [min, max].
//
template< class T >
inline T clamp( T const &val, T const &minVal, T const &maxVal )
{
if ( maxVal < minVal )
return maxVal;
else if( val < minVal )
return minVal;
else if( val > maxVal )
return maxVal;
else
return val;
}
// 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
{
public:
void SetPlane( int i, int nType, const Vector &vecNormal, float dist )
{
m_Plane[i].normal = vecNormal;
m_Plane[i].dist = dist;
m_Plane[i].type = nType;
m_Plane[i].signbits = SignbitsForPlane( &m_Plane[i] );
m_AbsNormal[i].Init( fabs(vecNormal.x), fabs(vecNormal.y), fabs(vecNormal.z) );
}
inline const cplane_t *GetPlane( int i ) const { return &m_Plane[i]; }
inline const Vector &GetAbsNormal( int i ) const { return m_AbsNormal[i]; }
private:
cplane_t m_Plane[FRUSTUM_NUMPLANES];
Vector m_AbsNormal[FRUSTUM_NUMPLANES];
};
// 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)
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, Frustum_t &frustum );
// 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 );
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 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];
};
#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
#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);
}
int Q_log2(int val);
// Math routines done in optimized assembly math package routines
void inline SinCos( float radians, float *sine, float *cosine )
{
#if defined( _X360 )
XMScalarSinCos( sine, cosine, radians );
#elif defined( PLATFORM_WINDOWS_PC32 )
_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( PLATFORM_WINDOWS_PC64 )
*sine = sin( radians );
*cosine = cos( radians );
#elif defined( POSIX )
double __cosr, __sinr;
__asm ("fsincos" : "=t" (__cosr), "=u" (__sinr) : "0" (radians));
*sine = __sinr;
*cosine = __cosr;
#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;
}
// 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 );
inline void MatrixGetTranslation( const matrix3x4_t &in, Vector &out )
{
MatrixGetColumn ( in, 3, out );
}
inline void MatrixSetTranslation( const Vector &in, matrix3x4_t &out )
{
MatrixSetColumn ( in, 3, out );
}
void MatrixScaleBy ( const float flScale, matrix3x4_t &out );
void MatrixScaleByZero ( 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);
// For identical interface w/ VMatrix
inline void MatrixMultiply ( const matrix3x4_t &in1, const matrix3x4_t &in2, matrix3x4_t &out )
{
ConcatTransforms( in1, in2, out );
}
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;
}
// 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 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 val >= B ? D : C;
float cVal = (val - A) / (B - A);
cVal = clamp( 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
/// Same as swap(), but won't cause problems with std::swap
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) ARRAYSIZE(x)
// 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 (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;
}
#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 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 )
{
MatrixGetColumn( matrix, 3, position );
}
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);
//
// 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(__i386__) || defined(_M_IX86) || defined( PLATFORM_WINDOWS_PC64 ) || defined(__x86_64__)
return _mm_cvtss_si32(_mm_load_ss(&f));
#elif defined( _X360 )
#ifdef Assert
Assert( IsFPUControlWordSet() );
#endif
union
{
double flResult;
int pResult[2];
};
flResult = __fctiw( f );
return pResult[1];
#else
#error Unknown architecture
#endif
}
FORCEINLINE unsigned char RoundFloatToByte(float f)
{
int nResult = RoundFloatToInt(f);
#ifdef Assert
Assert( (nResult & ~0xFF) == 0 );
#endif
return (unsigned char) nResult;
}
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];
#else // !X360
#if defined( PLATFORM_WINDOWS_PC64 )
uint nRet = ( uint ) f;
if ( nRet & 1 )
{
if ( ( f - floor( f ) >= 0.5 ) )
{
nRet++;
}
}
else
{
if ( ( f - floor( f ) > 0.5 ) )
{
nRet++;
}
}
return nRet;
#else // PLATFORM_WINDOWS_PC64
unsigned char nResult[8];
#if defined( _WIN32 )
__asm
{
fld f
fistp qword ptr nResult
}
#elif POSIX
__asm __volatile__ (
"fistpl %0;": "=m" (nResult): "t" (f) : "st"
);
#endif
return *((unsigned long*)nResult);
#endif // PLATFORM_WINDOWS_PC64
#endif // !X360
}
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];
#else // !X360
// Rely on compiler to generate CVTTSS2SI on x86
return (int) a;
#endif
}
// Over 15x faster than: (int)floor(value)
inline int Floor2Int( float a )
{
int RetVal;
#if defined( __i386__ )
// Convert to int and back, compare, subtract one if too big
__m128 a128 = _mm_set_ss(a);
RetVal = _mm_cvtss_si32(a128);
__m128 rounded128 = _mm_cvt_si2ss(_mm_setzero_ps(), RetVal);
RetVal -= _mm_comigt_ss( rounded128, a128 );
#else
RetVal = static_cast<int>( floor(a) );
#endif
return RetVal;
}
//-----------------------------------------------------------------------------
// Fast color conversion from float to unsigned char
//-----------------------------------------------------------------------------
FORCEINLINE unsigned int FastFToC( float c )
{
#if defined( __i386__ )
// IEEE float bit manipulation works for values between [0, 1<<23)
union { float f; int i; } convert = { c*255.0f + (float)(1<<23) };
return convert.i & 255;
#else
// consoles CPUs suffer from load-hit-store penalty
return Float2Int( c * 255.0f );
#endif
}
//-----------------------------------------------------------------------------
// Fast conversion from float to integer with magnitude less than 2**22
//-----------------------------------------------------------------------------
FORCEINLINE int FastFloatToSmallInt( float c )
{
#if defined( __i386__ )
// IEEE float bit manipulation works for values between [-1<<22, 1<<22)
union { float f; int i; } convert = { c + (float)(3<<22) };
return (convert.i & ((1<<23)-1)) - (1<<22);
#else
// consoles CPUs suffer from load-hit-store penalty
return Float2Int( c );
#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 0.001f * msec;
}
// Over 15x faster than: (int)ceil(value)
inline int Ceil2Int( float a )
{
int RetVal;
#if defined( __i386__ )
// Convert to int and back, compare, add one if too small
__m128 a128 = _mm_load_ss(&a);
RetVal = _mm_cvtss_si32(a128);
__m128 rounded128 = _mm_cvt_si2ss(_mm_setzero_ps(), RetVal);
RetVal += _mm_comilt_ss( rounded128, a128 );
#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 );
// 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_3DNowEnabled( void );
bool MathLib_MMXEnabled( void );
bool MathLib_SSEEnabled( void );
bool MathLib_SSE2Enabled( void );
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 );
void ComputeTrianglePlane( const Vector& v1, const Vector& v2, const Vector& v3, Vector& normal, float& intercept );
int PolyFromPlane( Vector *outVerts, const Vector& normal, float dist, float fHalfScale = 9000.0f );
int ClipPolyToPlane( Vector *inVerts, int vertCount, Vector *outVerts, const Vector& normal, float dist, float fOnPlaneEpsilon = 0.1f );
int ClipPolyToPlane_Precise( double *inVerts, int vertCount, double *outVerts, const double *normal, double dist, double fOnPlaneEpsilon = 0.1 );
//-----------------------------------------------------------------------------
// 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;
pNormal[2] = zSign*sqrtf( 1.0f - ( pNormal[0]*pNormal[0] + pNormal[1]*pNormal[1] ) );
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 );
}
//-----------------------------------------------------------------------------
// 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
//-----------------------------------------------------------------------------
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
//-----------------------------------------------------------------------------
// 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<EFBFBD>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 );
}
#endif // MATH_BASE_H