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HL2Overcharged/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 "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(fabsf(vecNormal.x), fabsf(vecNormal.y), fabsf(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
union
{
unsigned char nResult[8];
unsigned long ulResult;
} u;
#if defined( _WIN32 )
__asm
{
fld f
fistp qword ptr u.nResult
}
#elif POSIX
__asm __volatile__(
"fistpl %0;": "=m" (u.nResult) : "t" (f) : "st"
);
#endif
return u.ulResult;
#endif // PLATFORM_WINDOWS_PC64
#endif // !X360
}
FORCEINLINE bool IsIntegralValue(float flValue, float flTolerance = 0.001f)
{
return fabsf(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 fabsf(a - b) <= epsilon;
}
inline bool CloseEnough(const Vector &a, const Vector &b, float epsilon = EQUAL_EPSILON)
{
return fabsf(a.x - b.x) <= epsilon &&
fabsf(a.y - b.y) <= epsilon &&
fabsf(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<65>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
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