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GS.Geometry.pas
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GS.Geometry.pas
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//Pure extraction from the very nice work of Wouter van Nifterick (aka WouterVanNifterick)
//from his delphi-shader project ---> https://github.com/WouterVanNifterick/delphi-shader
//Aim here is to obtain fast and easy to maintain cross platform mathematics tools.
//So, all original texture and shader stuff has been removed, as well as dependancies.
unit GS.Geometry;
{$I GSCore.Inc}
interface
uses Classes,
SysUtils,
types,
Math;
{$R-}
{$IFNDEF CPUx64}
{$DEFINE DO_INLINE}
{$ENDIF}
{$IFDEF DEBUG}
{.$DEFINE DO_INLINE}
{$ENDIF}
const
M_LN2 = 0.693147180559945309417;
_EPSILON_ = 4.9406564584124654418e-324;
type
{$IFDEF CPUx64}
TVecType = type Double;
const
M_MXVT = MaxDouble;
{$ELSE}
TVecType = type Single;
const
M_MXVT = MaxSingle;
{$ENDIF}
Type
int = type Integer;
bool = type Boolean;
Float = type Double;
PVec2 = ^Vec2;
PVec3 = ^Vec3;
PVec4 = ^Vec4;
Vec1 = TVecType;
Vec2 = record
x, y: TVecType;
function Length: TVecType;{$IFDEF DO_INLINE} inline;{$ENDIF}
function Normalize: PVec2;{$IFDEF DO_INLINE} inline;{$ENDIF}
function Cross(const b: Vec2): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF}
function Dot(const b: Vec2): TVecType; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
constructor create(ax, ay: TVecType);overload;
constructor create(ax: TVecType);overload;
class operator explicit(const b:TVecType):Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Add(const a, b: Vec2): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Add(const a: Vec2; b: TVecType): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Add(a: TVecType; const b: Vec2): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Subtract(const a, b: Vec2): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Subtract(const a: Vec2; b: TVecType): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Subtract(a: TVecType; const b: Vec2): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Multiply(const a: Vec2; const b: Vec2): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Multiply(const a: Vec2; b: TVecType): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Multiply(a: TVecType; const b: Vec2): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Divide(const a: Vec2; const b: Vec2): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Divide(const a: Vec2; b: TVecType): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Divide(a: TVecType; const b: Vec2): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Negative(const a: Vec2): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Explicit(const a: Vec2): TPoint;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Explicit(const a: Vec2): TPointF;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Explicit(const a: TPoint): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Explicit(const a: TPointF): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF}
property r:TVecType read x write x;
property g:TVecType read y write y;
end;
Vec2s = array of Vec2;
Vec2sp = ^Vec2s;
Vec2sArray = Array of Vec2s;
Vec3 = record
function Length: TVecType;{$IFDEF DO_INLINE} inline;{$ENDIF}
function Normalize: PVec3;{$IFDEF DO_INLINE} inline;{$ENDIF}
procedure NormalizeSelf;{$IFDEF DO_INLINE} inline;{$ENDIF}
function Abs: Vec3; {$IFDEF DO_INLINE} inline;{$ENDIF}
function Cross(const b: Vec3): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF}
function Dot(const b: Vec3): TVecType; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
constructor create(ax, ay, az: TVecType);overload;
constructor create(ax: TVecType);overload;
constructor create(const xy:Vec2;az: TVecType);overload;
constructor create(aX:TVecType;const yz:Vec2);overload;
class operator Subtract(const a, b: Vec3): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Subtract(const a: Vec3; const b: Vec2): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Subtract(const a:Vec2; const b: Vec3): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Add(const a, b: Vec3): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Add(const a: Vec3; b: TVecType): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Negative(const a: Vec3): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Multiply(const a: Vec3; const b: Vec3): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Multiply(const a: Vec3; b: TVecType): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Multiply(a: TVecType; const b: Vec3): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Divide(const a: Vec3; const b: Vec3): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Divide(const a: Vec3; b: TVecType): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Implicit(a: TVecType): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF}
//Color 32 (int32 range test.
class operator Explicit(const a: Vec3): Int32;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Equal(const a,b:Vec3):Boolean;{$IFDEF DO_INLINE} inline;{$ENDIF}
var
x, y, z: TVecType;
property r:TVecType read x write x;
property g:TVecType read y write y;
property b:TVecType read z write z;
end;
Vec4 = record
function Dot(const b: Vec4): TVecType; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
constructor create(x: TVecType); overload;
constructor create(x, y, z, w: TVecType); overload;
constructor create(const x: Vec3; w: TVecType); overload;
constructor create(w: TVecType;const ax: Vec3 ); overload;
class operator Implicit(const a: Vec3): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Explicit(const a: Vec4): Int32;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Multiply(const a: Vec4; b: TVecType): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Multiply(const a: TVecType; const b: Vec4): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Multiply(const a,b: Vec4): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Multiply(const a:vec3;const b: Vec4): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Multiply(const a:vec4;const b: Vec3): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Divide(const a:vec4;b: TVecType): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Divide(const a:vec4;b: int64): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Add(const a, b: Vec4): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Add(a:TVecType; const b: Vec4): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Add(const a:Vec4; b: TVecType): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Subtract(const a,b: Vec4): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Negative(const a: Vec4): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF}
function getHeight: TVecType;
function getWidth: TVecType;
{
case RecType: byte of
0:(x, y, z, w: TVecType);
1:(r, g, b, a: TVecType);
}
var
x, y, z, w: TVecType;
property r:TVecType read x write x;
property g:TVecType read y write y;
property b:TVecType read z write z;
property a:TVecType read w write w;
property Left:TVecType read x write x;
property top:TVecType read y write y;
property right:TVecType read z write z;
property bottom:TVecType read w write w;
property Width:TVecType read getWidth;
property height:TVecType read getHeight;
end;
Mat3 = record
private
function getm11: TVecType;
procedure setmm11(const Value: TVecType);
public
r1,r2,r3:Vec3;
constructor Create(a1,a2,a3,b1,b2,b3,c1,c2,c3:TVecType);overload;
constructor Create(const a,b,c:Vec3);overload;
class operator Multiply(const a:Vec2;const b:Mat3):Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF} //Graphics one.
class operator Multiply(const a:Mat3;const b:Vec3):Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Multiply(const a:Vec3;const b:Mat3):Vec3;
class operator Multiply(const a:Mat3;const b:Mat3):Mat3;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Add(const a:Mat3;const b:Vec3):Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Negative(const a: Mat3): Mat3;{$IFDEF DO_INLINE} inline;{$ENDIF}
function Determinant : TVecType;
function Adjoint : Mat3;
function Inverse : Mat3;
function Scale(factor : TVecType) : Mat3;
end;
Mat4 = record
public
r1,r2,r3,r4:Vec4;
constructor Create(a1,a2,a3,a4,b1,b2,b3,b4,c1,c2,c3,c4,d1,d2,d3,d4:TVecType);
class operator Multiply(const a,b:Mat4):Mat4;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Multiply(const b: Vec4; const a: Mat4): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF}
class operator Multiply(const b:Vec3;const a:Mat4):Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF} //Graphics one. (vec3*Mat4)
// class operator Multiply(const a:Mat4;const b:Vec4):Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF}
function Determinant : TVecType;
function Adjoint : Mat4;
function Scale(factor : TVecType) : Mat4;
function Inverse : Mat4;
end;
///Mat3 related.
function Mat3Identity : Mat3;
function Mat3CreateRotation(angle : single) : Mat3;
function Mat3CreateTranslation(deltax, deltay : TvecType) : Mat3;
function Mat3CreateScaling(scalex, scaley : TVecType) : Mat3;
///Mat4 related.
function Mat4Identity : Mat4;
function Mat4CreateTranslation(translation : vec3) : Mat4;
function Mat4CreateRotationX(angle : single): Mat4;
function Mat4CreateRotationY(angle : single): Mat4;
function Mat4CreateRotationZ(angle : single): Mat4;
function Mat4CreateOrthoOffCenterRH(Left, Top, Right, Bottom, ZNear, ZFar: Single): Mat4;
function Mat4CreateLookAtDirLH(source,direction,ceiling : Vec3) : Mat4;
function Mat4CreatePerspectiveFovLH(const FOV, Aspect, ZNear, ZFar: Single;
const HorizontalFOV: Boolean = False): Mat4;
function _abs(x: Single) : Single;inline;overload;
function _abs(x: Double) : Double;inline;overload;
// function abs(x: Extended) : Extended;inline;overload;
function _pow(x, y: Double): Double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _radians(degrees: Double): Double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return T(M_PI/180)*degrees; }
function _degrees(radians: Double): Double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return T(180/M_PI)*radians; }
function _exp2(x: Double): Double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return T(cmath::exp(x * M_LN2)); }
function _log(x: Double): Double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return T(cmath::log(x) / M_LN2); }
function _log(x: vec2): vec2;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return T(cmath::log(x) / M_LN2); }
function _log(x: vec3): vec3;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return T(cmath::log(x) / M_LN2); }
function _log2(x: single): single;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return T(cmath::log2(x) / M_LN2); }
function _log2(x: double): double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return T(cmath::log2(x) / M_LN2); }
function _inversesqrt(x: Single): Single;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return 1/cmath::sqrt(x); }
function _inversesqrt(x: Double): Double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return 1/cmath::sqrt(x); }
function _sign(x: Double): Double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return T((x>0) ? T(1) : ((x<0) ? T(-1):T(0))); }
function _fract(x: Double): Double;inline;overload; { return x - cmath::floor(x); }
function _fract(const a: Vec2): Vec2;inline;overload; { return x - cmath::floor(x); }
function _fract(const a: Vec3): Vec3;inline;overload; { return x - cmath::floor(x); }
function _fract(const a: Vec4): Vec4;inline;overload; { return x - cmath::floor(x); }
function _floor(const a: Vec2): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return x - cmath::floor(x); }
function _floor(const a: Vec3): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return x - cmath::floor(x); }
function _floor(const a: Vec4): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return x - cmath::floor(x); }
function _clamp(x:Double; minVal:Double; maxVal: Double): Double;inline; overload; { return glsl::min(glsl::max(x,minVal),maxVal); }
function _clamp(x:Double): Double;inline; overload;
function _distance(p0, p1: Double): Double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return length(p0-p1); }
function _Dot(x, y: Single): Single;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return x*y; }
function _Dot(x, y: Double): Double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return x*y; }
function _Dot(const x, y: Vec2): Double; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return x*y; }
function _Dot(const x, y: Vec3): Double; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return x*y; }
function _Dot(const x, y: Vec4): Double; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return x*y; }
// function ceil(x: Double): Double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _ceil(const a: Vec2): Vec2; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _ceil(const a: Vec3): Vec3; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _ceil(const a: Vec4): Vec4; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _Reflect(I, n: Double): Double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return I - T(2)*N*I*N; }
function _Reflect(const I, n: Vec3): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return I - T(2)*N*I*N; }
function _FaceForward(const N,I,NRef:TVecType): TVecType;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _FaceForward(const N,I,NRef:Vec2): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _FaceForward(const N,I,NRef:Vec3): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _FaceForward(const N,I,NRef:Vec4): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _Refract(const I, N:TVecType; eta:Double):TVecType;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _Refract(const I, N:vec2; eta:Double):vec2;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _Refract(const I, N:vec3; eta:Double):vec3;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _Refract(const I, N:vec4; eta:Double):vec4;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
//function Abs(const x: TVecType): TVecType; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _Abs(const x: Vec2): Vec2; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _Abs(const x: Vec3): Vec3; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _Abs(const x: Vec4): Vec4; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _asin(x:Single):Single;overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _acos(x:Single):Single;overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _atan(x:Single):Single;overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _atan(x,y:Single):Single;overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _tan(x:Single):Single;overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _asin(x:Double):Double;overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _acos(x:Double):Double;overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _atan(x:Double):Double;overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _atan(x,y:Double):Double;overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _tan(x:Double):Double;overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _cross(const a,b: Vec3): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _smoothstep(edge0, edge1, x: Single): Single; {$IFDEF DO_INLINE} inline;{$ENDIF} overload; { T t = clamp((x-edge0) / (edge1-edge0), T(0), T(1)); return t * t * (3 - 2*t); }
function _smoothstep(edge0, edge1, x: Double): Double; {$IFDEF DO_INLINE} inline;{$ENDIF} overload; { T t = clamp((x-edge0) / (edge1-edge0), T(0), T(1)); return t * t * (3 - 2*t); }
function _smoothstep(const edge0, edge1, x: Vec2): Vec2; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { T t = clamp((x-edge0) / (edge1-edge0), T(0), T(1)); return t * t * (3 - 2*t); }
function _smoothstep(const edge0, edge1, x: Vec3): Vec3; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { T t = clamp((x-edge0) / (edge1-edge0), T(0), T(1)); return t * t * (3 - 2*t); }
function _smoothstep(const edge0, edge1, x: Vec4): Vec4; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { T t = clamp((x-edge0) / (edge1-edge0), T(0), T(1)); return t * t * (3 - 2*t); }
function _distance(const a,b: Vec2): double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return length(p0-p1); }
function _distance(const a,b: Vec3): double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return length(p0-p1); }
function _distance(const a,b: Vec4): double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return length(p0-p1); }
function _fmods(a, b: double): Double;overload;
function _mod(a, b: Double): Double;{$IFDEF CPUx64}inline;{$ENDIF} overload; { return T(cmath::fmod(x, y)); }
function _mod(const a, b: Vec2): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return T(cmath::fmod(x, y)); }
function _mod(const a, b: Vec3): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return T(cmath::fmod(x, y)); }
function _mod(const a, b: Vec4): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return T(cmath::fmod(x, y)); }
function _mod(const a: Vec2;b:TVecType): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return T(cmath::fmod(x, y)); }
function _mod(const a: Vec3;b:TVecType): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return T(cmath::fmod(x, y)); }
function _mod(const a: Vec4;b:TVecType): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return T(cmath::fmod(x, y)); }
function _min(x, y: Double): Double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return y < x ? y : x; }
function _min(const x, y: Vec2): Vec2; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return y < x ? y : x; }
function _min(const x, y: Vec3): Vec3; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _min(const x, y: Vec4): Vec4; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _max(x, y: Double): Double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return x < y ? y : x; }
function _max(const x, y: Vec2): Vec2; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return x < y ? y : x; }
function _max(const x, y: Vec3): Vec3; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return x < y ? y : x; }
function _max(const x, y: Vec4): Vec4; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return x < y ? y : x; }
function _maxComp(const p: Vec3): Double; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _pow(const x, y: Vec2): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _pow(const a, b: Vec3): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _pow(const x, y: Vec4): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
//function sqrt(const a: Single): Single;{$IFNDEF DEBUG} inline; {$ENDIF} overload;
function _sqrt(const a: Double): Double;{$IFDEF DO_INLINE}inline{$ENDIF} overload;
function _sqrt(const a: Vec2): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _sqrt(const a: Vec3): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _sqrt(const a: Vec4): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _sqrts(const a: TVecType): TVecType;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _sqrts(const a: Vec2): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _sqrts(const a: Vec3): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _sqrts(const a: Vec4): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _clamp(const x, minVal, maxVal: Vec2): Vec2; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return glsl::min(glsl::max(x,minVal),maxVal); }
function _clamp(const x, minVal, maxVal: Vec3): Vec3; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return glsl::min(glsl::max(x,minVal),maxVal); }
function _clamp(const x:Vec2; minVal, maxVal: Double): Vec2; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return glsl::min(glsl::max(x,minVal),maxVal); }
function _clamp(const x:Vec3; minVal, maxVal: Double): Vec3; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return glsl::min(glsl::max(x,minVal),maxVal); }
function _clamp(const x:Vec4; minVal, maxVal: Double): Vec4; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return glsl::min(glsl::max(x,minVal),maxVal); }
function _mix(x, y, a: Double): Double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return x*(1-a) + y*a; }
function _mix(const x, y, a: Vec2): Vec2; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return x*(1-a) + y*a; }
function _mix(const x, y, a: Vec3): Vec3; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return x*(1-a) + y*a; }
function _mix(const x, y, a: Vec4): Vec4; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return x*(1-a) + y*a; }
function _mix(const x, y:Vec2; a: TVecType): Vec2; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return x*(1-a) + y*a; }
function _mix(const x, y:Vec3; a: TVecType): Vec3; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return x*(1-a) + y*a; }
function _mix(const x, y:Vec4; a: TVecType): Vec4; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return x*(1-a) + y*a; }
function _step(edge, x: Double): Double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return x<=edge ? T(0) : T(1); }
function _step(const edge, x: Vec2): Vec2; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return x<=edge ? T(0) : T(1); }
function _step(const edge, x: Vec3): Vec3; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return x<=edge ? T(0) : T(1); }
function _step(const edge, x: Vec4): Vec4; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return x<=edge ? T(0) : T(1); }
function _Length(x: Double): Double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return cmath::sqrt(x*x); }
function _Length(const x: Vec2): Double; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return cmath::sqrt(x*x); }
function _Length(const x: Vec3): Double; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return cmath::sqrt(x*x); }
function _Length(const x: Vec4): Double; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return cmath::sqrt(x*x); }
function _length_sq(const x: Vec2): Double; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return cmath::sqrt(x*x); }
function _length_sq(const x: Vec3): Double; overload;{$IFDEF DO_INLINE} inline;{$ENDIF} { return cmath::sqrt(x*x); }
function _Normalize(x:double): Double; { return T(1); } inline; overload; // this is not the most useful function in the world
function _Normalize(const v: Vec2): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _Normalize(const v: Vec3): Vec3;{$IFDEF DO_INLINE} inline; {$ENDIF} overload;
function _normalizeS(const v:Vec3) : vec3;inline;{$IFDEF DO_INLINE} inline; {$ENDIF} overload;
function _Normalize(const v: Vec4): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _sinLarge(const x: TVecType): TVecType; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _sinLarge(const x: Vec2 ): Vec2 ; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _sinLarge(const x: Vec3 ): Vec3 ; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _sinLarge(const x: Vec4 ): Vec4 ; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _cosLarge(const x: TVecType): TVecType; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _cosLarge(const x: Vec2 ): Vec2 ; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _cosLarge(const x: Vec3 ): Vec3 ; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _cosLarge(const x: Vec4 ): Vec4 ; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _sin(const x: Vec2): Vec2; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _sin(const x: Vec3): Vec3; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _sin(const x: Vec4): Vec4; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _cos(const x: Vec2): Vec2; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _cos(const x: Vec3): Vec3; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _cos(const x: Vec4): Vec4; overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
procedure _cos(const x: Vec2;out Result:vec2); overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
procedure _cos(const x: Vec3;out Result:vec3); overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
procedure _cos(const x: Vec4;out Result:vec4); overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
procedure _Mult(const input: Vec3;out Result:vec3);inline;
function _Ifthen(c:Boolean;const a,b:Vec2):Vec2;overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _Ifthen(c:Boolean;const a,b:Vec3):Vec3;overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
function _Ifthen(c:Boolean;const a,b:Vec4):Vec4;overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
/// <summary>
/// Available only in the fragment shader, dFdx and dFdy return the partial derivative of expression p in x and y, respectively.
/// Deviatives are calculated using local differencing.
/// Expressions that imply higher order derivatives such as dFdx(dFdx(n)) have undefined results,
// as do mixed-order derivatives such as dFdx(dFdy(n)).
// It is assumed that the expression p is continuous and therefore,
// expressions evaluated via non-uniform control flow may be undefined.
/// </summary>
//function dFdx(a:TVecType):TVecType;
//function dFdx(a:Vec2):Vec2;
//function dFdx(a:Vec3):Vec3;
//function dFdx(a:Vec4):Vec4;
function _fwidth(const a: Vec2): TVecType;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _fwidth(const a: Vec3): TVecType;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _fwidth(const a: Vec4): TVecType;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
// Created by inigo quilez - iq/2013
// License Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
function _hash(n:Double):Double;overload;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _hash(const n:vec2):vec2;overload;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _hash(const n:vec3):vec3;overload;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _hash(const n:vec4):vec4;overload;{$IFDEF DO_INLINE} inline;{$ENDIF} overload;
function _lerp(a,b : TVecType; rel : TVecType) : TVecType;
procedure _vect2sArrayCopy(var source,target : Vec2sArray);
const
vec2Black:Vec2=(x:0;y:0);
vec2White:Vec2=(x:1;y:1);
vec2Gray:Vec2=(x:0.5;y:0.5);
vec2_3_3:Vec2=(x:3;y:3);
vec3Black:Vec3=(x:0;y:0;z:0);
vec3White:Vec3=(x:1;y:1;z:1);
vec3Gray:Vec3=(x:0.5;y:0.5;z:0.5);
vec3Green:Vec3=(x:0;y:1;z:0);
vecBlack:Vec3=(x:0;y:0;z:0);
vecWhite:Vec3=(x:1;y:1;z:1);
vec3Red:Vec3=(x:1;y:0;z:0);
vec4Black:Vec4=(x:0;y:0;z:0;w:0);
vec4White:Vec4=(x:1;y:1;z:1;w:1);
vec4Gray:Vec4=(x:0.5;y:0.5;z:0.5;w:0.5);
implementation
function Mat3Identity : Mat3;
begin
result := Mat3.Create( 1,0,0,
0,1,0,
0,0,1
);
end;
function Mat4Identity : Mat4;
begin
result := Mat4.Create( 1,0,0,0,
0,1,0,0,
0,0,1,0,
0,0,0,1
);
end;
function Mat4CreateLookAtDirLH(source,direction,ceiling : Vec3) : Mat4;
var
ZAxis, XAxis, YAxis: vec3;
begin
ZAxis := - direction.Normalize^;
XAxis := Ceiling.Cross(ZAxis).Normalize^;
YAxis := ZAxis.Cross(XAxis);
Result := Mat4Identity;
Result.r1.x := XAxis.X;
Result.r1.y := YAxis.X;
Result.r1.z := ZAxis.X;
Result.r2.x := XAxis.Y;
Result.r2.y := YAxis.Y;
Result.r2.z := ZAxis.Y;
Result.r3.x := XAxis.Z;
Result.r3.y := YAxis.Z;
Result.r3.z := ZAxis.Z;
Result.r4.x := - XAxis.Dot(source);
Result.r4.y := - YAxis.Dot(source);
Result.r4.z := - ZAxis.Dot(source);
end;
function Mat4CreatePerspectiveFovLH(const FOV, Aspect, ZNear, ZFar: Single;
const HorizontalFOV: Boolean = False): Mat4;
var
XScale, YScale: Single;
begin
if HorizontalFOV then
begin
XScale := 1 / Tan(FOV / 2);
YScale := XScale / Aspect;
end else
begin
YScale := 1 / Tan(FOV / 2);
XScale := YScale / Aspect;
end;
Result := Mat4Identity;
Result.r1.x := XScale;
Result.r2.y := YScale;
Result.r3.z := ZFar / (ZFar - ZNear);
Result.r3.w := 1;
Result.r4.z := -ZNear * ZFar / (ZFar - ZNear);
Result.r4.w := 0;
end;
function Mat4CreateRotationX(angle : single): Mat4;
var
Sine, Cosine: Single;
begin
Sine := System.sin(angle);
Cosine := System.cos(angle);
Result := Mat4Identity;
Result.r2.y := Cosine;
Result.r2.z := Sine;
Result.r3.y := - Result.r2.z;
Result.r3.z := Result.r2.y;
end;
function Mat4CreateRotationY(angle : single): Mat4;
var
Sine, Cosine: Single;
begin
Sine := System.sin(angle);
Cosine := System.cos(angle);
Result := Mat4Identity;
Result.r1.x := Cosine;
Result.r1.z := - Sine;
Result.r3.x := - Result.r1.z;
Result.r3.z := Result.r1.x;
end;
function Mat4CreateTranslation(translation : vec3) : Mat4;
begin
Result := Mat4Identity;
Result.r4.x := translation.X;
Result.r4.y := translation.Y;
Result.r4.z := translation.Z;
end;
function Mat4CreateRotationZ(angle : single): Mat4;
var
Sine, Cosine: Single;
begin
Sine := System.sin(angle);
Cosine := System.cos(angle);
Result := Mat4Identity;
Result.r1.x := Cosine;
Result.r1.y := Sine;
Result.r2.x := - Result.r1.y;
Result.r2.y := Result.r1.x;
end;
function Mat4CreateOrthoOffCenterRH(Left, Top, Right, Bottom, ZNear, ZFar: Single): Mat4;
begin
Result := Mat4Identity;
Result.r1.x := 2 / (Right - Left);
Result.r2.y := 2 / (Top - Bottom);
Result.r3.z := 1 / (ZFar - ZNear);
Result.r4.x := (Left + Right) / (Left - Right);
Result.r4.y := (Top + Bottom) / (Bottom - Top);
Result.r4.z := ZNear / (ZNear - ZFar);
end;
function Mat3CreateRotation(angle : single) : Mat3;
var
Sine, Cosine: Single;
begin
Sine := System.sin(angle);
Cosine := System.cos(angle);
Result := Mat3Identity;
Result.r1.x := Cosine;
Result.r1.y := Sine;
Result.r2.x := -Sine;
Result.r2.y := Cosine;
end;
function Mat3CreateTranslation(deltax, deltay : TVecType) : Mat3;
begin
result := Mat3Identity;
result.r3.x := deltax;
result.r3.y := deltay;
end;
function Mat3CreateScaling(scalex, scaley : TVecType) : Mat3;
begin
result := Mat3Identity;
result.r1.x := scalex;
result.r2.y := scaley;
end;
function _EnsureRange(const AValue, AMin, AMax: Single): Single;overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
begin
Result := AValue;
assert(AMin <= AMax);
if Result < AMin then
Result := AMin;
if Result > AMax then
Result := AMax;
end;
function _EnsureRange(const AValue, AMin, AMax: Double): Double;overload;{$IFDEF DO_INLINE} inline;{$ENDIF}
begin
Result := AValue;
assert(AMin <= AMax);
if Result < AMin then
Result := AMin;
if Result > AMax then
Result := AMax;
end;
{
function _fmod(a, b: extended): extended;
begin
if IsZero(b) then
Exit(0);
Result := a - b * floor(a / b);
end;
function _fmod(a, b: double): double;
begin
if IsZero(b) then
Exit(0);
Result := a - b * floor(a / b);
end;
}
function _fmod(a, b: single): single;overload; {$IFDEF DO_INLINE} inline;{$ENDIF}
begin
if IsZero(b) then
Exit(0);
Result := a - b * {math.floor}trunc(a / b);
end;
function _fmods(a, b: double): double;overload;
begin
if IsZero(b) then
Exit(0);
if a>1e10 then
Exit(0);
if a<-1e10 then
Exit(0);
Result := a - b * math.floor(a / b);
end;
function _fmod(a, b: double): double;overload;
{$IFDEF CPUx86}
asm
fld qword ptr[b]
fld qword ptr[a]
@r:
fprem
fstsw ax
sahf
jp @r
fstp st(1)
end;
{$ELSE}
begin
if IsZero(b) then
Exit(0);
// if a>1e10 then
// Exit(0);
// if a<-1e10 then
// Exit(0);
Result := a - b * {math.floor}trunc(a / b);
end;
{$ENDIF}
/// <summary>
/// pow returns the value of x raised to the y power. i.e., xy. Results are undefined if x0 or if x0 and y0.
/// </summary>
function _pow(x,y:double):double;
begin
if IsNaN(x) then
Exit(0.000001);
if x<0 then
x := -x;
if (x=0) and (y<0) then
Exit(0.000001);
Result := Math.Power(x,y)
end;
function _radians(degrees: double): double;
begin
Result := (pi / 180) * degrees;
end;
function _degrees(radians: double): double;
begin
Result := (180 / pi) * radians;
end;
function _exp2(x: double): double;
begin
Result := Power(2,x);
end;
function _log(x: double): double;overload;
begin
if x<0 then
x := -x
else
if x=0 then
exit(0);
Result := ln(x);
end;
function _log(x: vec2): vec2;overload;
begin
Result.x := ln(x.x);
Result.y := ln(x.y);
end;
function _log(x: vec3): vec3;overload;
begin
Result.x := ln(x.x);
Result.y := ln(x.y);
Result.z := ln(x.z);
end;
function _log2(x: single): single;
begin
if x<0 then
x := -x
else
if x=0 then
exit(0);
Result := Math.log2(x);
end;
function _log2(x: double): double;
begin
if x<0 then
x := -x
else
if x=0 then
exit(0);
Result := Math.log2(x);
end;
function _inversesqrt(x: single): single;
begin
if x=0 then
Exit(0)
else
if x<0 then
x:=-x;
Result := 1 / System.Sqrt(x);
end;
function _inversesqrt(x: double): double;
begin
if x=0 then
Exit(0)
else
if x<0 then
x:=-x;
Result := 1 / System.Sqrt(x);
end;
(*
// taken from:
// http://delphigamedev.com/forums/viewtopic.php?f=11&t=130
// it actually contains a bug, because this only works for 32 bits floats
function _inversesqrt(x: single): single;
var
XHalf: Single;
I: Integer Absolute X;
X2: Single Absolute I;
XB: Single;
begin
XB:= X;
XHalf:= 0.5 * X;
I:= $5f3759df - (I SHR 1);
X:= X2 * (1.5 - XHalf * X2 * X2);
Result:= XB * X;
end;
function _inversesqrt(x: double): double;
var
XHalf: Double;
I: Int64 Absolute X;
X2: Double Absolute I;
XB: Double;
begin
XB:= X;
XHalf:= 0.5 * X;
I:= $5fe6eb50c7b537a9 - (I SHR 1);
X:= X2 * (1.5 - XHalf * X2 * X2);
Result:= XB * X;
end;
*)
function _sign(x: double): double;
begin
if x > 0 then
Result := 1
else if x < 0 then
Result := -1
else
Result := 0;
end;
function _fract(x: double): double;
begin
// Result := x - Math.Floor(x);
// if IsNan(x) then Exit(0);
// if x>1e30 then
// exit(0);
// if x<-1e30 then
// exit(0);
Result := Trunc(X);
if (X < 0) and (X - Result <> 0) then
Result := Result-1;
Result := x - Result;
end;
function _fract(const a: vec2): vec2;
begin
// Result.x := x.x - Math.Floor(x.x);
// Result.y := x.y - Math.Floor(x.y);
Result.x := Trunc(a.x); if (a.x < 0) and (a.x - Result.x<>0) then Result.x := Result.x -1; Result.x := a.x - Result.x;
Result.y := Trunc(a.y); if (a.y < 0) and (a.y - Result.y<>0) then Result.y := Result.y -1; Result.y := a.y - Result.y;
end;
function _fract(const a: vec3): vec3;
begin
// Result.x := x.x - Math.Floor(x.x);
// Result.y := x.y - Math.Floor(x.y);
// Result.z := x.z - Math.Floor(x.z);
Result.x := Trunc(a.x); if (a.x < 0) and (a.x - Result.x<>0) then Result.x := Result.x -1; Result.x := a.x - Result.x;
Result.y := Trunc(a.y); if (a.y < 0) and (a.y - Result.y<>0) then Result.y := Result.y -1; Result.y := a.y - Result.y;
Result.z := Trunc(a.z); if (a.z < 0) and (a.z - Result.z<>0) then Result.z := Result.z -1; Result.z := a.z - Result.z;
end;
function _fract(const a: vec4): vec4;
begin
// Result.x := x.x - Math.Floor(x.x);
// Result.y := x.y - Math.Floor(x.y);
// Result.z := x.z - Math.Floor(x.z);
// Result.w := x.w - Math.Floor(x.w);
Result.x := Trunc(a.x); if (a.x < 0) and (a.x - Result.x<>0) then Result.x := Result.x -1; Result.x := a.x - Result.x;
Result.y := Trunc(a.y); if (a.y < 0) and (a.y - Result.y<>0) then Result.y := Result.y -1; Result.y := a.y - Result.y;
Result.z := Trunc(a.z); if (a.z < 0) and (a.z - Result.z<>0) then Result.z := Result.z -1; Result.z := a.z - Result.z;
Result.w := Trunc(a.w); if (a.w < 0) and (a.w - Result.w<>0) then Result.w := Result.w -1; Result.w := a.w - Result.w;
end;
//function _floor(x: Double): Double;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return x - cmath::floor(x); }
//begin
// Result := Math.Floor(x);
//end;
function _floor(const a: Vec2): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return x - cmath::floor(x); }
begin
// Result.x :=Math.Floor(x.x);
// Result.y :=Math.Floor(x.y);
Result.x := Trunc(a.x); if (a.x < 0) and (a.x-Result.x<>0) then Result.x := Result.x-1;
Result.y := Trunc(a.y); if (a.y < 0) and (a.y-Result.y<>0) then Result.y := Result.y-1;
end;
function _floor(const a: Vec3): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return x - cmath::floor(x); }
begin
{ Result.x := Math.Floor(x.x);
Result.y := Math.Floor(x.y);
Result.z := Math.Floor(x.z);
}
// Result.x := IntegerTrunc(X.x); if Frac(X.x) < 0 then Result.x := Result.x-1;
// Result.y := IntegerTrunc(X.y); if Frac(X.y) < 0 then Result.y := Result.y-1;
// Result.z := IntegerTrunc(X.z); if Frac(X.z) < 0 then Result.z := Result.z-1;
Result.x := Trunc(a.x); if (a.x < 0) and (a.x-Result.x<>0) then Result.x := Result.x-1;
Result.y := Trunc(a.y); if (a.y < 0) and (a.y-Result.y<>0) then Result.y := Result.y-1;
Result.z := Trunc(a.z); if (a.z < 0) and (a.z-Result.z<>0) then Result.z := Result.z-1;
end;
function _floor(const a: Vec4): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return x - cmath::floor(x); }
begin
{
Result.x := Math.Floor(x.x);
Result.y := Math.Floor(x.y);
Result.z := Math.Floor(x.z);
Result.w := Math.Floor(x.w);
}
// Result.x := IntegerTrunc(X.x); if Frac(X.x) < 0 then Result.x := Result.x-1;
// Result.y := IntegerTrunc(X.y); if Frac(X.y) < 0 then Result.y := Result.y-1;
// Result.z := IntegerTrunc(X.z); if Frac(X.z) < 0 then Result.z := Result.z-1;
// Result.w := IntegerTrunc(X.w); if Frac(X.w) < 0 then Result.w := Result.w-1;
Result.x := Trunc(a.x); if (a.x < 0) and (a.x-Result.x<>0) then Result.x := Result.x-1;
Result.y := Trunc(a.y); if (a.y < 0) and (a.y-Result.y<>0) then Result.y := Result.y-1;
Result.z := Trunc(a.z); if (a.z < 0) and (a.z-Result.z<>0) then Result.z := Result.z-1;
Result.w := Trunc(a.w); if (a.w < 0) and (a.w-Result.w<>0) then Result.w := Result.w-1;
end;
function _mod(a, b: double): double;
{$IFDEF CPUx86}
asm
fld qword ptr[b]
fld qword ptr[a]
@r:
fprem
fstsw ax
sahf
jp @r
fstp st(1)
end;
{$ELSE}
begin
if IsZero(b) then
Exit(0);
Result := a - b * math.Floor(a / b);
end;
{$ENDIF}
function _mod(const a, b: Vec2): Vec2;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return T(cmath::fmod(x, y)); }
begin
Result.x := _fMod(a.x, b.x);
Result.y := _fMod(a.y, b.y);
end;
function _mod(const a, b: Vec3): Vec3;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return T(cmath::fmod(x, y)); }
begin
Result.x := _fmod(a.x, b.x);
Result.y := _fmod(a.y, b.y);
Result.z := _fmod(a.z, b.z);
end;
function _mod(const a, b: Vec4): Vec4;{$IFDEF DO_INLINE} inline;{$ENDIF} overload; { return T(cmath::fmod(x, y)); }
begin
Result.x := _fmod(a.x, b.x);
Result.y := _fmod(a.y, b.y);
Result.z := _fmod(a.z, b.z);
Result.w := _fmod(a.w, b.w);
end;