mirror of
https://github.com/bkaradzic/bx.git
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581 lines
14 KiB
C++
581 lines
14 KiB
C++
/*
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* Copyright 2011-2018 Branimir Karadzic. All rights reserved.
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* License: https://github.com/bkaradzic/bx#license-bsd-2-clause
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*/
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// FPU math lib
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#ifndef BX_MATH_H_HEADER_GUARD
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#define BX_MATH_H_HEADER_GUARD
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#include "bx.h"
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#include "uint32_t.h"
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namespace bx
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{
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extern const float kPi;
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extern const float kPi2;
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extern const float kInvPi;
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extern const float kPiHalf;
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extern const float kPiQuarter;
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extern const float kSqrt2;
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extern const float kLogNat10;
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extern const float kInvLogNat2;
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extern const float kLogNat2Hi;
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extern const float kLogNat2Lo;
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extern const float kE;
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extern const float kNearZero;
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extern const float kInfinity;
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extern const float kFloatMin;
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extern const float kFloatMax;
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///
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typedef float (*LerpFn)(float _a, float _b, float _t);
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///
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struct Handness
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{
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enum Enum
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{
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Left,
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Right,
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};
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};
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///
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struct NearFar
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{
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enum Enum
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{
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Default,
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Reverse,
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};
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};
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/// Returns converted the argument _deg to radians.
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///
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BX_CONST_FUNC float toRad(float _deg);
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/// Returns converted the argument _rad to degrees.
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///
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BX_CONST_FUNC float toDeg(float _rad);
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/// Reinterprets the bit pattern of _a as uint32_t.
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///
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BX_CONST_FUNC uint32_t floatToBits(float _a);
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/// Reinterprets the bit pattern of _a as float.
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///
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BX_CONST_FUNC float bitsToFloat(uint32_t _a);
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/// Reinterprets the bit pattern of _a as uint64_t.
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///
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BX_CONST_FUNC uint64_t doubleToBits(double _a);
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/// Reinterprets the bit pattern of _a as double.
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///
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BX_CONST_FUNC double bitsToDouble(uint64_t _a);
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/// Returns sortable floating point value.
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///
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BX_CONST_FUNC uint32_t floatFlip(uint32_t _value);
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/// Returns true if _f is a number that is NaN.
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///
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BX_CONST_FUNC bool isNan(float _f);
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/// Returns true if _f is a number that is NaN.
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///
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BX_CONST_FUNC bool isNan(double _f);
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/// Returns true if _f is not infinite and is not a NaN.
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///
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BX_CONST_FUNC bool isFinite(float _f);
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/// Returns true if _f is not infinite and is not a NaN.
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///
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BX_CONST_FUNC bool isFinite(double _f);
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/// Returns true if _f is infinite and is not a NaN.
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///
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BX_CONST_FUNC bool isInfinite(float _f);
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/// Returns true if _f is infinite and is not a NaN.
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///
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BX_CONST_FUNC bool isInfinite(double _f);
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/// Returns the largest integer value not greater than _f.
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///
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BX_CONST_FUNC float floor(float _f);
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/// Returns the smallest integer value not less than _f.
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///
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BX_CONST_FUNC float ceil(float _f);
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/// Returns the nearest integer value to _f, rounding halfway cases away from zero,
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///
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BX_CONST_FUNC float round(float _f);
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/// Returns linear interpolation between two values _a and _b.
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///
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BX_CONST_FUNC float lerp(float _a, float _b, float _t);
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/// Returns the sign of _a.
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///
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BX_CONST_FUNC float sign(float _a);
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/// Returns the absolute of _a.
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///
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BX_CONST_FUNC float abs(float _a);
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/// Returns the square of _a.
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///
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BX_CONST_FUNC float square(float _a);
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/// Returns the cosine of the argument _a.
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///
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BX_CONST_FUNC float sin(float _a);
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/// Returns hyperbolic sine of the argument _a.
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///
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BX_CONST_FUNC float sinh(float _a);
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/// Returns radian angle between -pi/2 and +pi/2 whose sine is _a.
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///
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BX_CONST_FUNC float asin(float _a);
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/// Returns the cosine of the argument _a.
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///
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BX_CONST_FUNC float cos(float _a);
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/// Returns hyperbolic cosine of the argument _a.
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///
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BX_CONST_FUNC float cosh(float _a);
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/// Returns radian angle between 0 and pi whose cosine is _a.
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///
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BX_CONST_FUNC float acos(float _a);
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/// Returns the circular tangent of the radian argument _a.
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///
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BX_CONST_FUNC float tan(float _a);
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/// Returns hyperbolic tangent of the argument _a.
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///
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BX_CONST_FUNC float tanh(float _a);
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/// Returns radian angle between -pi/2 and +pi/2 whose tangent is _a.
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///
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BX_CONST_FUNC float atan(float _a);
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/// Retruns the inverse tangent of _y/_x.
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///
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BX_CONST_FUNC float atan2(float _y, float _x);
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/// Computes _a raised to the _b power.
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///
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BX_CONST_FUNC float pow(float _a, float _b);
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/// Returns the result of multiplying _a by 2 raised to the power of the exponent.
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///
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BX_CONST_FUNC float ldexp(float _a, int32_t _b);
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/// Returns decomposed given floating point value _a into a normalized fraction and
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/// an integral power of two.
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///
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float frexp(float _a, int32_t* _outExp);
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/// Returns e (2.71828...) raised to the _a power.
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///
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BX_CONST_FUNC float exp(float _a);
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/// Returns 2 raised to the _a power.
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///
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BX_CONST_FUNC float exp2(float _a);
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/// Returns the base e (2.71828...) logarithm of _a.
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///
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BX_CONST_FUNC float log(float _a);
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/// Returns the base 2 logarithm of _a.
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///
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BX_CONST_FUNC float log2(float _a);
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/// Returns the square root of _a.
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///
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BX_CONST_FUNC float sqrt(float _a);
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/// Returns reciprocal square root of _a.
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///
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BX_CONST_FUNC float rsqrt(float _a);
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/// Returns the nearest integer not greater in magnitude than _a.
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///
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BX_CONST_FUNC float trunc(float _a);
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/// Returns the fractional (or decimal) part of _a, which is greater than or equal to 0
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/// and less than 1.
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///
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BX_CONST_FUNC float fract(float _a);
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/// Returns result of multipla and add (_a * _b + _c).
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///
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BX_CONST_FUNC float mad(float _a, float _b, float _c);
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/// Returns the floating-point remainder of the division operation _a/_b.
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///
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BX_CONST_FUNC float mod(float _a, float _b);
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///
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BX_CONST_FUNC bool equal(float _a, float _b, float _epsilon);
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///
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BX_CONST_FUNC bool equal(const float* _a, const float* _b, uint32_t _num, float _epsilon);
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///
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BX_CONST_FUNC float wrap(float _a, float _wrap);
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///
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BX_CONST_FUNC float step(float _edge, float _a);
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///
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BX_CONST_FUNC float pulse(float _a, float _start, float _end);
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///
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BX_CONST_FUNC float smoothStep(float _a);
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// References:
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// - Bias And Gain Are Your Friend
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// http://blog.demofox.org/2012/09/24/bias-and-gain-are-your-friend/
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// - http://demofox.org/biasgain.html
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///
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BX_CONST_FUNC float bias(float _time, float _bias);
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///
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BX_CONST_FUNC float gain(float _time, float _gain);
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///
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BX_CONST_FUNC float angleDiff(float _a, float _b);
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/// Returns shortest distance linear interpolation between two angles.
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///
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BX_CONST_FUNC float angleLerp(float _a, float _b, float _t);
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///
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void vec3Move(float* _result, const float* _a);
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///
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void vec3Abs(float* _result, const float* _a);
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///
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void vec3Neg(float* _result, const float* _a);
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///
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void vec3Add(float* _result, const float* _a, const float* _b);
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///
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void vec3Add(float* _result, const float* _a, float _b);
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///
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void vec3Sub(float* _result, const float* _a, const float* _b);
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///
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void vec3Sub(float* _result, const float* _a, float _b);
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///
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void vec3Mul(float* _result, const float* _a, const float* _b);
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///
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void vec3Mul(float* _result, const float* _a, float _b);
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///
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float vec3Dot(const float* _a, const float* _b);
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///
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void vec3Cross(float* _result, const float* _a, const float* _b);
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///
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float vec3Length(const float* _a);
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///
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void vec3Lerp(float* _result, const float* _a, const float* _b, float _t);
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///
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void vec3Lerp(float* _result, const float* _a, const float* _b, const float* _c);
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///
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float vec3Norm(float* _result, const float* _a);
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///
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void vec3Min(float* _result, const float* _a, const float* _b);
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///
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void vec3Max(float* _result, const float* _a, const float* _b);
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///
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void vec3Rcp(float* _result, const float* _a);
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/// Calculate tangent frame from normal.
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///
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void vec3TangentFrame(const float* _n, float* _t, float* _b);
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/// Calculate tangent frame from normal and angle.
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///
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void vec3TangentFrame(const float* _n, float* _t, float* _b, float _angle);
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///
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void vec3FromLatLong(float* _vec, float _u, float _v);
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/// Convert direction to 2D latitude and longitude.
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///
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/// @param[out] _outU U-coordinate.
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/// @param[out] _outV V-coordinate.
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/// @param[in] _dir Normalized direction vector.
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///
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void vec3ToLatLong(float* _outU, float* _outV, const float* _dir);
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///
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void quatIdentity(float* _result);
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///
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void quatMove(float* _result, const float* _a);
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///
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void quatMulXYZ(float* _result, const float* _qa, const float* _qb);
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///
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void quatMul(float* _result, const float* _qa, const float* _qb);
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///
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void quatInvert(float* _result, const float* _quat);
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///
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float quatDot(const float* _a, const float* _b);
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///
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void quatNorm(float* _result, const float* _quat);
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///
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void quatToEuler(float* _result, const float* _quat);
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///
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void quatRotateAxis(float* _result, const float* _axis, float _angle);
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///
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void quatRotateX(float* _result, float _ax);
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///
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void quatRotateY(float* _result, float _ay);
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///
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void quatRotateZ(float* _result, float _az);
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///
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void vec3MulQuat(float* _result, const float* _vec, const float* _quat);
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///
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void mtxIdentity(float* _result);
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///
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void mtxTranslate(float* _result, float _tx, float _ty, float _tz);
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///
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void mtxScale(float* _result, float _sx, float _sy, float _sz);
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///
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void mtxScale(float* _result, float _scale);
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///
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void mtxFromNormal(float* _result, const float* _normal, float _scale, const float* _pos);
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///
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void mtxFromNormal(float* _result, const float* _normal, float _scale, const float* _pos, float _angle);
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///
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void mtxQuat(float* _result, const float* _quat);
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///
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void mtxQuatTranslation(float* _result, const float* _quat, const float* _translation);
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///
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void mtxQuatTranslationHMD(float* _result, const float* _quat, const float* _translation);
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///
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void mtxLookAtLh(float* _result, const float* _eye, const float* _at, const float* _up = NULL);
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///
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void mtxLookAtRh(float* _result, const float* _eye, const float* _at, const float* _up = NULL);
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///
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void mtxLookAt(float* _result, const float* _eye, const float* _at, const float* _up = NULL);
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///
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void mtxProj(float* _result, float _ut, float _dt, float _lt, float _rt, float _near, float _far, bool _oglNdc);
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///
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void mtxProj(float* _result, const float _fov[4], float _near, float _far, bool _oglNdc);
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///
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void mtxProj(float* _result, float _fovy, float _aspect, float _near, float _far, bool _oglNdc);
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///
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void mtxProjLh(float* _result, float _ut, float _dt, float _lt, float _rt, float _near, float _far, bool _oglNdc);
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///
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void mtxProjLh(float* _result, const float _fov[4], float _near, float _far, bool _oglNdc);
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///
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void mtxProjLh(float* _result, float _fovy, float _aspect, float _near, float _far, bool _oglNdc);
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///
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void mtxProjRh(float* _result, float _ut, float _dt, float _lt, float _rt, float _near, float _far, bool _oglNdc);
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///
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void mtxProjRh(float* _result, const float _fov[4], float _near, float _far, bool _oglNdc);
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///
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void mtxProjRh(float* _result, float _fovy, float _aspect, float _near, float _far, bool _oglNdc);
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///
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void mtxProjInf(float* _result, const float _fov[4], float _near, bool _oglNdc);
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///
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void mtxProjInf(float* _result, float _ut, float _dt, float _lt, float _rt, float _near, bool _oglNdc);
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///
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void mtxProjInf(float* _result, float _fovy, float _aspect, float _near, bool _oglNdc);
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///
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void mtxProjInfLh(float* _result, float _ut, float _dt, float _lt, float _rt, float _near, bool _oglNdc);
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///
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void mtxProjInfLh(float* _result, const float _fov[4], float _near, bool _oglNdc);
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///
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void mtxProjInfLh(float* _result, float _fovy, float _aspect, float _near, bool _oglNdc);
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///
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void mtxProjInfRh(float* _result, float _ut, float _dt, float _lt, float _rt, float _near, bool _oglNdc);
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///
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void mtxProjInfRh(float* _result, const float _fov[4], float _near, bool _oglNdc);
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///
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void mtxProjInfRh(float* _result, float _fovy, float _aspect, float _near, bool _oglNdc);
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///
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void mtxProjRevInfLh(float* _result, float _ut, float _dt, float _lt, float _rt, float _near, bool _oglNdc);
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///
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void mtxProjRevInfLh(float* _result, const float _fov[4], float _near, bool _oglNdc);
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///
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void mtxProjRevInfLh(float* _result, float _fovy, float _aspect, float _near, bool _oglNdc);
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///
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void mtxProjRevInfRh(float* _result, float _ut, float _dt, float _lt, float _rt, float _near, bool _oglNdc);
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///
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void mtxProjRevInfRh(float* _result, const float _fov[4], float _near, bool _oglNdc);
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///
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void mtxProjRevInfRh(float* _result, float _fovy, float _aspect, float _near, bool _oglNdc);
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///
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void mtxOrtho(float* _result, float _left, float _right, float _bottom, float _top, float _near, float _far, float _offset, bool _oglNdc);
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///
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void mtxOrthoLh(float* _result, float _left, float _right, float _bottom, float _top, float _near, float _far, float _offset, bool _oglNdc);
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///
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void mtxOrthoRh(float* _result, float _left, float _right, float _bottom, float _top, float _near, float _far, float _offset, bool _oglNdc);
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///
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void mtxRotateX(float* _result, float _ax);
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///
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void mtxRotateY(float* _result, float _ay);
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///
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void mtxRotateZ(float* _result, float _az);
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///
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void mtxRotateXY(float* _result, float _ax, float _ay);
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///
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void mtxRotateXYZ(float* _result, float _ax, float _ay, float _az);
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///
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void mtxRotateZYX(float* _result, float _ax, float _ay, float _az);
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///
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void mtxSRT(float* _result, float _sx, float _sy, float _sz, float _ax, float _ay, float _az, float _tx, float _ty, float _tz);
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///
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void vec3MulMtx(float* _result, const float* _vec, const float* _mat);
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///
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void vec3MulMtxXyz0(float* _result, const float* _vec, const float* _mat);
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///
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void vec3MulMtxH(float* _result, const float* _vec, const float* _mat);
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///
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void vec4Mul(float* _result, const float* _a, const float* _b);
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///
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void vec4Mul(float* _result, const float* _a, float _b);
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///
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void vec4MulMtx(float* _result, const float* _vec, const float* _mat);
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///
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void mtxMul(float* _result, const float* _a, const float* _b);
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///
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void mtxTranspose(float* _result, const float* _a);
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///
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void mtx3Inverse(float* _result, const float* _a);
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///
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void mtxInverse(float* _result, const float* _a);
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/// Convert LH to RH projection matrix and vice versa.
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///
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void mtxProjFlipHandedness(float* _dst, const float* _src);
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/// Convert LH to RH view matrix and vice versa.
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///
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void mtxViewFlipHandedness(float* _dst, const float* _src);
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///
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void calcNormal(float _result[3], const float _va[3], const float _vb[3], const float _vc[3]);
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///
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void calcPlane(float _result[4], const float _va[3], const float _vb[3], const float _vc[3]);
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///
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void calcLinearFit2D(float _result[2], const void* _points, uint32_t _stride, uint32_t _numPoints);
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///
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void calcLinearFit3D(float _result[3], const void* _points, uint32_t _stride, uint32_t _numPoints);
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///
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void rgbToHsv(float _hsv[3], const float _rgb[3]);
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///
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void hsvToRgb(float _rgb[3], const float _hsv[3]);
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///
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BX_CONST_FUNC float toLinear(float _a);
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///
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BX_CONST_FUNC float toGamma(float _a);
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} // namespace bx
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#include "inline/math.inl"
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#endif // BX_MATH_H_HEADER_GUARD
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