77 lines
2.4 KiB
C++
77 lines
2.4 KiB
C++
#ifndef HGL_ALGORITHM_MATH_FAST_TRIANGLE_FUNCTION_INCLUDE
|
||
#define HGL_ALGORITHM_MATH_FAST_TRIANGLE_FUNCTION_INCLUDE
|
||
|
||
#include<hgl/math/MathConst.h>
|
||
#include<math.h>
|
||
namespace hgl
|
||
{
|
||
double Lsin(int angle); ///<低精度sin计算,注意传入的参数为角度而非弧度
|
||
double Lcos(int angle); ///<低精度cos计算,注意传入的参数为角度而非弧度
|
||
void Lsincos(int angle, double &s, double &c); ///<低精度sin+cos计算,注意传入的参数为角度而非弧度
|
||
|
||
/**
|
||
* Approximates acos(x) with a max absolute error of 9.0x10^-3.
|
||
* Valid in the range -1..1.
|
||
*/
|
||
inline const float Lacos(float x)
|
||
{
|
||
// Lagarde 2014, "Inverse trigonometric functions GPU optimization for AMD GCN architecture"
|
||
// This is the approximation of degree 1, with a max absolute error of 9.0x10^-3
|
||
float y = fabs(x);
|
||
float p = -0.1565827 * y + 1.570796;
|
||
p *= sqrt(1.0 - y);
|
||
return x >= 0.0 ? p : HGL_PI - p;
|
||
}
|
||
|
||
/**
|
||
* Approximates acos(x) with a max absolute error of 9.0x10^-3.
|
||
* Valid only in the range 0..1.
|
||
*/
|
||
inline const float LacosPositive(float x)
|
||
{
|
||
return (-0.1565827 * x + 1.570796) * sqrt(1.0 - x);
|
||
}
|
||
|
||
inline constexpr double ApproxSin(double angle)
|
||
{
|
||
return angle*(1.27323954f-angle*angle*(0.405284735f-angle*angle*(0.075133f-angle*angle*0.0078f)));
|
||
}
|
||
|
||
inline constexpr double ApproxCos(double angle)
|
||
{
|
||
return 1.27323954f-angle*angle*(0.405284735f-angle*angle*(0.075133f-angle*angle*0.0078f));
|
||
}
|
||
|
||
inline constexpr double ApproxAtan2(double x,double y)
|
||
{
|
||
return x/(1.27323954f+y*y*(0.405284735f+y*y*(0.075133f+y*y*0.0078f)));
|
||
}
|
||
|
||
inline constexpr double ApproxAtan(double z)
|
||
{
|
||
return z*(1.27323954f-z*z*(0.405284735f-z*z*(0.075133f-z*z*0.0078f)));
|
||
}
|
||
|
||
/**
|
||
* 低精度atan函数
|
||
*/
|
||
inline constexpr double Latan(double z)
|
||
{
|
||
constexpr double n1 = 0.97239411f;
|
||
constexpr double n2 = -0.19194795f;
|
||
|
||
return (n1 + n2 * z * z) * z;
|
||
}
|
||
|
||
double Latan2(double y, double x); ///<低精度atan2函数
|
||
|
||
/**
|
||
* 近似Pow2.2，使用此函数等于pow(x,2.2)
|
||
*/
|
||
inline constexpr double LPow22(double x)
|
||
{
|
||
return x*(1.12*x - 0.12);
|
||
}
|
||
}//namespace hgl
|
||
#endif//HGL_ALGORITHM_MATH_FAST_TRIANGLE_FUNCTION_INCLUDE
|