#ifndef _MATH_HPP
#define _MATH_HPP
+#include <math.h>
+
namespace yasim {
class Math
{
public:
// Dumb utilities
- static float clamp(float val, float min, float max);
+ static inline float clamp(float val, float min, float max) {
+ if(val < min) return min;
+ if(val > max) return max;
+ return val;
+ }
// Simple wrappers around library routines
- static float abs(float f);
- static float sqrt(float f);
- static float ceil(float f);
- static float sin(float f);
- static float cos(float f);
- static float tan(float f);
- static float atan(float f);
- static float atan2(float y, float x);
- static float asin(float f);
- static float acos(float f);
- static float exp(float f);
- static float sqr(float f) {return f*f;}
+ static inline float abs(float f) { return (float)::fabs(f); }
+ static inline float sqrt(float f) { return (float)::sqrt(f); }
+ static inline float ceil(float f) { return (float)::ceil(f); }
+ static inline float sin(float f) { return (float)::sin(f); }
+ static inline float cos(float f) { return (float)::cos(f); }
+ static inline float tan(float f) { return (float)::tan(f); }
+ static inline float atan(float f) { return (float)::atan(f); }
+ static inline float atan2(float y, float x) { return (float)::atan2(y,x); }
+ static inline float asin(float f) { return (float)::asin(f); }
+ static inline float acos(float f) { return (float)::acos(f); }
+ static inline float exp(float f) { return (float)::exp(f); }
+ static inline float sqr(float f) { return f*f; }
// Takes two args and runs afoul of the Koenig rules.
- static float pow(double base, double exp);
+ static inline float pow(double base, double exp) { return (float)::pow(base, exp); }
// double variants of the above
- static double abs(double f);
- static double sqrt(double f);
- static double ceil(double f);
- static double sin(double f);
- static double cos(double f);
- static double tan(double f);
- static double atan2(double y, double x);
- static double floor(double x);
+ static inline double abs(double f) { return ::fabs(f); }
+ static inline double sqrt(double f) { return ::sqrt(f); }
+ static inline double ceil(double f) { return ::ceil(f); }
+ static inline double sin(double f) { return ::sin(f); }
+ static inline double cos(double f) { return ::cos(f); }
+ static inline double tan(double f) { return ::tan(f); }
+ static inline double atan2(double y, double x) { return ::atan2(y,x); }
+ static inline double floor(double x) { return ::floor(x); }
// Some 3D vector stuff. In all cases, it is permissible for the
// "out" vector to be the same as one of the inputs.
- static void set3(float* v, float* out);
- static float dot3(float* a, float* b);
- static void cross3(float* a, float* b, float* out);
- static void mul3(float scalar, float* v, float* out);
- static void add3(float* a, float* b, float* out);
- static void sub3(float* a, float* b, float* out);
- static float mag3(float* v);
- static void unit3(float* v, float* out);
+ static inline void set3(float* v, float* out) {
+ out[0] = v[0];
+ out[1] = v[1];
+ out[2] = v[2];
+ }
+
+ static inline float dot3(float* a, float* b) {
+ return a[0]*b[0] + a[1]*b[1] + a[2]*b[2];
+ }
+
+ static inline void cross3(float* a, float* b, float* out) {
+ float ax=a[0], ay=a[1], az=a[2];
+ float bx=b[0], by=b[1], bz=b[2];
+ out[0] = ay*bz - by*az;
+ out[1] = az*bx - bz*ax;
+ out[2] = ax*by - bx*ay;
+ }
+
+ static inline void mul3(float scalar, float* v, float* out)
+ {
+ out[0] = scalar * v[0];
+ out[1] = scalar * v[1];
+ out[2] = scalar * v[2];
+ }
+
+ static inline void add3(float* a, float* b, float* out){
+ out[0] = a[0] + b[0];
+ out[1] = a[1] + b[1];
+ out[2] = a[2] + b[2];
+ }
+
+ static inline void sub3(float* a, float* b, float* out) {
+ out[0] = a[0] - b[0];
+ out[1] = a[1] - b[1];
+ out[2] = a[2] - b[2];
+ }
+
+ static inline float mag3(float* v) {
+ return sqrt(dot3(v, v));
+ }
+
+ static inline void unit3(float* v, float* out) {
+ float imag = 1/mag3(v);
+ mul3(imag, v, out);
+ }
// Matrix array convention: 0 1 2
// 3 4 5
// 6 7 8
// Multiply two matrices
- static void mmul33(float* a, float* b, float* out);
+ static void mmul33(float* a, float* b, float* out) {
+ float tmp[9];
+ tmp[0] = a[0]*b[0] + a[1]*b[3] + a[2]*b[6];
+ tmp[3] = a[3]*b[0] + a[4]*b[3] + a[5]*b[6];
+ tmp[6] = a[6]*b[0] + a[7]*b[3] + a[8]*b[6];
+
+ tmp[1] = a[0]*b[1] + a[1]*b[4] + a[2]*b[7];
+ tmp[4] = a[3]*b[1] + a[4]*b[4] + a[5]*b[7];
+ tmp[7] = a[6]*b[1] + a[7]*b[4] + a[8]*b[7];
+
+ tmp[2] = a[0]*b[2] + a[1]*b[5] + a[2]*b[8];
+ tmp[5] = a[3]*b[2] + a[4]*b[5] + a[5]*b[8];
+ tmp[8] = a[6]*b[2] + a[7]*b[5] + a[8]*b[8];
+
+ for(int i=0; i<9; ++i)
+ out[i] = tmp[i];
+ }
// Multiply by vector
- static void vmul33(float* m, float* v, float* out);
+ static inline void vmul33(float* m, float* v, float* out) {
+ float x = v[0], y = v[1], z = v[2];
+ out[0] = x*m[0] + y*m[1] + z*m[2];
+ out[1] = x*m[3] + y*m[4] + z*m[5];
+ out[2] = x*m[6] + y*m[7] + z*m[8];
+ }
// Multiply the vector by the matrix transpose. Or pre-multiply the
// matrix by v as a row vector. Same thing.
- static void tmul33(float* m, float* v, float* out);
+ static inline void tmul33(float* m, float* v, float* out) {
+ float x = v[0], y = v[1], z = v[2];
+ out[0] = x*m[0] + y*m[3] + z*m[6];
+ out[1] = x*m[1] + y*m[4] + z*m[7];
+ out[2] = x*m[2] + y*m[5] + z*m[8];
+ }
// Invert matrix
- static void invert33(float* m, float* out);
+ static void invert33(float* m, float* out) {
+ // Compute the inverse as the adjoint matrix times 1/(det M).
+ // A, B ... I are the cofactors of a b c
+ // d e f
+ // g h i
+ float a=m[0], b=m[1], c=m[2];
+ float d=m[3], e=m[4], f=m[5];
+ float g=m[6], h=m[7], i=m[8];
+
+ float A = (e*i - h*f);
+ float B = -(d*i - g*f);
+ float C = (d*h - g*e);
+ float D = -(b*i - h*c);
+ float E = (a*i - g*c);
+ float F = -(a*h - g*b);
+ float G = (b*f - e*c);
+ float H = -(a*f - d*c);
+ float I = (a*e - d*b);
+
+ float id = 1/(a*A + b*B + c*C);
+
+ out[0] = id*A; out[1] = id*D; out[2] = id*G;
+ out[3] = id*B; out[4] = id*E; out[5] = id*H;
+ out[6] = id*C; out[7] = id*F; out[8] = id*I;
+ }
// Transpose matrix (for an orthonormal orientation matrix, this
// is the same as the inverse).
- static void trans33(float* m, float* out);
+ static inline void trans33(float* m, float* out) {
+ // 0 1 2 Elements 0, 4, and 8 are the same
+ // 3 4 5 Swap elements 1/3, 2/6, and 5/7
+ // 6 7 8
+ out[0] = m[0];
+ out[4] = m[4];
+ out[8] = m[8];
+
+ float tmp = m[1];
+ out[1] = m[3];
+ out[3] = tmp;
+
+ tmp = m[2];
+ out[2] = m[6];
+ out[6] = tmp;
+
+ tmp = m[5];
+ out[5] = m[7];
+ out[7] = tmp;
+ }
// Generates an orthonormal basis:
// xOut becomes the unit vector in the direction of x
// yOut is perpendicular to xOut in the x/y plane
// zOut becomes the unit vector: (xOut cross yOut)
static void ortho33(float* x, float* y,
- float* xOut, float* yOut, float* zOut);
+ float* xOut, float* yOut, float* zOut) {
+ float x0[3], y0[3];
+ set3(x, x0);
+ set3(y, y0);
+
+ unit3(x0, xOut);
+ cross3(xOut, y0, zOut);
+ unit3(zOut, zOut);
+ cross3(zOut, xOut, yOut);
+ }
};
}; // namespace yasim
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