201 lines
6.6 KiB
C++
201 lines
6.6 KiB
C++
#ifndef _MATH_HPP
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#define _MATH_HPP
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#include <cmath>
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namespace yasim {
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class Math
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{
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public:
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// Dumb utilities
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static inline float clamp(float val, float min, float max) {
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if(val < min) return min;
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if(val > max) return max;
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return val;
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}
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// Simple wrappers around library routines
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static inline float abs(float f) { return (float)::fabs(f); }
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static inline float sqrt(float f) { return (float)::sqrt(f); }
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static inline float ceil(float f) { return (float)::ceil(f); }
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static inline float sin(float f) { return (float)::sin(f); }
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static inline float cos(float f) { return (float)::cos(f); }
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static inline float tan(float f) { return (float)::tan(f); }
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static inline float atan(float f) { return (float)::atan(f); }
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static inline float atan2(float y, float x) { return (float)::atan2(y,x); }
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static inline float asin(float f) { return (float)::asin(f); }
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static inline float acos(float f) { return (float)::acos(f); }
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static inline float exp(float f) { return (float)::exp(f); }
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static inline float sqr(float f) { return f*f; }
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// Takes two args and runs afoul of the Koenig rules.
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static inline float pow(double base, double exp) { return (float)::pow(base, exp); }
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// double variants of the above
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static inline double abs(double f) { return ::fabs(f); }
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static inline double sqrt(double f) { return ::sqrt(f); }
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static inline double ceil(double f) { return ::ceil(f); }
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static inline double sin(double f) { return ::sin(f); }
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static inline double cos(double f) { return ::cos(f); }
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static inline double tan(double f) { return ::tan(f); }
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static inline double atan2(double y, double x) { return ::atan2(y,x); }
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static inline double floor(double x) { return ::floor(x); }
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// Some 3D vector stuff. In all cases, it is permissible for the
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// "out" vector to be the same as one of the inputs.
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static inline void set3(const float* v, float* out) {
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out[0] = v[0];
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out[1] = v[1];
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out[2] = v[2];
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}
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static void zero3(float* out) { out[0] = out[1] = out[2] = 0; }
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static inline float dot3(const float* a, const float* b) {
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return a[0]*b[0] + a[1]*b[1] + a[2]*b[2];
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}
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static inline void cross3(const float* a, const float* b, float* out) {
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float ax=a[0], ay=a[1], az=a[2];
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float bx=b[0], by=b[1], bz=b[2];
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out[0] = ay*bz - by*az;
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out[1] = az*bx - bz*ax;
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out[2] = ax*by - bx*ay;
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}
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static inline void mul3(const float scalar, const float* v, float* out)
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{
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out[0] = scalar * v[0];
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out[1] = scalar * v[1];
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out[2] = scalar * v[2];
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}
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static inline void add3(const float* a, const float* b, float* out){
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out[0] = a[0] + b[0];
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out[1] = a[1] + b[1];
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out[2] = a[2] + b[2];
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}
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static inline void sub3(const float* a, const float* b, float* out) {
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out[0] = a[0] - b[0];
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out[1] = a[1] - b[1];
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out[2] = a[2] - b[2];
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}
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static inline float mag3(const float* v) {
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return sqrt(dot3(v, v));
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}
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static inline void unit3(const float* v, float* out) {
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float imag = 1/mag3(v);
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mul3(imag, v, out);
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}
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// Matrix array convention: 0 1 2
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// 3 4 5
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// 6 7 8
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// Multiply two matrices
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static void mmul33(const float* a, const float* b, float* out) {
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float tmp[9];
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tmp[0] = a[0]*b[0] + a[1]*b[3] + a[2]*b[6];
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tmp[3] = a[3]*b[0] + a[4]*b[3] + a[5]*b[6];
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tmp[6] = a[6]*b[0] + a[7]*b[3] + a[8]*b[6];
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tmp[1] = a[0]*b[1] + a[1]*b[4] + a[2]*b[7];
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tmp[4] = a[3]*b[1] + a[4]*b[4] + a[5]*b[7];
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tmp[7] = a[6]*b[1] + a[7]*b[4] + a[8]*b[7];
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tmp[2] = a[0]*b[2] + a[1]*b[5] + a[2]*b[8];
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tmp[5] = a[3]*b[2] + a[4]*b[5] + a[5]*b[8];
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tmp[8] = a[6]*b[2] + a[7]*b[5] + a[8]*b[8];
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for(int i=0; i<9; ++i)
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out[i] = tmp[i];
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}
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// Multiply by vector
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static inline void vmul33(const float* m, const float* v, float* out) {
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float x = v[0], y = v[1], z = v[2];
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out[0] = x*m[0] + y*m[1] + z*m[2];
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out[1] = x*m[3] + y*m[4] + z*m[5];
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out[2] = x*m[6] + y*m[7] + z*m[8];
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}
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// Multiply the vector by the matrix transpose. Or pre-multiply the
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// matrix by v as a row vector. Same thing.
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static inline void tmul33(const float* m, const float* v, float* out) {
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float x = v[0], y = v[1], z = v[2];
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out[0] = x*m[0] + y*m[3] + z*m[6];
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out[1] = x*m[1] + y*m[4] + z*m[7];
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out[2] = x*m[2] + y*m[5] + z*m[8];
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}
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/// Invert symmetric matrix; ~1/3 less calculations due to symmetry
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static void invert33_sym(const float* m, float* out) {
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// Compute the inverse as the adjoint matrix times 1/(det M).
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// A, B ... I are the cofactors of a b c
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// d e f
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// g h i
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// symetric: d=b, g=c, h=f
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float a=m[0], b=m[1], c=m[2];
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float e=m[4], f=m[5];
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float i=m[8];
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float A = (e*i - f*f);
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float B = -(b*i - c*f);
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float C = (b*f - c*e);
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float E = (a*i - c*c);
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float F = -(a*f - c*b);
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float I = (a*e - b*b);
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float id = 1/(a*A + b*B + c*C);
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out[0] = id*A; out[1] = id*B; out[2] = id*C;
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out[3] = out[1]; out[4] = id*E; out[5] = id*F;
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out[6] = out[2]; out[7] = out[5]; out[8] = id*I;
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}
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// Transpose matrix (for an orthonormal orientation matrix, this
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// is the same as the inverse).
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static inline void trans33(const float* m, float* out) {
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// 0 1 2 Elements 0, 4, and 8 are the same
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// 3 4 5 Swap elements 1/3, 2/6, and 5/7
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// 6 7 8
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out[0] = m[0];
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out[4] = m[4];
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out[8] = m[8];
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float tmp = m[1];
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out[1] = m[3];
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out[3] = tmp;
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tmp = m[2];
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out[2] = m[6];
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out[6] = tmp;
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tmp = m[5];
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out[5] = m[7];
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out[7] = tmp;
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}
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// Generates an orthonormal basis:
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// xOut becomes the unit vector in the direction of x
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// yOut is perpendicular to xOut in the x/y plane
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// zOut becomes the unit vector: (xOut cross yOut)
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static void ortho33(const float* x, const float* y,
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float* xOut, float* yOut, float* zOut) {
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float x0[3], y0[3];
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set3(x, x0);
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set3(y, y0);
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unit3(x0, xOut);
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cross3(xOut, y0, zOut);
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unit3(zOut, zOut);
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cross3(zOut, xOut, yOut);
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}
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};
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}; // namespace yasim
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#endif // _MATH_HPP
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