From a4cf0b14abb17c313243d0fb84555aec2cef61a0 Mon Sep 17 00:00:00 2001 From: Mike Turvey Date: Tue, 7 Feb 2017 00:11:39 -0700 Subject: Merging math libraries --- redist/linmath.c | 219 +++++++++++++++++++++++++++++++++++++++++++++++++------ redist/linmath.h | 48 +++++++++++- 2 files changed, 241 insertions(+), 26 deletions(-) (limited to 'redist') diff --git a/redist/linmath.c b/redist/linmath.c index 60fbc21..ea44432 100644 --- a/redist/linmath.c +++ b/redist/linmath.c @@ -2,6 +2,7 @@ #include "linmath.h" #include +#include void cross3d( FLT * out, const FLT * a, const FLT * b ) { @@ -33,7 +34,7 @@ void scale3d( FLT * out, const FLT * a, FLT scalar ) void normalize3d( FLT * out, const FLT * in ) { - FLT r = 1./sqrtf( in[0] * in[0] + in[1] * in[1] + in[2] * in[2] ); + FLT r = ((FLT)1.) / FLT_SQRT(in[0] * in[0] + in[1] * in[1] + in[2] * in[2]); out[0] = in[0] * r; out[1] = in[1] * r; out[2] = in[2] * r; @@ -65,7 +66,7 @@ void copy3d( FLT * out, const FLT * in ) FLT magnitude3d( FLT * a ) { - return sqrt( a[0]*a[0] + a[1]*a[1] + a[2]*a[2] ); + return FLT_SQRT(a[0] * a[0] + a[1] * a[1] + a[2] * a[2]); } FLT anglebetween3d( FLT * a, FLT * b ) @@ -77,7 +78,7 @@ FLT anglebetween3d( FLT * a, FLT * b ) FLT dot = dot3d( a, b ); if( dot < -0.9999999 ) return LINMATHPI; if( dot > 0.9999999 ) return 0; - return acos( dot ); + return FLT_ACOS(dot); } /////////////////////////////////////QUATERNIONS////////////////////////////////////////// @@ -106,12 +107,12 @@ void quatfromeuler( FLT * q, const FLT * euler ) FLT Y = euler[1]/2.0f; //pitch FLT Z = euler[2]/2.0f; //yaw - FLT cx = cosf(X); - FLT sx = sinf(X); - FLT cy = cosf(Y); - FLT sy = sinf(Y); - FLT cz = cosf(Z); - FLT sz = sinf(Z); + FLT cx = FLT_COS(X); + FLT sx = FLT_SIN(X); + FLT cy = FLT_COS(Y); + FLT sy = FLT_SIN(Y); + FLT cz = FLT_COS(Z); + FLT sz = FLT_SIN(Z); //Correct according to //http://en.wikipedia.org/wiki/Conversion_between_MQuaternions_and_Euler_angles @@ -125,9 +126,9 @@ void quatfromeuler( FLT * q, const FLT * euler ) void quattoeuler( FLT * euler, const FLT * q ) { //According to http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles (Oct 26, 2009) - euler[0] = atan2( 2 * (q[0]*q[1] + q[2]*q[3]), 1 - 2 * (q[1]*q[1] + q[2]*q[2] ) ); - euler[1] = asin( 2 * (q[0] *q[2] - q[3]*q[1] ) ); - euler[2] = atan2( 2 * (q[0]*q[3] + q[1]*q[2]), 1 - 2 * (q[2]*q[2] + q[3]*q[3] ) ); + euler[0] = FLT_ATAN2(2 * (q[0] * q[1] + q[2] * q[3]), 1 - 2 * (q[1] * q[1] + q[2] * q[2])); + euler[1] = FLT_ASIN(2 * (q[0] * q[2] - q[3] * q[1])); + euler[2] = FLT_ATAN2(2 * (q[0] * q[3] + q[1] * q[2]), 1 - 2 * (q[2] * q[2] + q[3] * q[3])); } void quatfromaxisangle( FLT * q, const FLT * axis, FLT radians ) @@ -135,8 +136,8 @@ void quatfromaxisangle( FLT * q, const FLT * axis, FLT radians ) FLT v[3]; normalize3d( v, axis ); - FLT sn = sin(radians/2.0f); - q[0] = cos(radians/2.0f); + FLT sn = FLT_SIN(radians / 2.0f); + q[0] = FLT_COS(radians / 2.0f); q[1] = sn * v[0]; q[2] = sn * v[1]; q[3] = sn * v[2]; @@ -146,12 +147,12 @@ void quatfromaxisangle( FLT * q, const FLT * axis, FLT radians ) FLT quatmagnitude( const FLT * q ) { - return sqrt((q[0]*q[0])+(q[1]*q[1])+(q[2]*q[2])+(q[3]*q[3])); + return FLT_SQRT((q[0] * q[0]) + (q[1] * q[1]) + (q[2] * q[2]) + (q[3] * q[3])); } FLT quatinvsqmagnitude( const FLT * q ) { - return 1./((q[0]*q[0])+(q[1]*q[1])+(q[2]*q[2])+(q[3]*q[3])); + return ((FLT)1.)/((q[0]*q[0])+(q[1]*q[1])+(q[2]*q[2])+(q[3]*q[3])); } @@ -296,13 +297,13 @@ void quatslerp( FLT * q, const FLT * qa, const FLT * qb, FLT t ) if ( 1 - (cosTheta*cosTheta) <= 0 ) sinTheta = 0; else - sinTheta = sqrt(1 - (cosTheta*cosTheta)); + sinTheta = FLT_SQRT(1 - (cosTheta*cosTheta)); - FLT Theta = acos(cosTheta); //Theta is half the angle between the 2 MQuaternions + FLT Theta = FLT_ACOS(cosTheta); //Theta is half the angle between the 2 MQuaternions - if(fabs(Theta) < DEFAULT_EPSILON ) + if (FLT_FABS(Theta) < DEFAULT_EPSILON) quatcopy( q, qa ); - else if(fabs(sinTheta) < DEFAULT_EPSILON ) + else if (FLT_FABS(sinTheta) < DEFAULT_EPSILON) { quatadd( q, qa, qb ); quatscale( q, q, 0.5 ); @@ -311,10 +312,10 @@ void quatslerp( FLT * q, const FLT * qa, const FLT * qb, FLT t ) { FLT aside[4]; FLT bside[4]; - quatscale( bside, qb, sin( t * Theta ) ); - quatscale( aside, qa, sin((1-t)*Theta) ); + quatscale( bside, qb, FLT_SIN(t * Theta)); + quatscale( aside, qa, FLT_SIN((1 - t)*Theta)); quatadd( q, aside, bside ); - quatscale( q, q, 1./sinTheta ); + quatscale( q, q, ((FLT)1.)/sinTheta ); } } @@ -338,4 +339,176 @@ void quatrotatevector( FLT * vec3out, const FLT * quat, const FLT * vec3in ) } +// Matrix Stuff + +Matrix3x3 inverseM33(const Matrix3x3 mat) +{ + Matrix3x3 newMat; + for (int a = 0; a < 3; a++) + { + for (int b = 0; b < 3; b++) + { + newMat.val[a][b] = mat.val[a][b]; + } + } + + for (int i = 0; i < 3; i++) + { + for (int j = i + 1; j < 3; j++) + { + FLT tmp = newMat.val[i][j]; + newMat.val[i][j] = newMat.val[j][i]; + newMat.val[j][i] = tmp; + } + } + + return newMat; +} + +/////////////////////////////////////Matrix Rotations//////////////////////////////////// +//Originally from Stack Overflow +//Under cc by-sa 3.0 +// http://stackoverflow.com/questions/23166898/efficient-way-to-calculate-a-3x3-rotation-matrix-from-the-rotation-defined-by-tw +// Copyright 2014 by Campbell Barton +// Copyright 2017 by Michael Turvey + +/** +* Calculate a rotation matrix from 2 normalized vectors. +* +* v1 and v2 must be unit length. +*/ +void rotation_between_vecs_to_mat3(FLT m[3][3], const FLT v1[3], const FLT v2[3]) +{ + FLT axis[3]; + /* avoid calculating the angle */ + FLT angle_sin; + FLT angle_cos; + + cross3d(axis, v1, v2); + + angle_sin = normalize_v3(axis); + angle_cos = dot3d(v1, v2); + + if (angle_sin > FLT_EPSILON) { + axis_calc: + axis_angle_normalized_to_mat3_ex(m, axis, angle_sin, angle_cos); + } + else { + /* Degenerate (co-linear) vectors */ + if (angle_cos > 0.0f) { + /* Same vectors, zero rotation... */ + unit_m3(m); + } + else { + /* Colinear but opposed vectors, 180 rotation... */ + get_orthogonal_vector(axis, v1); + normalize_v3(axis); + angle_sin = 0.0f; /* sin(M_PI) */ + angle_cos = -1.0f; /* cos(M_PI) */ + goto axis_calc; + } + } +} + +void get_orthogonal_vector(FLT out[3], const FLT in[3]) +{ +#ifdef USE_DOUBLE + const FLT x = fabs(in[0]); + const FLT y = fabs(in[1]); + const FLT z = fabs(in[2]); +#else + const FLT x = fabsf(in[0]); + const FLT y = fabsf(in[1]); + const FLT z = fabsf(in[2]); +#endif + + if (x > y && x > z) + { + // x is dominant + out[0] = -in[1] - in[2]; + out[1] = in[0]; + out[2] = in[0]; + } + else if (y > z) + { + // y is dominant + out[0] = in[1]; + out[1] = -in[0] - in[2]; + out[2] = in[1]; + } + else + { + // z is dominant + out[0] = in[2]; + out[1] = in[2]; + out[2] = -in[0] - in[1]; + } +} + +void unit_m3(FLT mat[3][3]) +{ + mat[0][0] = 1; + mat[0][1] = 0; + mat[0][2] = 0; + mat[1][0] = 0; + mat[1][1] = 1; + mat[1][2] = 0; + mat[2][0] = 0; + mat[2][1] = 0; + mat[2][2] = 1; +} + + +FLT normalize_v3(FLT vect[3]) +{ + FLT distance = dot3d(vect, vect); + + if (distance < 1.0e-35f) + { + // distance is too short, just go to zero. + vect[0] = 0; + vect[1] = 0; + vect[2] = 0; + distance = 0; + } + else + { + distance = FLT_SQRT((FLT)distance); + scale3d(vect, vect, 1.0f / distance); + } + + return distance; +} + +/* axis must be unit length */ +void axis_angle_normalized_to_mat3_ex( + FLT mat[3][3], const FLT axis[3], + const FLT angle_sin, const FLT angle_cos) +{ + FLT nsi[3], ico; + FLT n_00, n_01, n_11, n_02, n_12, n_22; + + ico = (1.0f - angle_cos); + nsi[0] = axis[0] * angle_sin; + nsi[1] = axis[1] * angle_sin; + nsi[2] = axis[2] * angle_sin; + + n_00 = (axis[0] * axis[0]) * ico; + n_01 = (axis[0] * axis[1]) * ico; + n_11 = (axis[1] * axis[1]) * ico; + n_02 = (axis[0] * axis[2]) * ico; + n_12 = (axis[1] * axis[2]) * ico; + n_22 = (axis[2] * axis[2]) * ico; + + mat[0][0] = n_00 + angle_cos; + mat[0][1] = n_01 + nsi[2]; + mat[0][2] = n_02 - nsi[1]; + mat[1][0] = n_01 - nsi[2]; + mat[1][1] = n_11 + angle_cos; + mat[1][2] = n_12 + nsi[0]; + mat[2][0] = n_02 + nsi[1]; + mat[2][1] = n_12 - nsi[0]; + mat[2][2] = n_22 + angle_cos; +} + diff --git a/redist/linmath.h b/redist/linmath.h index 5cc7b7d..530d291 100644 --- a/redist/linmath.h +++ b/redist/linmath.h @@ -10,14 +10,37 @@ #define PFTHREE(x) x[0], x[1], x[2] #define PFFOUR(x) x[0], x[1], x[2], x[3] -#define LINMATHPI 3.141592653589 +#define LINMATHPI ((FLT)3.141592653589) + +//uncomment the following line to use double precision instead of single precision. +//#define USE_DOUBLE + +#ifdef USE_DOUBLE + +#define FLT double +#define FLT_SQRT sqrt +#define FLT_SIN sin +#define FLT_COS cos +#define FLT_ACOS acos +#define FLT_ASIN asin +#define FLT_ATAN2 atan2 +#define FLT_FABS fabs + +#else -//If you want, you can define FLT to be double for double precision. -#ifndef FLT #define FLT float +#define FLT_SQRT sqrtf +#define FLT_SIN sinf +#define FLT_COS cosf +#define FLT_ACOS acosf +#define FLT_ASIN asinf +#define FLT_ATAN2 atan2f +#define FLT_FABS fabsf + #endif + //NOTE: Inputs may never be output with cross product. void cross3d( FLT * out, const FLT * a, const FLT * b ); @@ -64,6 +87,25 @@ void quatoddproduct( FLT * outvec3, FLT * qa, FLT * qb ); void quatslerp( FLT * q, const FLT * qa, const FLT * qb, FLT t ); void quatrotatevector( FLT * vec3out, const FLT * quat, const FLT * vec3in ); +// Matrix Stuff + +typedef struct +{ + // row, column, (0,0) in upper left + FLT val[3][3]; +} Matrix3x3; + +Matrix3x3 inverseM33(const Matrix3x3 mat); +void get_orthogonal_vector(FLT out[3], const FLT in[3]); +void rotation_between_vecs_to_mat3(FLT m[3][3], const FLT v1[3], const FLT v2[3]); +void unit_m3(FLT m[3][3]); +FLT normalize_v3(FLT n[3]); +void axis_angle_normalized_to_mat3_ex( + FLT mat[3][3], + const FLT axis[3], + const FLT angle_sin, + const FLT angle_cos); + #endif -- cgit v1.2.3