[8] | 1 | //Copyright and Disclaimer: |
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| 2 | //This code is copyright Vienna University of Technology, 2004. |
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| 3 | |
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| 4 | #include <memory.h> |
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| 5 | #include <math.h> |
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| 6 | #include <float.h> |
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| 7 | #include <stdlib.h> |
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| 8 | #include <malloc.h> |
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| 9 | #include <stdio.h> |
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| 10 | #include "MathStuff.h" |
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| 11 | |
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| 12 | #ifndef M_PI |
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| 13 | #define M_PI (double)3.14159265358979323846 |
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| 14 | #endif |
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| 15 | |
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| 16 | const double DOUBLE_MAX = DBL_MAX; |
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| 17 | const double PI = M_PI; |
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| 18 | const double PI_2 = M_PI/2; |
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| 19 | const double PI_180 = M_PI/180; |
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| 20 | const Vector3 ZERO = {0.0, 0.0, 0.0}; |
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| 21 | const Vector3 UNIT_X = {1.0, 0.0, 0.0}; |
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| 22 | const Vector3 UNIT_Y = {0.0, 1.0, 0.0}; |
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| 23 | const Vector3 UNIT_Z = {0.0, 0.0, 1.0}; |
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| 24 | |
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| 25 | const Matrix4x4 IDENTITY = {1.0, 0.0, 0.0, 0.0, |
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| 26 | 0.0, 1.0, 0.0, 0.0, |
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| 27 | 0.0, 0.0, 1.0, 0.0, |
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| 28 | 0.0, 0.0, 0.0, 1.0}; |
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| 29 | |
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| 30 | double maximum(const double a, const double b) { |
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| 31 | return ( (a > b)? (a):(b) ); |
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| 32 | |
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| 33 | } |
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| 34 | |
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| 35 | void clamp(double* value, const double min, const double max) { |
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| 36 | if( (*value) > max) { |
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| 37 | (*value) = max; |
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| 38 | } |
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| 39 | else { |
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| 40 | if( (*value) < min) { |
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| 41 | (*value) = min; |
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| 42 | } |
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| 43 | } |
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| 44 | } |
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| 45 | |
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| 46 | double absDouble(const double a) { |
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| 47 | return ( (a < 0.0)? (-a):(a) ); |
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| 48 | } |
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| 49 | |
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| 50 | double signDouble(const double a) { |
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| 51 | return ( (a < 0.0)? (-1.0f): ( (a == 0.0)? (0.0f):(1.0f) ) ); |
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| 52 | } |
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| 53 | |
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| 54 | double coTan(const double vIn) { |
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| 55 | return (double)-tan(vIn+PI_2); |
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| 56 | } |
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| 57 | |
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| 58 | double relativeEpsilon(const double a, const double epsilon) { |
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| 59 | double relEpsilon = maximum(absDouble(a*epsilon),epsilon); |
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| 60 | return relEpsilon; |
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| 61 | } |
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| 62 | |
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| 63 | int alike(const double a, const double b, const double epsilon) { |
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| 64 | if(a == b) { |
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| 65 | return 1; |
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| 66 | } |
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| 67 | { |
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| 68 | double relEps = relativeEpsilon(a,epsilon); |
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| 69 | return (a-relEps <= b) && (b <= a+relEps); |
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| 70 | } |
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| 71 | } |
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| 72 | |
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| 73 | |
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| 74 | |
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| 75 | int alikeVector3(const Vector3 a, const Vector3 b, const double epsilon) { |
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| 76 | return |
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| 77 | alike(a[0],b[0],epsilon) && |
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| 78 | alike(a[1],b[1],epsilon) && |
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| 79 | alike(a[2],b[2],epsilon); |
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| 80 | } |
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| 81 | |
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| 82 | void linCombVector3(Vector3 result, const Vector3 pos, const Vector3 dir, const double t) { |
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| 83 | int i; |
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| 84 | for(i = 0; i < 3; i++) { |
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| 85 | result[i] = pos[i]+t*dir[i]; |
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| 86 | } |
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| 87 | } |
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| 88 | |
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| 89 | double squaredLength(const Vector3 vec) { |
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| 90 | int i; |
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| 91 | double tmp = 0.0; |
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| 92 | for(i = 0; i < 3; i++) { |
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| 93 | tmp += vec[i]*vec[i]; |
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| 94 | } |
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| 95 | return tmp; |
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| 96 | } |
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| 97 | |
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| 98 | void normalize(Vector3 vec) { |
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| 99 | int i; |
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| 100 | const double len = (double)(1.0/sqrt(squaredLength(vec))); |
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| 101 | for(i = 0; i < 3; i++) { |
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| 102 | vec[i] *= len; |
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| 103 | } |
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| 104 | } |
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| 105 | |
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| 106 | void copyNormalize(Vector3 vec, const Vector3 input) { |
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| 107 | copyVector3(vec,input), |
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| 108 | normalize(vec); |
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| 109 | } |
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| 110 | |
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| 111 | /* | a1 a2 | |
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| 112 | | b1 b2 | calculate the determinent of a 2x2 matrix*/ |
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| 113 | double det2x2(const double a1, const double a2, |
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| 114 | const double b1, const double b2) { |
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| 115 | return a1*b2 - b1*a2; |
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| 116 | } |
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| 117 | |
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| 118 | /* | a1 a2 a3 | |
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| 119 | | b1 b2 b3 | |
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| 120 | | c1 c2 c3 | calculate the determinent of a 3x3 matrix*/ |
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| 121 | double det3x3(const double a1, const double a2, const double a3, |
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| 122 | const double b1, const double b2, const double b3, |
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| 123 | const double c1, const double c2, const double c3) { |
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| 124 | return a1*det2x2(b2,b3,c2,c3) - b1*det2x2(a2,a3,c2,c3) + |
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| 125 | c1*det2x2(a2,a3,b2,b3); |
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| 126 | } |
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| 127 | void cross(Vector3 result, const Vector3 a, const Vector3 b) { |
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| 128 | result[0] = det2x2(a[1],b[1],a[2],b[2]); |
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| 129 | result[1] = -det2x2(a[0],b[0],a[2],b[2]); |
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| 130 | result[2] = det2x2(a[0],b[0],a[1],b[1]); |
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| 131 | } |
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| 132 | |
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| 133 | double dot(const Vector3 a, const Vector3 b) { |
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| 134 | return a[0]*b[0]+a[1]*b[1]+a[2]*b[2]; |
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| 135 | } |
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| 136 | |
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| 137 | void look(Matrix4x4 output, const Vector3 pos, const Vector3 dir, const Vector3 up) { |
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| 138 | Vector3 dirN; |
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| 139 | Vector3 upN; |
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| 140 | Vector3 lftN; |
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| 141 | |
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| 142 | cross(lftN,dir,up); |
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| 143 | normalize(lftN); |
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| 144 | |
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| 145 | cross(upN,lftN,dir); |
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| 146 | normalize(upN); |
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| 147 | copyNormalize(dirN,dir); |
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| 148 | |
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| 149 | output[ 0] = lftN[0]; |
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| 150 | output[ 1] = upN[0]; |
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| 151 | output[ 2] = -dirN[0]; |
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| 152 | output[ 3] = 0.0; |
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| 153 | |
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| 154 | output[ 4] = lftN[1]; |
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| 155 | output[ 5] = upN[1]; |
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| 156 | output[ 6] = -dirN[1]; |
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| 157 | output[ 7] = 0.0; |
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| 158 | |
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| 159 | output[ 8] = lftN[2]; |
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| 160 | output[ 9] = upN[2]; |
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| 161 | output[10] = -dirN[2]; |
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| 162 | output[11] = 0.0; |
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| 163 | |
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| 164 | output[12] = -dot(lftN,pos); |
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| 165 | output[13] = -dot(upN,pos); |
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| 166 | output[14] = dot(dirN,pos); |
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| 167 | output[15] = 1.0; |
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| 168 | } |
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| 169 | |
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| 170 | void makeScaleMtx(Matrix4x4 output, const double x, const double y, const double z) { |
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| 171 | output[ 0] = x; |
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| 172 | output[ 1] = 0.0; |
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| 173 | output[ 2] = 0.0; |
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| 174 | output[ 3] = 0.0; |
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| 175 | |
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| 176 | output[ 4] = 0.0; |
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| 177 | output[ 5] = y; |
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| 178 | output[ 6] = 0.0; |
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| 179 | output[ 7] = 0.0; |
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| 180 | |
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| 181 | output[ 8] = 0.0; |
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| 182 | output[ 9] = 0.0; |
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| 183 | output[10] = z; |
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| 184 | output[11] = 0.0; |
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| 185 | |
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| 186 | output[12] = 0.0; |
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| 187 | output[13] = 0.0; |
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| 188 | output[14] = 0.0; |
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| 189 | output[15] = 1.0; |
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| 190 | } |
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| 191 | |
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| 192 | void makeTranslationMtx(Matrix4x4 output, Vector3 translation) { |
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| 193 | output[ 0] = 1.0; |
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| 194 | output[ 1] = 0.0; |
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| 195 | output[ 2] = 0.0; |
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| 196 | output[ 3] = 0;//translation[0]; |
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| 197 | |
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| 198 | output[ 4] = 0.0; |
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| 199 | output[ 5] = 1.0; |
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| 200 | output[ 6] = 0.0; |
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| 201 | output[ 7] = 0;//translation[1]; |
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| 202 | |
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| 203 | output[ 8] = 0.0; |
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| 204 | output[ 9] = 0.0; |
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| 205 | output[10] = 1.0; |
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| 206 | output[11] = 0;//translation[2]; |
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| 207 | |
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| 208 | output[12] = translation[0];//0.0; |
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| 209 | output[13] = translation[1];//0.0; |
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| 210 | output[14] = translation[2];//0.0; |
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| 211 | output[15] = 1.0; |
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| 212 | } |
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| 213 | |
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| 214 | void makeRotationZMtx(Matrix4x4 output, const double rad) |
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| 215 | { |
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| 216 | output[ 0] = cos(rad); |
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| 217 | output[ 1] = sin(rad); |
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| 218 | output[ 2] = 0.0; |
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| 219 | output[ 3] = 0.0; |
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| 220 | |
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| 221 | output[ 4] = -sin(rad); |
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| 222 | output[ 5] = cos(rad); |
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| 223 | output[ 6] = 0.0; |
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| 224 | output[ 7] = 0.0; |
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| 225 | |
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| 226 | output[ 8] = 0.0; |
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| 227 | output[ 9] = 0.0; |
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| 228 | output[10] = 1.0; |
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| 229 | output[11] = 0.0; |
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| 230 | |
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| 231 | output[12] = 0.0; |
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| 232 | output[13] = 0.0; |
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| 233 | output[14] = 0.0; |
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| 234 | output[15] = 1.0; |
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| 235 | } |
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| 236 | |
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| 237 | void makeRotationXMtx(Matrix4x4 output, const double rad) |
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| 238 | { |
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| 239 | output[ 0] = 1.0; |
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| 240 | output[ 1] = 0.0; |
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| 241 | output[ 2] = 0.0; |
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| 242 | output[ 3] = 0.0; |
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| 243 | |
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| 244 | output[ 4] = 0.0; |
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| 245 | output[ 5] = cos(rad); |
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| 246 | output[ 6] = sin(rad); |
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| 247 | output[ 7] = 0.0; |
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| 248 | |
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| 249 | output[ 8] = 0.0; |
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| 250 | output[ 9] = -sin(rad); |
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| 251 | output[10] = cos(rad); |
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| 252 | output[11] = 0.0; |
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| 253 | |
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| 254 | output[12] = 0.0; |
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| 255 | output[13] = 0.0; |
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| 256 | output[14] = 0.0; |
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| 257 | output[15] = 1.0; |
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| 258 | } |
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| 259 | |
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| 260 | void makeRotationYMtx(Matrix4x4 output, const double rad) |
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| 261 | { |
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| 262 | output[ 0] = cos(rad); |
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| 263 | output[ 1] = 0.0; |
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| 264 | output[ 2] = -sin(rad); |
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| 265 | output[ 3] = 0.0; |
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| 266 | |
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| 267 | output[ 4] = 0.0; |
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| 268 | output[ 5] = 1.0; |
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| 269 | output[ 6] = 0.0; |
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| 270 | output[ 7] = 0.0; |
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| 271 | |
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| 272 | output[ 8] = sin(rad); |
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| 273 | output[ 9] = 0.0; |
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| 274 | output[10] = cos(rad); |
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| 275 | output[11] = 0.0; |
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| 276 | |
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| 277 | output[12] = 0.0; |
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| 278 | output[13] = 0.0; |
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| 279 | output[14] = 0.0; |
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| 280 | output[15] = 1.0; |
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| 281 | } |
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| 282 | |
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| 283 | void scaleTranslateToFit(Matrix4x4 output, const Vector3 vMin, const Vector3 vMax) { |
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| 284 | output[ 0] = 2/(vMax[0]-vMin[0]); |
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| 285 | output[ 4] = 0; |
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| 286 | output[ 8] = 0; |
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| 287 | output[12] = -(vMax[0]+vMin[0])/(vMax[0]-vMin[0]); |
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| 288 | |
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| 289 | output[ 1] = 0; |
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| 290 | output[ 5] = 2/(vMax[1]-vMin[1]); |
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| 291 | output[ 9] = 0; |
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| 292 | output[13] = -(vMax[1]+vMin[1])/(vMax[1]-vMin[1]); |
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| 293 | |
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| 294 | output[ 2] = 0; |
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| 295 | output[ 6] = 0; |
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| 296 | output[10] = 2/(vMax[2]-vMin[2]); |
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| 297 | output[14] = -(vMax[2]+vMin[2])/(vMax[2]-vMin[2]); |
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| 298 | |
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| 299 | output[ 3] = 0; |
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| 300 | output[ 7] = 0; |
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| 301 | output[11] = 0; |
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| 302 | output[15] = 1; |
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| 303 | } |
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| 304 | |
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| 305 | void perspectiveRad(Matrix4x4 output, const double vFovy, const double vAspect, |
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| 306 | const double vNearDis, const double vFarDis) { |
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| 307 | const double f = coTan(vFovy/2); |
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| 308 | const double dif = 1/(vNearDis-vFarDis); |
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| 309 | |
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| 310 | output[ 0] = f/vAspect; |
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| 311 | output[ 4] = 0; |
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| 312 | output[ 8] = 0; |
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| 313 | output[12] = 0; |
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| 314 | |
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| 315 | output[ 1] = 0; |
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| 316 | output[ 5] = f; |
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| 317 | output[ 9] = 0; |
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| 318 | output[13] = 0; |
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| 319 | |
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| 320 | output[ 2] = 0; |
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| 321 | output[ 6] = 0; |
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| 322 | output[10] = (vFarDis+vNearDis)*dif; |
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| 323 | output[14] = 2*vFarDis*vNearDis*dif; |
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| 324 | |
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| 325 | output[ 3] = 0; |
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| 326 | output[ 7] = 0; |
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| 327 | output[11] = -1; |
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| 328 | output[15] = 0; |
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| 329 | } |
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| 330 | |
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| 331 | void perspectiveDeg(Matrix4x4 output, const double vFovy, const double vAspect, |
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| 332 | const double vNearDis, const double vFarDis) { |
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| 333 | perspectiveRad(output,vFovy*PI_180,vAspect,vNearDis,vFarDis); |
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| 334 | } |
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| 335 | |
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| 336 | void invert(Matrix4x4 output, const Matrix4x4 i) { |
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| 337 | double a11 = det3x3(i[5],i[6],i[7],i[9],i[10],i[11],i[13],i[14],i[15]); |
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| 338 | double a21 = -det3x3(i[1],i[2],i[3],i[9],i[10],i[11],i[13],i[14],i[15]); |
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| 339 | double a31 = det3x3(i[1],i[2],i[3],i[5],i[6],i[7],i[13],i[14],i[15]); |
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| 340 | double a41 = -det3x3(i[1],i[2],i[3],i[5],i[6],i[7],i[9],i[10],i[11]); |
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| 341 | |
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| 342 | double a12 = -det3x3(i[4],i[6],i[7],i[8],i[10],i[11],i[12],i[14],i[15]); |
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| 343 | double a22 = det3x3(i[0],i[2],i[3],i[8],i[10],i[11],i[12],i[14],i[15]); |
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| 344 | double a32 = -det3x3(i[0],i[2],i[3],i[4],i[6],i[7],i[12],i[14],i[15]); |
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| 345 | double a42 = det3x3(i[0],i[2],i[3],i[4],i[6],i[7],i[8],i[10],i[11]); |
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| 346 | |
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| 347 | double a13 = det3x3(i[4],i[5],i[7],i[8],i[9],i[11],i[12],i[13],i[15]); |
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| 348 | double a23 = -det3x3(i[0],i[1],i[3],i[8],i[9],i[11],i[12],i[13],i[15]); |
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| 349 | double a33 = det3x3(i[0],i[1],i[3],i[4],i[5],i[7],i[12],i[13],i[15]); |
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| 350 | double a43 = -det3x3(i[0],i[1],i[3],i[4],i[5],i[7],i[8],i[9],i[11]); |
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| 351 | |
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| 352 | double a14 = -det3x3(i[4],i[5],i[6],i[8],i[9],i[10],i[12],i[13],i[14]); |
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| 353 | double a24 = det3x3(i[0],i[1],i[2],i[8],i[9],i[10],i[12],i[13],i[14]); |
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| 354 | double a34 = -det3x3(i[0],i[1],i[2],i[4],i[5],i[6],i[12],i[13],i[14]); |
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| 355 | double a44 = det3x3(i[0],i[1],i[2],i[4],i[5],i[6],i[8],i[9],i[10]); |
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| 356 | |
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| 357 | double det = (i[0]*a11) + (i[4]*a21) + (i[8]*a31) + (i[12]*a41); |
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| 358 | double oodet = 1/det; |
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| 359 | |
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| 360 | output[ 0] = a11*oodet; |
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| 361 | output[ 1] = a21*oodet; |
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| 362 | output[ 2] = a31*oodet; |
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| 363 | output[ 3] = a41*oodet; |
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| 364 | |
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| 365 | output[ 4] = a12*oodet; |
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| 366 | output[ 5] = a22*oodet; |
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| 367 | output[ 6] = a32*oodet; |
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| 368 | output[ 7] = a42*oodet; |
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| 369 | |
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| 370 | output[ 8] = a13*oodet; |
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| 371 | output[ 9] = a23*oodet; |
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| 372 | output[10] = a33*oodet; |
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| 373 | output[11] = a43*oodet; |
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| 374 | |
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| 375 | output[12] = a14*oodet; |
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| 376 | output[13] = a24*oodet; |
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| 377 | output[14] = a34*oodet; |
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| 378 | output[15] = a44*oodet; |
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| 379 | } |
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| 380 | |
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| 381 | void multUnSave(Matrix4x4 output, const Matrix4x4 a, const Matrix4x4 b) { |
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| 382 | const int SIZE = 4; |
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| 383 | int iCol; |
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| 384 | for(iCol = 0; iCol < SIZE; iCol++) { |
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| 385 | const int cID = iCol*SIZE; |
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| 386 | int iRow; |
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| 387 | for(iRow = 0; iRow < SIZE; iRow++) { |
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| 388 | const int id = iRow+cID; |
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| 389 | int k; |
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| 390 | output[id] = a[iRow]*b[cID]; |
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| 391 | for(k = 1; k < SIZE; k++) { |
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| 392 | output[id] += a[iRow+k*SIZE]*b[k+cID]; |
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| 393 | } |
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| 394 | } |
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| 395 | } |
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| 396 | } |
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| 397 | |
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| 398 | void mult(Matrix4x4 output, const Matrix4x4 a, const Matrix4x4 b) { |
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| 399 | if(a == output) { |
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| 400 | Matrix4x4 tmpA; |
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| 401 | copyMatrix(tmpA,a); |
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| 402 | if(b == output) { |
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| 403 | multUnSave(output,tmpA,tmpA); |
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| 404 | } |
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| 405 | else { |
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| 406 | multUnSave(output,tmpA,b); |
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| 407 | } |
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| 408 | } |
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| 409 | else { |
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| 410 | if(b == output) { |
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| 411 | Matrix4x4 tmpB; |
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| 412 | copyMatrix(tmpB,b); |
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| 413 | multUnSave(output,a,tmpB); |
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| 414 | } |
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| 415 | else { |
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| 416 | multUnSave(output,a,b); |
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| 417 | } |
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| 418 | } |
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| 419 | } |
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| 420 | |
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| 421 | void mulHomogenPoint(Vector3 output, const Matrix4x4 m, const Vector3 v) { |
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| 422 | //if v == output -> overwriting problems -> so store in temp |
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| 423 | double x = m[0]*v[0] + m[4]*v[1] + m[ 8]*v[2] + m[12]; |
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| 424 | double y = m[1]*v[0] + m[5]*v[1] + m[ 9]*v[2] + m[13]; |
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| 425 | double z = m[2]*v[0] + m[6]*v[1] + m[10]*v[2] + m[14]; |
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| 426 | double w = m[3]*v[0] + m[7]*v[1] + m[11]*v[2] + m[15]; |
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| 427 | |
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| 428 | output[0] = x/w; |
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| 429 | output[1] = y/w; |
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| 430 | output[2] = z/w; |
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| 431 | } |
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| 432 | |
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| 433 | void appendToCubicHull(Vector3 min, Vector3 max, const Vector3 v) { |
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| 434 | int j; |
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| 435 | for(j = 0; j < 3; j++) { |
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| 436 | if(v[j] < min[j]) { |
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| 437 | min[j] = v[j]; |
---|
| 438 | } |
---|
| 439 | else if(v[j] > max[j]) { |
---|
| 440 | max[j] = v[j]; |
---|
| 441 | } |
---|
| 442 | } |
---|
| 443 | } |
---|
| 444 | |
---|
| 445 | void calcCubicHull(Vector3 min, Vector3 max, const Vector3* ps, const int size) { |
---|
| 446 | if(size > 0) { |
---|
| 447 | int i; |
---|
| 448 | copyVector3(min,ps[0]); |
---|
| 449 | copyVector3(max,ps[0]); |
---|
| 450 | for(i = 1; i < size; i++) { |
---|
| 451 | appendToCubicHull(min,max,ps[i]); |
---|
| 452 | } |
---|
| 453 | } |
---|
| 454 | } |
---|
| 455 | |
---|
| 456 | void calcViewFrustumWorldCoord(Vector3x8 points, const Matrix4x4 invEyeProjView) { |
---|
| 457 | const struct AABox box = { |
---|
| 458 | {-1, -1, -1}, |
---|
| 459 | {1, 1, 1} |
---|
| 460 | }; |
---|
| 461 | int i; |
---|
| 462 | calcAABoxPoints(points,box); //calc unit cube corner points |
---|
| 463 | for(i = 0; i < 8; i++) { |
---|
| 464 | mulHomogenPoint(points[i],invEyeProjView,points[i]); //camera to world frame |
---|
| 465 | } |
---|
| 466 | //viewFrustumWorldCoord[0] == near-bottom-left |
---|
| 467 | //viewFrustumWorldCoord[1] == near-bottom-right |
---|
| 468 | //viewFrustumWorldCoord[2] == near-top-right |
---|
| 469 | //viewFrustumWorldCoord[3] == near-top-left |
---|
| 470 | //viewFrustumWorldCoord[4] == far-bottom-left |
---|
| 471 | //viewFrustumWorldCoord[5] == far-bottom-right |
---|
| 472 | //viewFrustumWorldCoord[6] == far-top-right |
---|
| 473 | //viewFrustumWorldCoord[7] == far-top-left |
---|
| 474 | } |
---|
| 475 | |
---|
| 476 | void calcViewFrustObject(struct Object* obj, const Vector3x8 p) { |
---|
| 477 | int i; |
---|
| 478 | Vector3* ps; |
---|
| 479 | objectSetSize(obj,6); |
---|
| 480 | for(i = 0; i < 6; i++) { |
---|
| 481 | vecPointSetSize(&obj->poly[i],4); |
---|
| 482 | } |
---|
| 483 | //near poly ccw |
---|
| 484 | ps = obj->poly[0].points; |
---|
| 485 | for(i = 0; i < 4; i++) { |
---|
| 486 | copyVector3(ps[i],p[i]); |
---|
| 487 | } |
---|
| 488 | //far poly ccw |
---|
| 489 | ps = obj->poly[1].points; |
---|
| 490 | for(i = 4; i < 8; i++) { |
---|
| 491 | copyVector3(ps[i-4],p[11-i]); |
---|
| 492 | } |
---|
| 493 | //left poly ccw |
---|
| 494 | ps = obj->poly[2].points; |
---|
| 495 | copyVector3(ps[0],p[0]); |
---|
| 496 | copyVector3(ps[1],p[3]); |
---|
| 497 | copyVector3(ps[2],p[7]); |
---|
| 498 | copyVector3(ps[3],p[4]); |
---|
| 499 | //right poly ccw |
---|
| 500 | ps = obj->poly[3].points; |
---|
| 501 | copyVector3(ps[0],p[1]); |
---|
| 502 | copyVector3(ps[1],p[5]); |
---|
| 503 | copyVector3(ps[2],p[6]); |
---|
| 504 | copyVector3(ps[3],p[2]); |
---|
| 505 | //bottom poly ccw |
---|
| 506 | ps = obj->poly[4].points; |
---|
| 507 | copyVector3(ps[0],p[4]); |
---|
| 508 | copyVector3(ps[1],p[5]); |
---|
| 509 | copyVector3(ps[2],p[1]); |
---|
| 510 | copyVector3(ps[3],p[0]); |
---|
| 511 | //top poly ccw |
---|
| 512 | ps = obj->poly[5].points; |
---|
| 513 | copyVector3(ps[0],p[6]); |
---|
| 514 | copyVector3(ps[1],p[7]); |
---|
| 515 | copyVector3(ps[2],p[3]); |
---|
| 516 | copyVector3(ps[3],p[2]); |
---|
| 517 | } |
---|
| 518 | |
---|
| 519 | void transformVecPoint(struct VecPoint* poly, const Matrix4x4 xForm) { |
---|
| 520 | if(0 != poly) { |
---|
| 521 | int i; |
---|
| 522 | for(i = 0; i < poly->size; i++) { |
---|
| 523 | mulHomogenPoint(poly->points[i],xForm,poly->points[i]); |
---|
| 524 | } |
---|
| 525 | } |
---|
| 526 | } |
---|
| 527 | |
---|
| 528 | void transformObject(struct Object* obj, const Matrix4x4 xForm) { |
---|
| 529 | if(0 != obj) { |
---|
| 530 | int i; |
---|
| 531 | for(i = 0; i < obj->size; i++) { |
---|
| 532 | transformVecPoint( &(obj->poly[i]) ,xForm); |
---|
| 533 | } |
---|
| 534 | } |
---|
| 535 | } |
---|
| 536 | |
---|
| 537 | void calcObjectCubicHull(Vector3 min, Vector3 max, const struct Object obj) { |
---|
| 538 | if(0 < obj.size) { |
---|
| 539 | int i; |
---|
| 540 | calcCubicHull(min,max,obj.poly[0].points,obj.poly[0].size); |
---|
| 541 | for(i = 1; i < obj.size; i++) { |
---|
| 542 | struct VecPoint* p = &(obj.poly[i]); |
---|
| 543 | int j; |
---|
| 544 | for(j = 0; j < p->size; j++) { |
---|
| 545 | appendToCubicHull(min,max,p->points[j]); |
---|
| 546 | } |
---|
| 547 | } |
---|
| 548 | } |
---|
| 549 | } |
---|
| 550 | |
---|
| 551 | int findSamePointInVecPoint(const struct VecPoint poly, const Vector3 p) { |
---|
| 552 | int i; |
---|
| 553 | for(i = 0; i < poly.size; i++) { |
---|
| 554 | if(alikeVector3(poly.points[i],p,(double)0.001)) { |
---|
| 555 | return i; |
---|
| 556 | } |
---|
| 557 | } |
---|
| 558 | return -1; |
---|
| 559 | } |
---|
| 560 | |
---|
| 561 | int findSamePointInObjectAndSwapWithLast(struct Object *inter, const Vector3 p) { |
---|
| 562 | int i; |
---|
| 563 | if(0 == inter) { |
---|
| 564 | return -1; |
---|
| 565 | } |
---|
| 566 | if(1 > inter->size) { |
---|
| 567 | return -1; |
---|
| 568 | } |
---|
| 569 | for(i = inter->size; i > 0; i--) { |
---|
| 570 | struct VecPoint* poly = &(inter->poly[i-1]); |
---|
| 571 | if(2 == poly->size) { |
---|
| 572 | const int nr = findSamePointInVecPoint(*poly,p); |
---|
| 573 | if(0 <= nr) { |
---|
| 574 | //swap with last |
---|
| 575 | swapVecPoint(poly, &(inter->poly[inter->size-1]) ); |
---|
| 576 | return nr; |
---|
| 577 | } |
---|
| 578 | } |
---|
| 579 | } |
---|
| 580 | return -1; |
---|
| 581 | } |
---|
| 582 | |
---|
| 583 | void appendIntersectionVecPoint(struct Object* obj, struct Object* inter) { |
---|
| 584 | struct VecPoint *polyOut; |
---|
| 585 | struct VecPoint *polyIn; |
---|
| 586 | int size = obj->size; |
---|
| 587 | int i; |
---|
| 588 | //you need at least 3 sides for a polygon |
---|
| 589 | if(3 > inter->size) { |
---|
| 590 | return; |
---|
| 591 | } |
---|
| 592 | //compact inter: remove poly.size != 2 from end on forward |
---|
| 593 | for(i = inter->size; 0 < i; i--) { |
---|
| 594 | if(2 == inter->poly[i-1].size) { |
---|
| 595 | break; |
---|
| 596 | } |
---|
| 597 | } |
---|
| 598 | objectSetSize(inter,i); |
---|
| 599 | //you need at least 3 sides for a polygon |
---|
| 600 | if(3 > inter->size) { |
---|
| 601 | return; |
---|
| 602 | } |
---|
| 603 | //make place for one additional polygon in obj |
---|
| 604 | objectSetSize(obj,size+1); |
---|
| 605 | polyOut = &(obj->poly[size]); |
---|
| 606 | //we have line segments in each poly of inter |
---|
| 607 | //take last linesegment as first and second point |
---|
| 608 | polyIn = &(inter->poly[inter->size-1]); |
---|
| 609 | append2VecPoint(polyOut,polyIn->points[0]); |
---|
| 610 | append2VecPoint(polyOut,polyIn->points[1]); |
---|
| 611 | //remove last poly from inter, because it is already saved |
---|
| 612 | objectSetSize(inter,inter->size-1); |
---|
| 613 | |
---|
| 614 | //iterate over inter until their is no line segment left |
---|
| 615 | while(0 < inter->size) { |
---|
| 616 | //pointer on last point to compare |
---|
| 617 | Vector3 *lastPt = &(polyOut->points[polyOut->size-1]); |
---|
| 618 | //find same point in inter to continue polygon |
---|
| 619 | const int nr = findSamePointInObjectAndSwapWithLast(inter,*lastPt); |
---|
| 620 | if(0 <= nr) { |
---|
| 621 | //last line segment |
---|
| 622 | polyIn = &(inter->poly[inter->size-1]); |
---|
| 623 | //get the other point in this polygon and save into polyOut |
---|
| 624 | append2VecPoint(polyOut,polyIn->points[(nr+1)%2]); |
---|
| 625 | } |
---|
| 626 | //remove last poly from inter, because it is already saved or degenerated |
---|
| 627 | objectSetSize(inter,inter->size-1); |
---|
| 628 | } |
---|
| 629 | //last point can be deleted, because he is the same as the first (closes polygon) |
---|
| 630 | vecPointSetSize(polyOut,polyOut->size-1); |
---|
| 631 | } |
---|
| 632 | |
---|
| 633 | double pointPlaneDistance(const struct Plane A, const Vector3 p) { |
---|
| 634 | return dot(A.n,p)+(A.d); |
---|
| 635 | } |
---|
| 636 | |
---|
| 637 | int pointBeforePlane(const struct Plane A, const Vector3 p) { |
---|
| 638 | return pointPlaneDistance(A,p) > 0.0; |
---|
| 639 | } |
---|
| 640 | |
---|
| 641 | int intersectPlaneEdge(Vector3 output, const struct Plane A, const Vector3 a, const Vector3 b) { |
---|
| 642 | Vector3 diff; |
---|
| 643 | double t; |
---|
| 644 | diffVector3(diff,b,a); |
---|
| 645 | t = dot(A.n,diff); |
---|
| 646 | if(0.0 == t) |
---|
| 647 | return 0; |
---|
| 648 | t = (A.d-dot(A.n,a))/t; |
---|
| 649 | if(t < 0.0 || 1.0 < t) |
---|
| 650 | return 0; |
---|
| 651 | linCombVector3(output,a,diff,t); |
---|
| 652 | return 1; |
---|
| 653 | } |
---|
| 654 | |
---|
| 655 | void clipVecPointByPlane(const struct VecPoint poly, const struct Plane A, struct VecPoint* polyOut, struct VecPoint* interPts) { |
---|
| 656 | int i; |
---|
| 657 | int *outside = 0; |
---|
| 658 | if(poly.size < 3 || 0 == polyOut) { |
---|
| 659 | return; |
---|
| 660 | } |
---|
| 661 | outside = (int*)realloc(outside,sizeof(int)*poly.size); |
---|
| 662 | //for each point |
---|
| 663 | for(i = 0; i < poly.size; i++) { |
---|
| 664 | outside[i] = pointBeforePlane(A,poly.points[i]); |
---|
| 665 | } |
---|
| 666 | for(i = 0; i < poly.size; i++) { |
---|
| 667 | int idNext = (i+1) % poly.size; |
---|
| 668 | //both outside -> save none |
---|
| 669 | if(outside[i] && outside[idNext]) { |
---|
| 670 | continue; |
---|
| 671 | } |
---|
| 672 | //outside to inside -> calc intersection save intersection and save i+1 |
---|
| 673 | if(outside[i]) { |
---|
| 674 | Vector3 inter; |
---|
| 675 | if(intersectPlaneEdge(inter,A,poly.points[i],poly.points[idNext])) { |
---|
| 676 | append2VecPoint(polyOut,inter); |
---|
| 677 | if(0 != interPts) { |
---|
| 678 | append2VecPoint(interPts,inter); |
---|
| 679 | } |
---|
| 680 | } |
---|
| 681 | append2VecPoint(polyOut,poly.points[idNext]); |
---|
| 682 | continue; |
---|
| 683 | } |
---|
| 684 | //inside to outside -> calc intersection save intersection |
---|
| 685 | if(outside[idNext]) { |
---|
| 686 | Vector3 inter; |
---|
| 687 | if(intersectPlaneEdge(inter,A,poly.points[i],poly.points[idNext])) { |
---|
| 688 | append2VecPoint(polyOut,inter); |
---|
| 689 | if(0 != interPts) { |
---|
| 690 | append2VecPoint(interPts,inter); |
---|
| 691 | } |
---|
| 692 | } |
---|
| 693 | continue; |
---|
| 694 | } |
---|
| 695 | //both inside -> save point i+1 |
---|
| 696 | append2VecPoint(polyOut,poly.points[idNext]); |
---|
| 697 | } |
---|
| 698 | outside = (int*)realloc(outside,0); |
---|
| 699 | } |
---|
| 700 | |
---|
| 701 | void clipObjectByPlane(const struct Object obj, const struct Plane A, struct Object* objOut) { |
---|
| 702 | int i; |
---|
| 703 | struct Object inter = OBJECT_NULL; |
---|
| 704 | struct Object objIn = OBJECT_NULL; |
---|
| 705 | if(0 == obj.size || 0 == objOut) |
---|
| 706 | return; |
---|
| 707 | if(obj.poly == objOut->poly) { |
---|
| 708 | //need to copy object if input and output are the same |
---|
| 709 | copyObject(&objIn,obj); |
---|
| 710 | } |
---|
| 711 | else { |
---|
| 712 | objIn = obj; |
---|
| 713 | } |
---|
| 714 | emptyObject(objOut); |
---|
| 715 | |
---|
| 716 | for(i = 0; i < objIn.size; i++) |
---|
| 717 | { |
---|
| 718 | int size = objOut->size; |
---|
| 719 | objectSetSize(objOut,size+1); |
---|
| 720 | objectSetSize(&inter,size+1); |
---|
| 721 | clipVecPointByPlane(objIn.poly[i],A, &(objOut->poly[size]) , &(inter.poly[size])); |
---|
| 722 | //if whole poly was clipped away -> delete empty poly |
---|
| 723 | if(0 == objOut->poly[size].size) { |
---|
| 724 | objectSetSize(objOut,size); |
---|
| 725 | objectSetSize(&inter,size); |
---|
| 726 | } |
---|
| 727 | } |
---|
| 728 | //add a polygon of all intersection points with plane to close the object |
---|
| 729 | appendIntersectionVecPoint(objOut,&inter); |
---|
| 730 | emptyObject(&inter); |
---|
| 731 | emptyObject(&objIn); |
---|
| 732 | } |
---|
| 733 | |
---|
| 734 | |
---|
| 735 | void clipObjectByAABox(struct Object* obj, const struct AABox box) { |
---|
| 736 | struct VecPlane planes = VECPLANE_NULL; |
---|
| 737 | int i; |
---|
| 738 | if(0 == obj) { |
---|
| 739 | return; |
---|
| 740 | } |
---|
| 741 | |
---|
| 742 | calcAABoxPlanes(&planes,box); |
---|
| 743 | for(i = 0; i < planes.size; i++) { |
---|
| 744 | clipObjectByPlane(*obj,planes.plane[i],obj); |
---|
| 745 | } |
---|
| 746 | |
---|
| 747 | emptyVecPlane(&planes); |
---|
| 748 | } |
---|
| 749 | |
---|
| 750 | int clipTest(const double p, const double q, double* u1, double* u2) { |
---|
| 751 | // Return value is 'true' if line segment intersects the current test |
---|
| 752 | // plane. Otherwise 'false' is returned in which case the line segment |
---|
| 753 | // is entirely clipped. |
---|
| 754 | if(0 == u1 || 0 == u2) { |
---|
| 755 | return 0; |
---|
| 756 | } |
---|
| 757 | if(p < 0.0) { |
---|
| 758 | double r = q/p; |
---|
| 759 | if(r > (*u2)) { |
---|
| 760 | return 0; |
---|
| 761 | } |
---|
| 762 | else { |
---|
| 763 | if(r > (*u1)) { |
---|
| 764 | (*u1) = r; |
---|
| 765 | } |
---|
| 766 | return 1; |
---|
| 767 | } |
---|
| 768 | } |
---|
| 769 | else { |
---|
| 770 | if(p > 0.0) { |
---|
| 771 | double r = q/p; |
---|
| 772 | if(r < (*u1)) { |
---|
| 773 | return 0; |
---|
| 774 | } |
---|
| 775 | else { |
---|
| 776 | if(r < (*u2)) { |
---|
| 777 | (*u2) = r; |
---|
| 778 | } |
---|
| 779 | return 1; |
---|
| 780 | } |
---|
| 781 | } |
---|
| 782 | else { |
---|
| 783 | return q >= 0.0; |
---|
| 784 | } |
---|
| 785 | } |
---|
| 786 | } |
---|
| 787 | |
---|
| 788 | int intersectionLineAABox(Vector3 v, const Vector3 p, const Vector3 dir, const struct AABox b) { |
---|
| 789 | double t1 = 0.0; |
---|
| 790 | double t2 = DOUBLE_MAX; |
---|
| 791 | int intersect = |
---|
| 792 | clipTest(-dir[2],p[2]-b.min[2],&t1,&t2) && clipTest(dir[2],b.max[2]-p[2],&t1,&t2) && |
---|
| 793 | clipTest(-dir[1],p[1]-b.min[1],&t1,&t2) && clipTest(dir[1],b.max[1]-p[1],&t1,&t2) && |
---|
| 794 | clipTest(-dir[0],p[0]-b.min[0],&t1,&t2) && clipTest(dir[0],b.max[0]-p[0],&t1,&t2); |
---|
| 795 | if(!intersect) { |
---|
| 796 | return 0; |
---|
| 797 | } |
---|
| 798 | intersect = 0; |
---|
| 799 | if(0 <= t1) { |
---|
| 800 | linCombVector3(v,p,dir,t1); |
---|
| 801 | intersect = 1; |
---|
| 802 | } |
---|
| 803 | if(0 <= t2) { |
---|
| 804 | linCombVector3(v,p,dir,t2); |
---|
| 805 | intersect = 1; |
---|
| 806 | } |
---|
| 807 | return intersect; |
---|
| 808 | } |
---|
| 809 | |
---|
| 810 | |
---|
| 811 | void includeObjectLightVolume(struct VecPoint* points, const struct Object obj, |
---|
| 812 | const Vector3 lightDir, const struct AABox sceneAABox) { |
---|
| 813 | if(0 != points) { |
---|
| 814 | int i, size; |
---|
| 815 | Vector3 ld; |
---|
| 816 | copyVector3Values(ld,-lightDir[0],-lightDir[1],-lightDir[2]); |
---|
| 817 | convObject2VecPoint(points,obj); |
---|
| 818 | size = points->size; |
---|
| 819 | //for each point add the point on the ray in -lightDir |
---|
| 820 | //intersected with the sceneAABox |
---|
| 821 | for(i = 0; i < size; i++) { |
---|
| 822 | Vector3 pt; |
---|
| 823 | if(intersectionLineAABox(pt,points->points[i],ld,sceneAABox) ) { |
---|
| 824 | append2VecPoint(points,pt); |
---|
| 825 | } |
---|
| 826 | } |
---|
| 827 | } |
---|
| 828 | } |
---|
| 829 | |
---|
| 830 | void calcFocusedLightVolumePoints(struct VecPoint* points, const Matrix4x4 invEyeProjView, |
---|
| 831 | const Vector3 lightDir,const struct AABox sceneAABox) { |
---|
| 832 | Vector3x8 pts; |
---|
| 833 | struct Object obj = OBJECT_NULL; |
---|
| 834 | |
---|
| 835 | calcViewFrustumWorldCoord(pts,invEyeProjView); |
---|
| 836 | calcViewFrustObject(&obj, pts); |
---|
| 837 | clipObjectByAABox(&obj,sceneAABox); |
---|
| 838 | includeObjectLightVolume(points,obj,lightDir,sceneAABox); |
---|
| 839 | emptyObject(&obj); |
---|
| 840 | } |
---|
| 841 | |
---|
| 842 | void calcViewFrustumPlanes(struct VecPlane* planes, const Matrix4x4 eyeProjView) { |
---|
| 843 | if(0 != planes) { |
---|
| 844 | int i; |
---|
| 845 | |
---|
| 846 | planesSetSize(planes, 6); |
---|
| 847 | |
---|
| 848 | //---- extract the plane equations |
---|
| 849 | for (i = 0; i < 4; i++) { |
---|
| 850 | setPlaneCoeff(eyeProjView[i * 4 + 3] - eyeProjView[i * 4 + 0], planes->plane + 0, i); // right plane |
---|
| 851 | setPlaneCoeff(eyeProjView[i * 4 + 3] + eyeProjView[i * 4 + 0], planes->plane + 1, i); // left plane |
---|
| 852 | setPlaneCoeff(eyeProjView[i * 4 + 3] + eyeProjView[i * 4 + 1], planes->plane + 2, i); // bottom plane |
---|
| 853 | setPlaneCoeff(eyeProjView[i * 4 + 3] - eyeProjView[i * 4 + 1], planes->plane + 3, i); // top plane |
---|
| 854 | setPlaneCoeff(eyeProjView[i * 4 + 3] - eyeProjView[i * 4 + 2], planes->plane + 4, i); // far plane |
---|
| 855 | setPlaneCoeff(eyeProjView[i * 4 + 3] + eyeProjView[i * 4 + 2], planes->plane + 5, i); // near plane |
---|
| 856 | } |
---|
| 857 | |
---|
| 858 | //---- normalize the coefficients |
---|
| 859 | for (i = 0; i < 6; i++) { |
---|
| 860 | float invLength = 1; |
---|
| 861 | float length = (float)sqrt(squaredLength(planes->plane[i].n)); |
---|
| 862 | |
---|
| 863 | if(length) invLength = 1.0f / length; |
---|
| 864 | |
---|
| 865 | planes->plane[i].n[0] *= invLength; |
---|
| 866 | planes->plane[i].n[1] *= invLength; |
---|
| 867 | planes->plane[i].n[2] *= invLength; |
---|
| 868 | |
---|
| 869 | planes->plane[i].d *= invLength; |
---|
| 870 | } |
---|
| 871 | } |
---|
| 872 | } |
---|
| 873 | |
---|
| 874 | int calcAABNearestVertexIdx(Vector3 clipPlaneNormal) { |
---|
| 875 | int index; |
---|
| 876 | |
---|
| 877 | // 7+------+6 |
---|
| 878 | // /| /| |
---|
| 879 | // / | / | |
---|
| 880 | // / 4+---/--+5 |
---|
| 881 | // 3+------+2 / y z |
---|
| 882 | // | / | / | / |
---|
| 883 | // |/ |/ |/ |
---|
| 884 | // 0+------+1 *---x |
---|
| 885 | if (clipPlaneNormal[0] <= 0.0f) { |
---|
| 886 | index = (clipPlaneNormal[1] <= 0.0f) ? 0 : 3; |
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| 887 | } |
---|
| 888 | else { |
---|
| 889 | index = (clipPlaneNormal[1] <= 0.0f) ? 1 : 2; |
---|
| 890 | } |
---|
| 891 | |
---|
| 892 | return (clipPlaneNormal[2] <= 0.0f) ? index : 4 + index; |
---|
| 893 | } |
---|
| 894 | |
---|
| 895 | int calcAABFarthestVertexIdx(Vector3 clipPlaneNormal) { |
---|
| 896 | int index; |
---|
| 897 | |
---|
| 898 | if (clipPlaneNormal[0] > 0.0f) { |
---|
| 899 | index = (clipPlaneNormal[1] > 0.0f) ? 0 : 3; |
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| 900 | } |
---|
| 901 | else { |
---|
| 902 | index = (clipPlaneNormal[1] > 0.0f) ? 1 : 2; |
---|
| 903 | } |
---|
| 904 | |
---|
| 905 | return (clipPlaneNormal[2] > 0.0f) ? index : 4 + index; |
---|
| 906 | } |
---|
| 907 | |
---|
| 908 | void calcAABNPVertexIndices(int *vertexIndices, const struct VecPlane planes) { |
---|
| 909 | int i; |
---|
| 910 | for (i = 0; i < 6; i++) |
---|
| 911 | { |
---|
| 912 | vertexIndices[i * 2 + 0] = calcAABNearestVertexIdx(planes.plane[i].n); // n-vertex |
---|
| 913 | vertexIndices[i * 2 + 1] = calcAABFarthestVertexIdx(planes.plane[i].n); // p-vertex |
---|
| 914 | } |
---|
| 915 | } |
---|
| 916 | |
---|
| 917 | void combineAABoxes(struct AABox *a, const struct AABox b) { |
---|
| 918 | appendToCubicHull(a->min, a->max, b.min); |
---|
| 919 | appendToCubicHull(a->min, a->max, b.max); |
---|
| 920 | } |
---|
| 921 | |
---|
| 922 | double calcAABoxVolume(const struct AABox aab) |
---|
| 923 | { |
---|
| 924 | return (aab.max[0] - aab.min[0]) * |
---|
| 925 | (aab.max[1] - aab.min[1]) * |
---|
| 926 | (aab.max[2] - aab.min[2]); |
---|
| 927 | } |
---|
| 928 | |
---|
| 929 | |
---|
| 930 | void calcAABoxCenter(Vector3 vec, const struct AABox aab) |
---|
| 931 | { |
---|
| 932 | diffVector3(vec, aab.max, aab.min); |
---|
| 933 | vec[0] *= 0.5f; vec[1] *= 0.5f; vec[2] *= 0.5f; |
---|
| 934 | |
---|
| 935 | addVector3(vec, aab.min, vec); |
---|
| 936 | } |
---|
| 937 | |
---|
| 938 | |
---|
| 939 | double calcAABoxSurface(const struct AABox aab) |
---|
| 940 | { |
---|
| 941 | return 2 * (aab.max[0] - aab.min[0]) * (aab.max[1] - aab.min[1]) + |
---|
| 942 | 2 * (aab.max[0] - aab.min[0]) * (aab.max[2] - aab.min[2]) + |
---|
| 943 | 2 * (aab.max[1] - aab.min[1]) * (aab.max[2] - aab.min[2]); |
---|
| 944 | } |
---|
| 945 | |
---|
| 946 | void clipAABoxByAABox(struct AABox *aab, const struct AABox enclosed) |
---|
| 947 | { |
---|
| 948 | int i; |
---|
| 949 | for(i=0; i < 3; i++) |
---|
| 950 | { |
---|
| 951 | if(aab->min[i] < enclosed.min[i]) |
---|
| 952 | aab->min[i] = enclosed.min[i]; |
---|
| 953 | if(aab->max[i] > enclosed.max[i]) |
---|
| 954 | aab->max[i] = enclosed.max[i]; |
---|
| 955 | } |
---|
| 956 | } |
---|
| 957 | |
---|
| 958 | |
---|
| 959 | void rotateVectorZ(Vector3 v, double rad) |
---|
| 960 | { |
---|
| 961 | Vector3 temp; |
---|
| 962 | |
---|
| 963 | temp[0] = v[0]*cos(rad) - v[1]*sin(rad);
|
---|
| 964 | temp[1] = v[0]*sin(rad) + v[1]*cos(rad);
|
---|
| 965 | temp[2] = v[2]; |
---|
| 966 | |
---|
| 967 | copyVector3(v, temp); |
---|
| 968 | } |
---|
| 969 | |
---|
| 970 | |
---|
| 971 | void rotateVectorX(Vector3 v, double rad) |
---|
| 972 | { |
---|
| 973 | Vector3 temp; |
---|
| 974 | |
---|
| 975 | temp[0] = v[0]; |
---|
| 976 | temp[1] = v[1]*cos(rad) - v[2]*sin(rad);
|
---|
| 977 | temp[2] = v[1]*sin(rad) + v[2]*cos(rad);
|
---|
| 978 | |
---|
| 979 | copyVector3(v, temp); |
---|
| 980 | } |
---|
| 981 | |
---|
| 982 | |
---|
| 983 | void rotateVectorY(Vector3 v, double rad) |
---|
| 984 | { |
---|
| 985 | Vector3 temp; |
---|
| 986 | |
---|
| 987 | temp[0] = v[2]*sin(rad) + v[0]*cos(rad);
|
---|
| 988 | temp[1] = v[1];
|
---|
| 989 | temp[2] = v[2]*cos(rad) - v[0]*sin(rad); |
---|
| 990 | |
---|
| 991 | copyVector3(v, temp); |
---|
| 992 | } |
---|
| 993 | |
---|
| 994 |
|
---|
| 995 |
|
---|
| 996 | void rotateVector(Vector3 result, const Vector3 input, const float rad, const Vector3 axis)
|
---|
| 997 | {
|
---|
| 998 | // using quaternions (vector and scalar part)
|
---|
| 999 | float s = (float)cos(rad * 0.5);
|
---|
| 1000 | float h = (float)sin(rad * 0.5);
|
---|
| 1001 | float p_v_dot;
|
---|
| 1002 |
|
---|
| 1003 | Vector3 hvec = {axis[0] * h, axis[1]* h, axis[2] * h};
|
---|
| 1004 | Vector3 hvec2;
|
---|
| 1005 | Vector3 hvec3;
|
---|
| 1006 |
|
---|
| 1007 | cross(hvec2, hvec, input);
|
---|
| 1008 | cross(hvec3, hvec, hvec2);
|
---|
| 1009 |
|
---|
| 1010 | p_v_dot = (float)dot(input, hvec);
|
---|
| 1011 |
|
---|
| 1012 | result[0] = s * s * input[0] + hvec[0] * p_v_dot +
|
---|
| 1013 | 2.0f * s * hvec2[0] + hvec3[0];
|
---|
| 1014 |
|
---|
| 1015 | result[1] = s * s * input[1] + hvec[1] * p_v_dot +
|
---|
| 1016 | 2.0f * s *hvec2[1] + hvec3[1];
|
---|
| 1017 |
|
---|
| 1018 | result[2] = s * s * input[2] + hvec[2] * p_v_dot +
|
---|
| 1019 | 2.0f * s *hvec2[2] + hvec3[2];
|
---|
| 1020 |
|
---|
| 1021 | }
|
---|
| 1022 |
|
---|
| 1023 |
|
---|
| 1024 | void vectorNormal(Vector3 result, const Vector3 vec)
|
---|
| 1025 | {
|
---|
| 1026 | result[0] = 0.0f;
|
---|
| 1027 | result[1] = 0.0f;
|
---|
| 1028 | result[2] = 0.0f;
|
---|
| 1029 |
|
---|
| 1030 | // to avoid 0-vector: look if at least one component is not 0)
|
---|
| 1031 | if((vec[0] != 0.0f) || (vec[1] != 0.0f))
|
---|
| 1032 | {
|
---|
| 1033 | result[0] = -vec[1];
|
---|
| 1034 | result[1] = vec[0];
|
---|
| 1035 | }
|
---|
| 1036 | else
|
---|
| 1037 | {
|
---|
| 1038 | result[0] = -vec[2];
|
---|
| 1039 | result[1] = vec[0];
|
---|
| 1040 | }
|
---|
| 1041 | } |
---|