KiCad PCB EDA Suite
3d_math.h
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24 
30 #ifndef _3D_MATH_H
31 #define _3D_MATH_H
32 
34 #include "3d_fastmath.h"
35 
43 inline SFVEC3F SphericalToCartesian( float aInclination, float aAzimuth )
44 {
45  float sinInc = glm::sin( aInclination );
46 
47  return SFVEC3F( sinInc * glm::cos( aAzimuth ), sinInc * glm::sin( aAzimuth ),
48  glm::cos( aInclination ) );
49 }
50 
51 
56 {
57  // It was experienced that this function is slow! do not use it :/
58  // SFVEC3F b( (rand()/(float)RAND_MAX) - 0.5f,
59  // (rand()/(float)RAND_MAX) - 0.5f,
60  // (rand()/(float)RAND_MAX) - 0.5f );
61 
62  SFVEC3F b( Fast_RandFloat() * 0.5f, Fast_RandFloat() * 0.5f, Fast_RandFloat() * 0.5f );
63 
64  return b;
65 }
66 
67 
68 // https://pathtracing.wordpress.com/2011/03/03/cosine-weighted-hemisphere/
70 {
71  const float Xi1 = (float) rand() / (float) RAND_MAX;
72  const float Xi2 = (float) rand() / (float) RAND_MAX;
73 
74  const float theta = acos( sqrt( 1.0f - Xi1 ) );
75  const float phi = 2.0f * glm::pi<float>() * Xi2;
76 
77  const float xs = sinf( theta ) * cosf( phi );
78  const float ys = cosf( theta );
79  const float zs = sinf( theta ) * sinf( phi );
80 
81  const SFVEC3F y( n.x, n.y, n.z );
82  SFVEC3F h = y;
83 
84  if( fabs( h.x ) <= fabs( h.y ) && fabs( h.x ) <= fabs( h.z ) )
85  h.x= 1.0f;
86  else if( fabs( h.y ) <= fabs( h.x ) && fabs( h.y ) <= fabs( h.z ) )
87  h.y= 1.0f;
88  else
89  h.z= 1.0f;
90 
91 
92  const SFVEC3F x = glm::normalize( glm::cross( h, y ) );
93  const SFVEC3F z = glm::normalize( glm::cross( x, y ) );
94 
95  SFVEC3F direction = xs * x + ys * y + zs * z;
96  return glm::normalize( direction );
97 }
98 
99 
112 inline bool Refract( const SFVEC3F &aInVector, const SFVEC3F &aNormal, float aRin_over_Rout,
113  SFVEC3F& aOutVector )
114 {
115  float cosThetaI = -glm::dot( aNormal, aInVector );
116  float sin2ThetaI = glm::max( 0.0f, 1.0f - cosThetaI * cosThetaI );
117  float sin2ThetaT = aRin_over_Rout * aRin_over_Rout * sin2ThetaI;
118 
119  // Handle total internal reflection for transmission
120  if( sin2ThetaT >= 1.0f )
121  return false;
122 
123  float cosThetaT = sqrtf( 1.0f - sin2ThetaT );
124 
125  aOutVector = glm::normalize( aRin_over_Rout * aInVector +
126  ( aRin_over_Rout * cosThetaI - cosThetaT ) *
127  aNormal );
128 
129  return true;
130 }
131 
132 
133 inline float mapf( float x, float in_min, float in_max, float out_min, float out_max )
134 {
135  x = glm::clamp( x, in_min, in_max );
136 
137  return (x - in_min) * (out_max - out_min) / (in_max - in_min) + out_min;
138 }
139 
140 inline float RGBtoGray( const SFVEC3F &aColor )
141 {
142  return (aColor.r * 0.2126f +
143  aColor.g * 0.7152f +
144  aColor.b * 0.0722f);
145 }
146 
147 inline SFVEC3F MaterialDiffuseToColorCAD( const SFVEC3F &aDiffuseColor )
148 {
149  // convert to a discret scale of grays
150  const float luminance = glm::min(
151  ( ( (float) ( (unsigned int) ( 4.0f * RGBtoGray( aDiffuseColor ) ) ) + 0.5f ) / 4.0f )
152  * 1.0f,
153  1.0f );
154 
155  const float maxValue = glm::max( glm::max( glm::max( aDiffuseColor.r, aDiffuseColor.g ),
156  aDiffuseColor.b ), FLT_EPSILON );
157 
158  return ( aDiffuseColor / SFVEC3F( maxValue ) ) * 0.125f + luminance * 0.875f;
159 }
160 
161 
162 // http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4KngqMiIsImNvbG9yIjoiIzAwMDAwMCJ9LHsidHlwZSI6MCwiZXEiOiItKCh4LTEpXjIpKjIrMSIsImNvbG9yIjoiIzAwMDAwMCJ9LHsidHlwZSI6MTAwMCwid2luZG93IjpbIi0xLjM4NzUwMDAwMDAwMDAwMDIiLCIxLjg2MjQ5OTk5OTk5OTk5OTgiLCItMC43IiwiMS4zIl19XQ--
163 inline float QuadricEasingInOut( float t )
164 {
165  if( t <= 0.5f )
166  {
167  return t * t * 2.0f;
168  }
169  else
170  {
171  t = t - 1.0f;
172 
173  return -2.0f * ( t * t ) + 1.0f;
174  }
175 }
176 
177 
178 // http://www.wolframalpha.com/input/?i=t%5E2(3-2t)
179 inline float BezierBlend( float t )
180 {
181  return t * t * ( 3.0f - 2.0f * t );
182 }
183 
184 #endif // 3D_MATH_H
float RGBtoGray(const SFVEC3F &aColor)
Definition: 3d_math.h:140
Defines math related functions.
float BezierBlend(float t)
Definition: 3d_math.h:179
float QuadricEasingInOut(float t)
Definition: 3d_math.h:163
float mapf(float x, float in_min, float in_max, float out_min, float out_max)
Definition: 3d_math.h:133
SFVEC3F CosWeightedRandomHemisphereDirection(const SFVEC3F &n)
Definition: 3d_math.h:69
float Fast_RandFloat()
Definition: 3d_fastmath.cpp:45
bool Refract(const SFVEC3F &aInVector, const SFVEC3F &aNormal, float aRin_over_Rout, SFVEC3F &aOutVector)
Based on: https://github.com/mmp/pbrt-v3/blob/master/src/core/reflection.h See also: http://www....
Definition: 3d_math.h:112
SFVEC3F UniformRandomHemisphereDirection()
Definition: 3d_math.h:55
SFVEC3F MaterialDiffuseToColorCAD(const SFVEC3F &aDiffuseColor)
Definition: 3d_math.h:147
glm::vec3 SFVEC3F
Definition: xv3d_types.h:44
SFVEC3F SphericalToCartesian(float aInclination, float aAzimuth)
https://en.wikipedia.org/wiki/Spherical_coordinate_system
Definition: 3d_math.h:43