3d_math.h

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/*
 * This program source code file is part of KiCad, a free EDA CAD application.
 *
 * Copyright (C) 2015-2016 Mario Luzeiro <[email protected]>
 * Copyright (C) 1992-2020 KiCad Developers, see AUTHORS.txt for contributors.
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 *
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 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, you may find one here:
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 * or you may search the http://www.gnu.org website for the version 2 license,
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 */
 
#ifndef _3D_MATH_H
#define _3D_MATH_H
 
#include <plugins/3dapi/xv3d_types.h>
#include "3d_fastmath.h"
 
inline SFVEC3F SphericalToCartesian( float aInclination, float aAzimuth )
{
 float sinInc = glm::sin( aInclination );
 
 return SFVEC3F( sinInc * glm::cos( aAzimuth ), sinInc * glm::sin( aAzimuth ),
 glm::cos( aInclination ) );
}
 
 
inline SFVEC3F UniformRandomHemisphereDirection()
{
 // It was experienced that this function is slow! do not use it :/
 // SFVEC3F b( (rand()/(float)RAND_MAX) - 0.5f,
 // (rand()/(float)RAND_MAX) - 0.5f,
 // (rand()/(float)RAND_MAX) - 0.5f );
 
 SFVEC3F b( Fast_RandFloat() * 0.5f, Fast_RandFloat() * 0.5f, Fast_RandFloat() * 0.5f );
 
 return b;
}
 
 
// https://pathtracing.wordpress.com/2011/03/03/cosine-weighted-hemisphere/
inline SFVEC3F CosWeightedRandomHemisphereDirection( const SFVEC3F& n )
{
 const float Xi1 = (float) rand() / (float) RAND_MAX;
 const float Xi2 = (float) rand() / (float) RAND_MAX;
 
 const float theta = acos( sqrt( 1.0f - Xi1 ) );
 const float phi = 2.0f * glm::pi<float>() * Xi2;
 
 const float xs = sinf( theta ) * cosf( phi );
 const float ys = cosf( theta );
 const float zs = sinf( theta ) * sinf( phi );
 
 const SFVEC3F y( n.x, n.y, n.z );
 SFVEC3F h = y;
 
 if( fabs( h.x ) <= fabs( h.y ) && fabs( h.x ) <= fabs( h.z ) )
 h.x= 1.0f;
 else if( fabs( h.y ) <= fabs( h.x ) && fabs( h.y ) <= fabs( h.z ) )
 h.y= 1.0f;
 else
 h.z= 1.0f;
 
 
 const SFVEC3F x = glm::normalize( glm::cross( h, y ) );
 const SFVEC3F z = glm::normalize( glm::cross( x, y ) );
 
 SFVEC3F direction = xs * x + ys * y + zs * z;
 return glm::normalize( direction );
}
 
 
inline bool Refract( const SFVEC3F &aInVector, const SFVEC3F &aNormal, float aRin_over_Rout,
 SFVEC3F& aOutVector )
{
 float cosThetaI = -glm::dot( aNormal, aInVector );
 float sin2ThetaI = glm::max( 0.0f, 1.0f - cosThetaI * cosThetaI );
 float sin2ThetaT = aRin_over_Rout * aRin_over_Rout * sin2ThetaI;
 
 // Handle total internal reflection for transmission
 if( sin2ThetaT >= 1.0f )
 return false;
 
 float cosThetaT = sqrtf( 1.0f - sin2ThetaT );
 
 aOutVector = glm::normalize( aRin_over_Rout * aInVector +
 ( aRin_over_Rout * cosThetaI - cosThetaT ) *
 aNormal );
 
 return true;
}
 
 
inline float mapf( float x, float in_min, float in_max, float out_min, float out_max )
{
 x = glm::clamp( x, in_min, in_max );
 
 return (x - in_min) * (out_max - out_min) / (in_max - in_min) + out_min;
}
 
inline float RGBtoGray( const SFVEC3F &aColor )
{
 return (aColor.r * 0.2126f +
 aColor.g * 0.7152f +
 aColor.b * 0.0722f);
}
 
inline SFVEC3F MaterialDiffuseToColorCAD( const SFVEC3F &aDiffuseColor )
{
 // convert to a discret scale of grays
 const float luminance = glm::min(
 ( ( (float) ( (unsigned int) ( 4.0f * RGBtoGray( aDiffuseColor ) ) ) + 0.5f ) / 4.0f )
 * 1.0f,
 1.0f );
 
 const float maxValue = glm::max( glm::max( glm::max( aDiffuseColor.r, aDiffuseColor.g ),
 aDiffuseColor.b ), FLT_EPSILON );
 
 return ( aDiffuseColor / SFVEC3F( maxValue ) ) * 0.125f + luminance * 0.875f;
}
 
 
// http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4KngqMiIsImNvbG9yIjoiIzAwMDAwMCJ9LHsidHlwZSI6MCwiZXEiOiItKCh4LTEpXjIpKjIrMSIsImNvbG9yIjoiIzAwMDAwMCJ9LHsidHlwZSI6MTAwMCwid2luZG93IjpbIi0xLjM4NzUwMDAwMDAwMDAwMDIiLCIxLjg2MjQ5OTk5OTk5OTk5OTgiLCItMC43IiwiMS4zIl19XQ--
inline float QuadricEasingInOut( float t )
{
 if( t <= 0.5f )
 {
 return t * t * 2.0f;
 }
 else
 {
 t = t - 1.0f;
 
 return -2.0f * ( t * t ) + 1.0f;
 }
}
 
 
// http://www.wolframalpha.com/input/?i=t%5E2(3-2t)
inline float BezierBlend( float t )
{
 return t * t * ( 3.0f - 2.0f * t );
}
 
#endif // 3D_MATH_H