3d_math.h

/*
 * This program source code file is part of KiCad, a free EDA CAD application.
 *
 * Copyright (C) 2015-2016 Mario Luzeiro <mrluzeiro@ua.pt>
 * 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.
 *
 * This program is distributed in the hope that it will be useful,
 * 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:
 * http://www.gnu.org/licenses/old-licenses/gpl-2.0.html
 * or you may search the http://www.gnu.org website for the version 2 license,
 * or you may write to the Free Software Foundation, Inc.,
 * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA
 */

/**
 * @file  3d_math.h
 * @brief Defines math related functions
 */

#ifndef _3D_MATH_H
#define _3D_MATH_H

#include <plugins/3dapi/xv3d_types.h>
#include "3d_fastmath.h"

/**
 * https://en.wikipedia.org/wiki/Spherical_coordinate_system
 *
 * @param aInclination θ ∈ [0, π]
 * @param aAzimuth φ ∈ [0, 2π]
 * @return Cartesian coordinates
 */
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 ) );
}


/**
 * @todo This is not correct because it is not a gaussian random.
 */
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 );
}


/**
 * Based on:
 *     https://github.com/mmp/pbrt-v3/blob/master/src/core/reflection.h
 * See also:
 *     http://www.flipcode.com/archives/Raytracing_Topics_Techniques-Part_3_Refractions_and_Beers_Law.shtml
 *
 * @param aInVector incoming vector.
 * @param aNormal normal in the intersection point.
 * @param aRin_over_Rout incoming refraction index / out refraction index.
 * @param aOutVector the refracted vector.
 * @return true
 */
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