include/crbn/matter/fresnel.hpp

#ifndef _FRESNEL_HPP_
#define _FRESNEL_HPP_

#include <crbn/basic/scalar.hpp>

// http://scienceworld.wolfram.com/physics/FresnelEquations.html
// ----> http://citadels.no-ip.info/~mooz/renderDiamond_WCGS00.pdf
// ----> http://citadels.no-ip.info/~mooz/reflectance.pdf
// ----> http://www.tf.uni-kiel.de/matwis/amat/semi_en/kap_5/backbone/r5_2_2.html
// http://www.integra.co.jp/webpages/inspirer/whitepap/ch3/ch3.htm
// ----> http://www.imagico.de/pov/water/water_app1.html
// ----> http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/freseq.html
// http://www.atis.org/tg2k/_absorption_index.html
//

// Compute fresnel term

// FresnelPerpendicularReflect :
// Ratio of amplitudes of reflected to incoming electric 
// fields perpendicular to the plane of incidence
inline float FresnelPerpendicularReflect(const float& n1, const float& cos_alpha, 
                                         const float& n2, const float& cos_beta ) {
        return ((n1 * cos_alpha) - (n2 * cos_beta)) / ((n1 * cos_alpha) + (n2 * cos_beta));
}

// FresnelParallelReflect :
// Ratio of amplitudes of reflected to incoming electric
// fields parallel to the plane of incidence
inline float FresnelParallelReflect(const float& n1, const float& cos_alpha,
                                    const float& n2, const float& cos_beta ) {
        return ((n2 * cos_alpha) - (n1 * cos_beta)) / ((n1 * cos_beta) + (n2 * cos_alpha));
}

// FresnelPerpendicularTransmit :
// Ratio of amplitudes of transmitted to incoming electric
// fields perpendicular to the plane of incidence
inline float FresnelPerpendicularTransmit(const float& n1, const float& cos_alpha,
                                          const float& n2, const float& cos_beta ) {
        return (2.0 * n1 * cos_alpha) / ((n1 * cos_alpha) + (n2 * cos_beta));
}

// FresnelParallelTransmit :
// Ratio of amplitudes of transmitted to incoming electric
// fields parallel to the plane of incidence
inline float FresnelParallelTransmit(const float& n1, const float& cos_alpha,
                                     const float& n2, const float& cos_beta ) {
        return (2.0 * n1 * cos_alpha) / ((n1 * cos_beta) + (n2 * cos_alpha));
}

// Reflected + Transmitted = 1
// Reflected power
inline float Reflected(const float& n1, const float& cos_alpha,
                       const float& n2, const float& cos_beta ) {
        float parallel      = FresnelParallelReflect(n1, cos_alpha, n2, cos_beta);
        float perpendicular = FresnelPerpendicularReflect(n1, cos_alpha, n2, cos_beta);
        return 0.5 * (sqr(parallel) + sqr(perpendicular));
}

// Transmitted power
inline float Transmitted(const float& n1, const float& cos_alpha,
                         const float& n2, const float& cos_beta ) {
        float parallel      = FresnelParallelTransmit(n1, cos_alpha, n2, cos_beta);
        float perpendicular = FresnelPerpendicularTransmit(n1, cos_alpha, n2, cos_beta);

        return ((n2 * cos_beta) / (n1 * cos_alpha)) * 0.5 * (sqr(parallel) + sqr(perpendicular)); 
}

#endif

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