distribution_transformations.h

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/** @file
 *  @author Bram de Greve (bramz@users.sourceforge.net)
 *  @author Tom De Muer (tomdemuer@users.sourceforge.net)
 *
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 *  the License. You may obtain a copy of the License at 
 *  http://lass.sourceforge.net/cpal-license. The License is based on the 
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 *  the Original Developer. In addition, Exhibit A has been modified to be consistent 
 *  with Exhibit B.
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 *  Software distributed under the License is distributed on an "AS IS" basis, WITHOUT 
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 *  language governing rights and limitations under the License.
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 *  The Original Code is LASS - Library of Assembled Shared Sources.
 *  
 *  The Initial Developer of the Original Code is Bram de Greve and Tom De Muer.
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/** @defgroup DistributionTransformations
 *
 *  A set of functions to transform samples between distribution
 */

#ifndef LASS_GUARDIAN_OF_INCLUSION_NUM_DISTRIBUTION_TRANSFORMATIONS_H
#define LASS_GUARDIAN_OF_INCLUSION_NUM_DISTRIBUTION_TRANSFORMATIONS_H

#include "num_common.h"
#include "../prim/point_2d.h"
#include "../prim/point_3d.h"

namespace lass
{
namespace num
{

/** @ingroup DistributionTransformations
 */
template <typename T>
const prim::Point3D<T> uniformSphere(const prim::Point2D<T>& sample, T& pdf)
{
    const T z = 1 - 2 * sample.x;
    const T rho = sqrt(std::max<T>(0, 1 - z * z));
    const T theta = 2 * num::NumTraits<T>::pi * sample.y;
    pdf = inv(4 * num::NumTraits<T>::pi);
    return prim::Point3D<T>(rho * cos(theta), rho * sin(theta), z);
}

/** @ingroup DistributionTransformations
 */
template <typename T>
const prim::Point3D<T> uniformCone(const prim::Point2D<T>& sample, T minCosTheta, T& pdf)
{
    const T z = minCosTheta + sample.x * (1 - minCosTheta);
    const T rho = sqrt(std::max<T>(0, 1 - z * z));
    const T theta = 2 * NumTraits<T>::pi * sample.y;
    pdf = inv(2 * NumTraits<T>::pi * (1 - minCosTheta));
    return prim::Point3D<T>(rho * cos(theta), rho * sin(theta), z);
}

/** @ingroup DistributionTransformations
 */
template <typename T>
const prim::Point2D<T> uniformDisk(const prim::Point2D<T>& sample, T& pdf)
{
    T rho, theta;
    const T x = 2 * sample.x - 1;
    const T y = 2 * sample.y - 1;
    const T pi_4 = num::NumTraits<T>::pi / 4;

    if (x > -y) 
    {
        if (x > y) 
        {
            rho = x;
            theta = pi_4 * (y / x);
        }
        else       
        {
            rho = y;
            theta = pi_4 * (2 - (x / y));
        }
    }
    else 
    {
        if (x < y) 
        {   
            rho = -x;
            theta = pi_4 * (4 + (y / x));
        }
        else       
        {
            rho = -y;
            if (y != 0)
            {
                theta = pi_4 * (6 - (x / y));
            }
            else
            {
                theta = 0;
            }
        }
    }

    pdf = inv(NumTraits<T>::pi);
    return prim::Point2D<T>(rho * cos(theta), rho * sin(theta));
}

/** @ingroup DistributionTransformations
 */
template <typename T>
const prim::Point3D<T> cosineHemisphere(const prim::Point2D<T>& sample, T& pdf)
{
    const prim::Point2D<T> xy = uniformDisk(sample, pdf);
    const T z = num::sqrt(std::max(T(), 1 - xy.position().squaredNorm()));
    pdf *= z;
    return prim::Point3D<T>(xy.x, xy.y, z);
}

}

}

#endif

// EOF