warp.h

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/*
    This file is part of Mitsuba, a physically based rendering system.

    Copyright (c) 2007-2014 by Wenzel Jakob and others.

    Mitsuba is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License Version 3
    as published by the Free Software Foundation.

    Mitsuba 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, see <http://www.gnu.org/licenses/>.
*/

#pragma once
#if !defined(__MITSUBA_CORE_WARP_H_)
#define __MITSUBA_CORE_WARP_H_

#include <mitsuba/core/frame.h>

MTS_NAMESPACE_BEGIN

/**
 * \brief Implements common warping techniques that map from the unit
 * square to other domains, such as spheres, hemispheres, etc.
 *
 * The main application of this class is to generate uniformly
 * distributed or weighted point sets in certain common target domains.
 */
namespace warp {
        // =============================================================
        //! @{ \name Warping techniques related to spheres and subsets
        // =============================================================

        /// Uniformly sample a vector on the unit sphere with respect to solid angles
        extern MTS_EXPORT_CORE Vector squareToUniformSphere(const Point2 &sample);

        /// Density of \ref squareToUniformSphere() with respect to solid angles
        extern MTS_EXPORT_CORE inline Float squareToUniformSpherePdf() { return INV_FOURPI; }

        /// Uniformly sample a vector on the unit hemisphere with respect to solid angles
        extern MTS_EXPORT_CORE Vector squareToUniformHemisphere(const Point2 &sample);

        /// Density of \ref squareToUniformHemisphere() with respect to solid angles
        extern MTS_EXPORT_CORE inline Float squareToUniformHemispherePdf() { return INV_TWOPI; }

        /// Sample a cosine-weighted vector on the unit hemisphere with respect to solid angles
        extern MTS_EXPORT_CORE Vector squareToCosineHemisphere(const Point2 &sample);

        /// Density of \ref squareToCosineHemisphere() with respect to solid angles
        extern MTS_EXPORT_CORE inline Float squareToCosineHemispherePdf(const Vector &d)
                { return INV_PI * Frame::cosTheta(d); }

        /**
         * \brief Uniformly sample a vector that lies within a given
         * cone of angles around the Z axis
         *
         * \param cosCutoff Cosine of the cutoff angle
         * \param sample A uniformly distributed sample on \f$[0,1]^2\f$
         */
        extern MTS_EXPORT_CORE Vector squareToUniformCone(Float cosCutoff, const Point2 &sample);

        /**
         * \brief Uniformly sample a vector that lies within a given
         * cone of angles around the Z axis
         *
         * \param cosCutoff Cosine of the cutoff angle
         * \param sample A uniformly distributed sample on \f$[0,1]^2\f$
         */
        extern MTS_EXPORT_CORE inline Float squareToUniformConePdf(Float cosCutoff) {
                return INV_TWOPI / (1-cosCutoff);
        }

        //! @}
        // =============================================================

        // =============================================================
        //! @{ \name Warping techniques that operate in the plane
        // =============================================================

        /// Uniformly sample a vector on a 2D disk
        extern MTS_EXPORT_CORE Point2 squareToUniformDisk(const Point2 &sample);

        /// Density of \ref squareToUniformDisk per unit area
        extern MTS_EXPORT_CORE inline Float squareToUniformDiskPdf() { return INV_PI; }

        /// Low-distortion concentric square to disk mapping by Peter Shirley (PDF: 1/PI)
        extern MTS_EXPORT_CORE Point2 squareToUniformDiskConcentric(const Point2 &sample);

        /// Inverse of the mapping \ref squareToUniformDiskConcentric
        extern MTS_EXPORT_CORE Point2 uniformDiskToSquareConcentric(const Point2 &p);

        /// Density of \ref squareToUniformDisk per unit area
        extern MTS_EXPORT_CORE inline Float squareToUniformDiskConcentricPdf() { return INV_PI; }

        /// Convert an uniformly distributed square sample into barycentric coordinates
        extern MTS_EXPORT_CORE Point2 squareToUniformTriangle(const Point2 &sample);

        /**
         * \brief Sample a point on a 2D standard normal distribution
         *
         * Internally uses the Box-Muller transformation
         */
        extern MTS_EXPORT_CORE Point2 squareToStdNormal(const Point2 &sample);

        /// Density of \ref squareToStdNormal per unit area
        extern MTS_EXPORT_CORE Float squareToStdNormalPdf(const Point2 &pos);

        /// Warp a uniformly distributed square sample to a 2D tent distribution
        extern MTS_EXPORT_CORE Point2 squareToTent(const Point2 &sample);

        /**
         * \brief Warp a uniformly distributed sample on [0, 1] to a nonuniform
         * tent distribution with nodes <tt>{a, b, c}</tt>
         */
        extern MTS_EXPORT_CORE Float intervalToNonuniformTent(Float a, Float b, Float c, Float sample);

        //! @}
        // =============================================================
};

MTS_NAMESPACE_END

#endif /* __MITSUBA_CORE_WARP_H_ */