sampling.inl

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/*
    Sheep - A Rigid Body Dynamics Engine
    Copyright (C) 2001-2004 Francois Beaune
    Contact: http://toxicengine.sourceforge.net/

    This file is part of Sheep.

    Sheep 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.

    Sheep 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 Sheep; if not, write to the Free Software
    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
*/

inline
sheep::Point2 UniformDiskSampling(sheep::Real xi1, sheep::Real xi2) {
    assert(xi1 >= 0.0 && xi1 <= 1.0);
    assert(xi2 >= 0.0 && xi2 <= 1.0);

    // Peter Shirley and Kenneth Chiu. A low distortion map between disk and square.
    // Journal of Graphics Tools, 2(3):45-52, 1997.
    // http://www.acm.org/jgt/papers/ShirleyChiu97/.

    const sheep::Real a = xi1 + xi1 - 1.0;
    const sheep::Real b = xi2 + xi2 - 1.0;

    sheep::Real phi, r;

    if(a > -b) {        // region 1 or 2
        if(a > b) {     // region 1, also |a| > |b|
            r = a;
            phi = (sheep::PI / 4.0) * (b / a);
        } else {        // region 2, also |b| > |a|
            r = b;
            phi = (sheep::PI / 4.0) * (2.0 - (a / b));
        }
    } else {            // region 3 or 4
        if(a < b) {     // region 3, also |a| >= |b|, a != 0
            r = -a;
            phi = (sheep::PI / 4.0) * (4.0 + (b / a));
        } else {        // region 4, |b| >= |a|, but a == 0 and b == 0 could occur
            r = -b;
            if (b != 0.0)
                phi = (sheep::PI / 4.0) * (6.0 - (a / b));
            else
                phi = 0.0;
        }
    }

    return sheep::Point2(r * cos(phi), r * sin(phi));
}

inline
sheep::Point3 UniformSphereSampling(sheep::Real xi1, sheep::Real xi2) {
    assert(xi1 >= 0.0 && xi1 <= 1.0);
    assert(xi2 >= 0.0 && xi2 <= 1.0);

    const sheep::Real r = 2.0 * sqrt(xi1 * (1.0 - xi1));    //!\todo Turn the multiplication into an addition.
    const sheep::Real phi = 2.0 * sheep::PI * xi2;  //!\todo Turn the multiplication into an addition.

    return sheep::Point3(r * cos(phi), 1.0 - 2.0 * xi1, r * sin(phi));  //!\todo Turn the multiplication into an addition.
}

inline
sheep::Point3 UniformHemisphereSampling(sheep::Real xi1, sheep::Real xi2) {
    assert(xi1 >= 0.0 && xi1 <= 1.0);
    assert(xi2 >= 0.0 && xi2 <= 1.0);

    const sheep::Real r = sqrt(1.0 - xi1 * xi1);
    const sheep::Real phi = 2.0 * sheep::PI * xi2;  //!\todo Turn the multiplication into an addition.

    return sheep::Point3(r * cos(phi), xi1, r * sin(phi));
}

inline
sheep::Point3 CosineHemisphereSampling(sheep::Real xi1, sheep::Real xi2) {
    assert(xi1 >= 0.0 && xi1 <= 1.0);
    assert(xi2 >= 0.0 && xi2 <= 1.0);

    const sheep::Real r = sqrt(1.0 - xi1);
    const sheep::Real phi = 2.0 * sheep::PI * xi2;  //!\todo Turn the multiplication into an addition.

    return sheep::Point3(r * cos(phi), sqrt(xi1), r * sin(phi));
}

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