/**
 * jQuery Roundabout Shapes v1.1
 * http://fredhq.com/projects/roundabout-shapes/
 * 
 * Provides additional paths along which items can move for the
 * jQuery Roundabout plugin (v1.0+).
 *
 * Terms of Use // jQuery Roundabout Shapes
 *
 * Open source under the BSD license
 *
 * Copyright (c) 2009, Fred LeBlanc
 * All rights reserved.
 * 
 * Redistribution and use in source and binary forms, with or without 
 * modification, are permitted provided that the following conditions are met:
 * 
 *   - Redistributions of source code must retain the above copyright
 *     notice, this list of conditions and the following disclaimer.
 *   - Redistributions in binary form must reproduce the above 
 *     copyright notice, this list of conditions and the following 
 *     disclaimer in the documentation and/or other materials provided 
 *     with the distribution.
 *   - Neither the name of the author nor the names of its contributors 
 *     may be used to endorse or promote products derived from this 
 *     software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE 
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 
 * POSSIBILITY OF SUCH DAMAGE.
 */
jQuery.extend(jQuery.roundabout_shape,
{
    theJuggler: function(r, a, t) { 
        return {
            x: Math.sin(r + a), 
            y: Math.tan(Math.exp(Math.log(r)) + a) / (t - 1), 
            z: (Math.cos(r + a) + 1) / 2,
            scale: (Math.sin(r + Math.PI/2 + a) / 2) + 0.5
        };
    },
    figure8: function(r, a, t) {
        return {
            x: Math.sin(r * 2 + a), 
            y: (Math.sin(r + Math.PI/2 + a) / 8) * t, 
            z: (Math.cos(r + a) + 1) / 2,
            scale: (Math.sin(r + Math.PI/2 + a) / 2) + 0.5
        };
    },
    waterWheel: function(r, a, t) {
        return {
            x: (Math.sin(r + Math.PI/2 + a) / 8) * t, 
            y: Math.sin(r + a) / (Math.PI/2), 
            z: (Math.cos(r + a) + 1) / 2,
            scale: (Math.sin(r + Math.PI/2 + a) / 2) + 0.5
        };
    },
    square: function(r, a, t) {
        var sq_x, sq_y, sq_z;
        
        if (r <= Math.PI/2) {
            sq_x = (2/Math.PI) * r;
            sq_y = -(2/Math.PI) * r + 1;
            sq_z = -(1/Math.PI) * r + 1;
        } else if (r > Math.PI/2 && r <= Math.PI) {
            sq_x = -(2/Math.PI) * r + 2;
            sq_y = -(2/Math.PI) * r + 1;
            sq_z = -(1/Math.PI) * r + 1;
        } else if (r > Math.PI && r <= (3 * Math.PI) / 2) {
            sq_x = -(2/Math.PI) * r + 2;
            sq_y = (2/Math.PI) * r - 3;
            sq_z = (1/Math.PI) * r - 1;
        } else {
            sq_x = (2/Math.PI) * r - 4;
            sq_y = (2/Math.PI) * r - 3;
            sq_z = (1/Math.PI) * r - 1;
        }
        
        return {
            x: sq_x,
            y: sq_y * t, 
            z: sq_z,
            scale: sq_z
        }
    },
    conveyorBeltLeft: function(r, a, t) {
        return {
            x: -Math.cos(r + a), 
            y: (Math.cos(r + 3*Math.PI/2 + a) / 8) * t, 
            z: (Math.sin(r + a) + 1) / 2,
            scale: (Math.sin(r + Math.PI/2 + a) / 2) + 0.5
        };
    },
    conveyorBeltRight: function(r, a, t) {
        return {
            x: Math.cos(r + a), 
            y: (Math.cos(r + 3*Math.PI/2 + a) / 8) * t, 
            z: (Math.sin(r + a) + 1) / 2,
            scale: (Math.sin(r + Math.PI/2 + a) / 2) + 0.5
        };
    },
    goodbyeCruelWorld: function(r, a, t) {
        return {
            x: Math.sin(r + a), 
            y: (Math.tan(r + 3*Math.PI/2 + a) / 8) * (t + 0.5), 
            z: (Math.sin(r + a) + 1) / 2,
            scale: (Math.sin(r + Math.PI/2 + a) / 2) + 0.5
        };
    },
    diagonalRingLeft: function(r, a, t) {
        return {
            x: Math.sin(r + a), 
            y: -Math.cos(r + Math.tan(Math.cos(a))) / (t + 1.5), 
            z: (Math.cos(r + a) + 1) / 2,
            scale: (Math.sin(r + Math.PI/2 + a) / 2) + 0.5
        };
    },
    diagonalRingRight: function(r, a, t) {
        return {
            x: Math.sin(r + a), 
            y: Math.cos(r + Math.tan(Math.cos(a))) / (t + 1.5), 
            z: (Math.cos(r + a) + 1) / 2,
            scale: (Math.sin(r + Math.PI/2 + a) / 2) + 0.5
        };
    },
    rollerCoaster: function(r, a, t) {
        return {
            x: Math.sin(r + a), 
            y: Math.sin((2 + t) * r), 
            z: (Math.cos(r + a) + 1) / 2,
            scale: (Math.sin(r + Math.PI/2 + a) / 2) + 0.5
        }
    },
    tearDrop: function(r, a, t) {
        return {
            x: Math.sin(r + a), 
            y: -Math.sin(r/2 + t) + 0.35, 
            z: (Math.cos(r + a) + 1) / 2,
            scale: (Math.sin(r + Math.PI/2 + a) / 2) + 0.5
        }
    }
});