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/**
 * InterpolateBezier.java
 *
 * Copyright (c) 2013-2016, F(X)yz
 * 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 F(X)yz, any associated website, 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 F(X)yz 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.
 */ 

package org.fxyz3d.shapes.primitives.helper;

import java.util.ArrayList;
import java.util.List;
import org.fxyz3d.geometry.Point3D;

/** Given N 3D points (knots), N-1 Bezier cubic curves will be generated, 
 *  passing through these knots, by adding 2(N-1) control points
 *  Conditions if spline is open: 
 *  - C2 in all the inner knots (2 ecuations x N-2 knots)
 *  - On external knots r''=0 (2 ecuations)
 *  Conditions if spline is closed (knot[0]==knot[N]:
 * - C2 in all the inner knots (2 ecuations x N-2 knots)

*  Tridiagonal linear system -  Thomas algorithm
 *  See: http://www.particleincell.com/blog/2012/bezier-splines/
 * 
 * @author jpereda
 */
public class InterpolateBezier {

    private final List knots;
    private final int numSplines;
    private final boolean isClosed;
    
    private final List splines;
    
    public InterpolateBezier(List knots){
        this.knots=knots;
        numSplines = knots.size()-1;
        
        isClosed=knots.get(0).equals(knots.get(numSplines));
        
        splines = new ArrayList<>(numSplines);
        calculateControlPoints();
    }
    
    public List getSplines() { return splines; }
    
    private void calculateControlPoints(){
        
        if(isClosed){
            List p1=new ArrayList<>(numSplines);
            for(int j=0; j=0; j--){
                    p1[j] = (cr[j]-cc[j]*p1[j+1])/cb[j];
                }
                for(int j=0; j