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/* * Copyright (C) 2012 W. Patrick Hooper <wphooper@gmail.com> * * This program 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. * * This program 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, write to the Free Software * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. */ package path; import geometry.Similarity; import number.Complex; /** * A substitution fractal is the limit of a sequence of polygonal approximations. * * It is obtained by the following construction. Let p be an arbitrary polygonal * path. This will be the first polygonal approximation of our path. * * Let gamma be a polygonal path which starts at zero and ends at one. We call * this the substitution path. The * second polygonal approximation is obtained by replacing each edge of * p by the image of gamma under a similarity sending the endpoints of gamma * to the endpoints of the edge. The third approximation is obtained by * applying the same process to the second approximation, and so on. * * @author W. Patrick Hooper */ public class SubstitutionFractal implements Path { final PolygonalPath p; // Starting path final PolygonalPath gamma; // "substituted" for every line segment in p. /** Construct a Substitution path with a given first polygonal approximation * p and a substitution path gamma. */ public SubstitutionFractal(PolygonalPath p, PolygonalPath gamma) { this.p=p; this.gamma=gamma; } /** Construct a Substitution path with gamma serving as both the first * polygonal approximation and the substitution path. */ public SubstitutionFractal(PolygonalPath gamma) { this.p=gamma; this.gamma=gamma; } // Inner class which allows us to build an iterator: private class SubstitutionIterator implements PathIterator { private EdgeIterator it; public SubstitutionIterator() { it=p.iterator(); } @Override public boolean hasNext() { return it.hasNext(); } @Override public SubstitutionFractal next() { Similarity sim=new Similarity(it.next()); // sim is the similarity sending 0 and 1 to the endpoints of the segment it.next(). // "new VertexPath(gamma,sim)" gives the image of gamma under the similarity. return new SubstitutionFractal(new VertexPath(gamma, sim),gamma); } } /** Return an iterator over the sub-paths */ @Override public PathIterator iterator() { return new SubstitutionIterator(); } /** Return the ending point of the path */ @Override public Complex endingPoint() { return p.endingPoint(); } /** Return the starting point of the path */ @Override public Complex startingPoint() { return p.startingPoint(); } }

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