What follows is the highlighted source code with comments. You can also download this file directly: Similarity.java.

/* * This work by W. Patrick Hooper <wphooper@gmail.com> is free of known copyright restrictions. * The work is in the public domain. * * Author's website: <a href="http://wphooper.com">http://wphooper.com</a>. */ package geometry; import number.Complex; /** * This class represents an orientation preserving similarity of the plane. * These maps are of the form z maps to w*z+a, for complex numbers w and a. * * @author W. Patrick Hooper */ public final class Similarity implements PlanarMap { private final Complex w, a; /** * Construct the similarity z maps to w*z+a. */ public Similarity(Complex w, Complex a) { this.w = w; this.a = a; } /** * Construct the similarity sending zero to the starting point of the * segment and one to the ending point. */ public Similarity(LineSegment s) { this.w = s.endingPoint().minus(s.startingPoint()); this.a = s.startingPoint(); } /** * Apply the similarity to z. */ public Complex map(Complex z) { return w.mult(z).add(a); } /** * Return a representation of the similarity as a string. */ public String toString() { return "z -> "+w+"*z + "+a; } }

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