+/**
+ * File written by Raphael Champeimont
+ * UMR 7238 Genomique des Microorganismes
+ */
+package fr.orsay.lri.varna.models.geom;
+
+public class ComputeArcCenter {
+
+ /**
+ * Given an arc length (l) and segment length (delta) of the arc,
+ * find where to put the center, returned as a position of the perpendicular
+ * bisector of the segment. The positive side is the one where the arc is drawn.
+ * It works using Newton's method.
+ */
+ public static double computeArcCenter(double delta, double l) {
+ double x_n = 0;
+ double x_n_plus_1, f_x_n, f_x_n_plus_1;
+ f_x_n = f(x_n,delta);
+ while (true) {
+ x_n_plus_1 = x_n - (f_x_n - l)/fprime(x_n,delta);
+ f_x_n_plus_1 = f(x_n_plus_1,delta);
+ // We want a precision of 0.1 on arc length
+ if (x_n_plus_1 == Double.NEGATIVE_INFINITY || Math.abs(f_x_n_plus_1 - f_x_n) < 0.1) {
+ //System.out.println("computeArcCenter: steps = " + steps + " result = " + x_n_plus_1);
+ return x_n_plus_1;
+ }
+ x_n = x_n_plus_1;
+ f_x_n = f_x_n_plus_1;
+ }
+ }
+
+ private static double f(double c, double delta) {
+ if (c < 0) {
+ return 2*Math.atan(delta/(-2*c)) * Math.sqrt(delta*delta/4 + c*c);
+ } else if (c != 0) { // c > 0
+ return (2*Math.PI - 2*Math.atan(delta/(2*c))) * Math.sqrt(delta*delta/4 + c*c);
+ } else { // c == 0
+ return Math.PI * Math.sqrt(delta*delta/4 + c*c);
+ }
+ }
+
+ /**
+ * d/dc f(c,delta)
+ */
+ private static double fprime(double c, double delta) {
+ if (c < 0) {
+ return delta/(c*c + delta/4)*Math.sqrt(delta*delta/4 + c*c) + 2*Math.atan(delta/(-2*c))*c/Math.sqrt(delta*delta/4 + c*c);
+ } else if (c != 0) { // c > 0
+ return delta/(c*c + delta/4)*Math.sqrt(delta*delta/4 + c*c) + (2*Math.PI - 2*Math.atan(delta/(-2*c)))*c/Math.sqrt(delta*delta/4 + c*c);
+ } else { // c == 0
+ return 2;
+ }
+ }
+}
\ No newline at end of file