+/**
+ * File written by Raphael Champeimont
+ * UMR 7238 Genomique des Microorganismes
+ */
+package fr.orsay.lri.varna.models.geom;
+
+public class ComputeEllipseAxis {
+ public static boolean debug = false;
+
+ /**
+ * Given one axis half-length b and the circumference l,
+ * find the other axis half-length a.
+ * Returns 0 if there is no solution.
+ * Implemented with Newton's method.
+ */
+ public static double computeEllipseAxis(double b, double l) {
+ if (l/4 <= b || b <= 0 || l <= 0) {
+ // No such ellipse can exist.
+ return 0;
+ } else {
+ int steps = 0;
+ double x_n = 10;
+ double x_n_plus_1, f_x_n, f_x_n_plus_1;
+ f_x_n = f(x_n,b) - l;
+ while (true) {
+ //System.out.println("x_n = " + x_n + " f(x_n)=" + f_x_n);
+ x_n_plus_1 = x_n - f_x_n/fprime(x_n,b);
+ f_x_n_plus_1 = f(x_n_plus_1,b) - l;
+ if (x_n_plus_1 < 0) {
+ System.out.println("ComputeEllipseAxis: x_n < 0 => returning 0");
+ return 0;
+ }
+ // We want a precision of 0.01 on arc length
+ if (Math.abs(f_x_n_plus_1 - f_x_n) < 0.01) {
+ if (debug) System.out.println("#steps = " + steps);
+ return x_n_plus_1;
+ }
+ x_n = x_n_plus_1;
+ f_x_n = f_x_n_plus_1;
+ steps++;
+ }
+ }
+ }
+
+
+
+ private static double f(double a, double b) {
+ // This is Ramanujan's approximation of an ellipse circumference
+ // Nice because it is fast to compute (no need to compute an integral)
+ // and the derivative is also simple (and fast to compute).
+ return Math.PI*(3*(a+b) - Math.sqrt(10*a*b + 3*(a*a + b*b)));
+ }
+
+ private static double fprime(double a, double b) {
+ return Math.PI*(3 - (5*b + 3*a)/Math.sqrt(10*a*b + 3*(a*a + b*b)));
+ }
+
+
+ /*
+ private static void test(double a, double b, double l) {
+ double a2 = computeEllipseAxis(b, l);
+ System.out.println("true a=" + a + " l=" + l + " estimated a=" + a2 + " l(from true a)=" + f(a,b));
+ }
+
+ private static void test(double b, double l) {
+ double a2 = computeEllipseAxis(b, l);
+ System.out.println("true l=" + l + " estimated a=" + a2);
+ }
+
+
+ public static void main(String[] args) {
+ double b = 4;
+ test(100, b, 401.3143);
+ test(7, b, 35.20316);
+ test(4, b, 25.13274);
+ test(1, b, 17.15684);
+ test(0.5, b, 16.37248);
+ test(0.25, b, 16.11448);
+ test(0.1, b, 16.02288);
+ test(0.01, b, 16.00034);
+ test(0, b, 16);
+ test(10000, b, 40000.03);
+ }
+ */
+
+ /*
+ public static void main(String[] args) {
+ test(222.89291150684895, 2240);
+ }
+ */
+
+}