-/**
- * 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);
- }
- */
-
-}