--- /dev/null
+package fr.orsay.lri.varna.models.geom;
+
+
+import java.awt.geom.AffineTransform;
+import java.awt.geom.Point2D;
+
+
+/**
+ * Ellipse, with axis = X and Y.
+ * This class is useful for constant speed parameterization
+ * (just like CubicBezierCurve).
+ * The ellipse drawn is in fact an half-ellipse, from 0 to PI.
+ *
+ * @author Raphael Champeimont
+ */
+public class HalfEllipse {
+
+ /**
+ * The four points defining the curve.
+ */
+ private double a, b;
+
+
+
+ private int n;
+ /**
+ * The number of lines approximating the curve.
+ */
+ public int getN() {
+ return n;
+ }
+
+
+ /**
+ * Get the (exact) length of the approximation curve.
+ */
+ public double getApproxCurveLength() {
+ return lengths[n-1];
+ }
+
+
+
+ /**
+ * The n+1 points between the n lines.
+ */
+ private Point2D.Double[] points;
+
+
+
+ /**
+ * Array of length n.
+ * lengths[i] is the sum of lengths of lines up to and including the
+ * line starting at point points[i].
+ */
+ private double[] lengths;
+
+
+ /**
+ * Array of length n.
+ * The vectors along each line, with a norm of 1.
+ */
+ private Point2D.Double[] unitVectors;
+
+
+
+ /**
+ * The standard ellipse parameterization.
+ * Argument t must be in [0,1].
+ */
+ public Point2D.Double standardParam(double t) {
+ double x = a*Math.cos(t*Math.PI);
+ double y = b*Math.sin(t*Math.PI);
+ return new Point2D.Double(x, y);
+ }
+
+
+
+
+
+ /**
+ * Uniform approximated parameterization.
+ * A value in t must be in [0, getApproxCurveLength()].
+ * We have built a function f such that f(t) is the position of
+ * the point on the approximation curve (n straight lines).
+ * The interesting property is that the length of the curve
+ * { f(t), t in [0,l] } is exactly l.
+ * The java function is simply the application of f over each element
+ * of a sorted array, ie. uniformParam(t)[k] = f(t[k]).
+ * Computation time is O(n+m) where n is the number of lines in which
+ * the curve is divided and m is the length of the array given as an
+ * argument. The use of a sorted array instead of m calls to the
+ * function enables us to have a complexity of O(n+m) instead of O(n*m)
+ * because we don't need to search in all the n possible lines for
+ * each value in t (as we know their are in increasing order).
+ */
+ public Point2D.Double[] uniformParam(double[] t) {
+ int m = t.length;
+ Point2D.Double[] result = new Point2D.Double[m];
+ int line = 0;
+ for (int i=0; i<m; i++) {
+ while ((line<n) && (lengths[line] < t[i])) {
+ line++;
+ }
+ if (line >= n) {
+ // In theory should not happen, but float computation != math.
+ line = n-1;
+ }
+ if (t[i] < 0) {
+ throw (new IllegalArgumentException("t[" + i + "] < 0"));
+ }
+ // So now we know on which line we are
+ double lengthOnLine = t[i] - (line != 0 ? lengths[line-1] : 0);
+ double x = points[line].x + unitVectors[line].x * lengthOnLine;
+ double y = points[line].y + unitVectors[line].y * lengthOnLine;
+ result[i] = new Point2D.Double(x, y);
+ }
+ return result;
+ }
+
+
+
+ /**
+ * An ellipse that has axis equal to X and Y axis needs only
+ * two numbers (half-axis lengths) to be defined.
+ * They are resp. a for X axis and b for Y axis.
+ * n = how many line segments we want to cut the curve
+ * (if n is bigger the computation takes longer but the precision is better).
+ * The number of lines must be at least 1.
+ */
+ public HalfEllipse(double a, double b, int n) {
+ this.a = a;
+ this.b = b;
+ this.n = n;
+ if (n < 1) {
+ throw (new IllegalArgumentException("n must be at least 1"));
+ }
+ computeData();
+ }
+
+
+ /**
+ * Returns that affine transform that moves the ellipse
+ * given by this class such that its 0/pi axis matches P0-P1.
+ */
+ public static AffineTransform matchAxisA(Point2D.Double P0, Point2D.Double P1) {
+ double theta = MiscGeom.angleFromVector(P0.x-P1.x, P0.y-P1.y);
+ Point2D.Double mid = new Point2D.Double((P0.x+P1.x)/2, (P0.y+P1.y)/2);
+ AffineTransform transform = new AffineTransform();
+ transform.translate(mid.x, mid.y);
+ transform.rotate(theta);
+ return transform;
+ }
+
+
+ private void computeData() {
+ points = new Point2D.Double[n+1];
+ for (int k=0; k<=n; k++) {
+ points[k] = standardParam(((double) k) / n);
+ }
+
+ lengths = new double[n];
+ unitVectors = new Point2D.Double[n];
+ double sum = 0;
+ for (int i=0; i<n; i++) {
+ double l = lineLength(points[i], points[i+1]);
+ double dx = (points[i+1].x - points[i].x) / l;
+ double dy = (points[i+1].y - points[i].y) / l;
+ unitVectors[i] = new Point2D.Double(dx, dy);
+ sum += l;
+ lengths[i] = sum;
+ }
+
+
+
+ }
+
+
+ private double lineLength(Point2D.Double P1, Point2D.Double P2) {
+ return P2.distance(P1);
+ }
+
+ public double getA() {
+ return a;
+ }
+
+ public double getB() {
+ return b;
+ }
+
+
+
+}
git://source.jalview.org / jalview.git / blobdiff