+++ /dev/null
-package fr.orsay.lri.varna.models.geom;
-
-
-import java.awt.geom.Point2D;
-
-/**
- * This class implements a cubic Bezier curve
- * with a constant speed parametrization.
- * The Bezier curve is approximated by a sequence of n straight lines,
- * where the n+1 points between the lines are
- * { B(k/n), k=0,1,...,n } where B is the standard
- * parametrization given here:
- * http://en.wikipedia.org/wiki/Bezier_curve#Cubic_B.C3.A9zier_curves
- * You can then use the constant speed parametrization over this sequence
- * of straight lines.
- *
- * @author Raphael Champeimont
- */
-public class CubicBezierCurve {
-
- /**
- * The four points defining the curve.
- */
- private Point2D.Double P0, P1, P2, P3;
-
-
-
- private int n;
- /**
- * The number of lines approximating the Bezier 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 exact cubic Bezier curve parametrization.
- * Argument t must be in [0,1].
- */
- public Point2D.Double standardParam(double t) {
- double x = Math.pow(1-t,3) * P0.x
- + 3 * Math.pow(1-t,2) * t * P1.x
- + 3 * (1-t) * t * t * P2.x
- + t * t * t * P3.x;
- double y = Math.pow(1-t,3) * P0.y
- + 3 * Math.pow(1-t,2) * t * P1.y
- + 3 * (1-t) * t * t * P2.y
- + t * t * t * P3.y;
- 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;
- }
-
-
-
- /**
- * A Bezier curve can be defined by four points,
- * see http://en.wikipedia.org/wiki/Bezier_curve#Cubic_B.C3.A9zier_curves
- * Here we give this four points and a integer to say in how many
- * line segments we want to cut the Bezier curve (if n is bigger
- * the computation takes longer but the precision is better).
- * The number of lines must be at least 1.
- */
- public CubicBezierCurve(
- Point2D.Double P0,
- Point2D.Double P1,
- Point2D.Double P2,
- Point2D.Double P3,
- int n) {
- this.P0 = P0;
- this.P1 = P1;
- this.P2 = P2;
- this.P3 = P3;
- this.n = n;
- if (n < 1) {
- throw (new IllegalArgumentException("n must be at least 1"));
- }
- computeData();
- }
-
-
- 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 Point2D.Double getP0() {
- return P0;
- }
-
- public Point2D.Double getP1() {
- return P1;
- }
-
- public Point2D.Double getP2() {
- return P2;
- }
-
- public Point2D.Double getP3() {
- return P3;
- }
-
-
-
-
-
-}
git://source.jalview.org / jalview.git / blobdiff