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105 lines
2.7 KiB
105 lines
2.7 KiB
2 years ago
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'use strict';
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/* eslint-disable space-infix-ops */
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// The precision used to consider an ellipse as a circle
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//
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var epsilon = 0.0000000001;
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// To convert degree in radians
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//
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var torad = Math.PI / 180;
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// Class constructor :
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// an ellipse centred at 0 with radii rx,ry and x - axis - angle ax.
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//
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function Ellipse(rx, ry, ax) {
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if (!(this instanceof Ellipse)) { return new Ellipse(rx, ry, ax); }
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this.rx = rx;
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this.ry = ry;
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this.ax = ax;
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}
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// Apply a linear transform m to the ellipse
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// m is an array representing a matrix :
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// - -
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// | m[0] m[2] |
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// | m[1] m[3] |
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// - -
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//
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Ellipse.prototype.transform = function (m) {
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// We consider the current ellipse as image of the unit circle
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// by first scale(rx,ry) and then rotate(ax) ...
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// So we apply ma = m x rotate(ax) x scale(rx,ry) to the unit circle.
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var c = Math.cos(this.ax * torad), s = Math.sin(this.ax * torad);
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var ma = [
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this.rx * (m[0]*c + m[2]*s),
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this.rx * (m[1]*c + m[3]*s),
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this.ry * (-m[0]*s + m[2]*c),
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this.ry * (-m[1]*s + m[3]*c)
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];
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// ma * transpose(ma) = [ J L ]
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// [ L K ]
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// L is calculated later (if the image is not a circle)
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var J = ma[0]*ma[0] + ma[2]*ma[2],
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K = ma[1]*ma[1] + ma[3]*ma[3];
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// the discriminant of the characteristic polynomial of ma * transpose(ma)
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var D = ((ma[0]-ma[3])*(ma[0]-ma[3]) + (ma[2]+ma[1])*(ma[2]+ma[1])) *
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((ma[0]+ma[3])*(ma[0]+ma[3]) + (ma[2]-ma[1])*(ma[2]-ma[1]));
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// the "mean eigenvalue"
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var JK = (J + K) / 2;
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// check if the image is (almost) a circle
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if (D < epsilon * JK) {
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// if it is
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this.rx = this.ry = Math.sqrt(JK);
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this.ax = 0;
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return this;
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}
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// if it is not a circle
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var L = ma[0]*ma[1] + ma[2]*ma[3];
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D = Math.sqrt(D);
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// {l1,l2} = the two eigen values of ma * transpose(ma)
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var l1 = JK + D/2,
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l2 = JK - D/2;
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// the x - axis - rotation angle is the argument of the l1 - eigenvector
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/*eslint-disable indent*/
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this.ax = (Math.abs(L) < epsilon && Math.abs(l1 - K) < epsilon) ?
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90
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:
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Math.atan(Math.abs(L) > Math.abs(l1 - K) ?
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(l1 - J) / L
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:
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L / (l1 - K)
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) * 180 / Math.PI;
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/*eslint-enable indent*/
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// if ax > 0 => rx = sqrt(l1), ry = sqrt(l2), else exchange axes and ax += 90
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if (this.ax >= 0) {
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// if ax in [0,90]
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this.rx = Math.sqrt(l1);
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this.ry = Math.sqrt(l2);
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} else {
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// if ax in ]-90,0[ => exchange axes
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this.ax += 90;
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this.rx = Math.sqrt(l2);
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this.ry = Math.sqrt(l1);
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}
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return this;
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};
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// Check if the ellipse is (almost) degenerate, i.e. rx = 0 or ry = 0
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//
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Ellipse.prototype.isDegenerate = function () {
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return (this.rx < epsilon * this.ry || this.ry < epsilon * this.rx);
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};
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module.exports = Ellipse;
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