Current Dev State

static/js/ketcher2/node_modules/svgpath/lib/ellipse.js

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