scratchfoundation/paper.js
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Further clean ups.

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This commit is contained in:
Jürg Lehni 2011-06-05 22:09:19 +01:00
parent 68eb14c00d
commit 9e25047b91
1 changed files with 24 additions and 25 deletions
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47
src/path/PathFitter.js
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@ -93,15 +93,14 @@ var PathFitter = Base.extend({
// Use least-squares method to find Bezier control points for region. // Use least-squares method to find Bezier control points for region.
generateBezier: function(first, last, uPrime, tan1, tan2) { generateBezier: function(first, last, uPrime, tan1, tan2) {
var nPts = last - first + 1, var epsilon = Numerical.TOLERANCE,
pt1 = this.points[first], pt1 = this.points[first],
pt2 = this.points[last]; pt2 = this.points[last],
// Create the C and X matrices // Create the C and X matrices
var C = [[0, 0], [0, 0]], C = [[0, 0], [0, 0]],
X = [0, 0]; X = [0, 0];
for (var i = 0; i < nPts; i++) { for (var i = 0, l = last - first + 1; i < l; i++) {
var u = uPrime[i], var u = uPrime[i],
t = 1 - u, t = 1 - u,
b = 3 * u * t, b = 3 * u * t,
@ -124,46 +123,46 @@ var PathFitter = Base.extend({
} }
// Compute the determinants of C and X // Compute the determinants of C and X
var det_C0_C1 = C[0][0] * C[1][1] - C[1][0] * C[0][1], var detC0C1 = C[0][0] * C[1][1] - C[1][0] * C[0][1],
alpha_l, alpha_r; alpha1, alpha2;
if (Math.abs(det_C0_C1) > Numerical.TOLERANCE) { if (Math.abs(detC0C1) > epsilon) {
// Kramer's rule // Kramer's rule
var det_C0_X = C[0][0] * X[1] - C[1][0] * X[0], var detC0X = C[0][0] * X[1] - C[1][0] * X[0],
det_X_C1 = X[0] * C[1][1] - X[1] * C[0][1]; detXC1 = X[0] * C[1][1] - X[1] * C[0][1];
// Derive alpha values // Derive alpha values
alpha_l = det_X_C1 / det_C0_C1; alpha1 = detXC1 / detC0C1;
alpha_r = det_C0_X / det_C0_C1; alpha2 = detC0X / detC0C1;
} else { } else {
// Matrix is under-determined, try assuming alpha_l == alpha_r // Matrix is under-determined, try assuming alpha1 == alpha2
var c0 = C[0][0] + C[0][1], var c0 = C[0][0] + C[0][1],
c1 = C[1][0] + C[1][1]; c1 = C[1][0] + C[1][1];
if (Math.abs(c0) > Numerical.TOLERANCE) { if (Math.abs(c0) > epsilon) {
alpha_l = alpha_r = X[0] / c0; alpha1 = alpha2 = X[0] / c0;
} else if (Math.abs(c0) > Numerical.TOLERANCE) { } else if (Math.abs(c0) > epsilon) {
alpha_l = alpha_r = X[1] / c1; alpha1 = alpha2 = X[1] / c1;
} else { } else {
// Handle below // Handle below
alpha_l = alpha_r = 0.; alpha1 = alpha2 = 0.;
} }
} }
// If alpha negative, use the Wu/Barsky heuristic (see text) // If alpha negative, use the Wu/Barsky heuristic (see text)
// (if alpha is 0, you get coincident control points that lead to // (if alpha is 0, you get coincident control points that lead to
// divide by zero in any subsequent NewtonRaphsonRootFind() call. // divide by zero in any subsequent NewtonRaphsonRootFind() call.
var segLength = pt2.getDistance(pt1), var segLength = pt2.getDistance(pt1);
epsilon = Numerical.TOLERANCE * segLength; epsilon *= segLength;
if (alpha_l < epsilon || alpha_r < epsilon) { if (alpha1 < epsilon || alpha2 < epsilon) {
// fall back on standard (probably inaccurate) formula, // fall back on standard (probably inaccurate) formula,
// and subdivide further if needed. // and subdivide further if needed.
alpha_l = alpha_r = segLength / 3; alpha1 = alpha2 = segLength / 3;
} }
// First and last control points of the Bezier curve are // First and last control points of the Bezier curve are
// positioned exactly at the first and last data points // positioned exactly at the first and last data points
// Control points 1 and 2 are positioned an alpha distance out // Control points 1 and 2 are positioned an alpha distance out
// on the tangent vectors, left and right, respectively // on the tangent vectors, left and right, respectively
return [pt1, pt1.add(tan1.normalize(alpha_l)), return [pt1, pt1.add(tan1.normalize(alpha1)),
pt2.add(tan2.normalize(alpha_r)), pt2]; pt2.add(tan2.normalize(alpha2)), pt2];
}, },
// Given set of points and their parameterization, try to find // Given set of points and their parameterization, try to find