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Implement Curve#getCurvatureAt().

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This commit is contained in:
Jürg Lehni 2013-04-20 17:26:51 -07:00
parent 163036ec72
commit 1952e3dc7d
1 changed files with 25 additions and 10 deletions
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35
src/path/Curve.js
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@ -433,9 +433,9 @@ statics: {
x, y;
// Handle special case at beginning / end of curve
if (type == 0 && (t == 0 || t == 1)) {
x = t == 0 ? p1x : p2x;
y = t == 0 ? p1y : p2y;
if (type === 0 && (t === 0 || t === 1)) {
x = t === 0 ? p1x : p2x;
y = t === 0 ? p1y : p2y;
} else {
// TODO: Find a better solution for this:
// Prevent tangents and normals of length 0:
@ -452,20 +452,23 @@ statics: {
cy = 3 * (c1y - p1y),
by = 3 * (c2y - c1y) - cy,
ay = p2y - p1y - cy - by;
switch (type) {
case 0: // point
// Calculate the curve point at parameter value t
x = ((ax * t + bx) * t + cx) * t + p1x;
y = ((ay * t + by) * t + cy) * t + p1y;
break;
case 1: // tangent
case 2: // normal
case 1: // tangent, 1st derivative
case 2: // normal, 1st derivative
// Simply use the derivation of the bezier function for both
// the x and y coordinates:
x = (3 * ax * t + 2 * bx) * t + cx;
y = (3 * ay * t + 2 * by) * t + cy;
break;
case 3: // curvature, 2nd derivative
x = 6 * ax * t + 2 * bx;
y = 6 * ay * t + 2 * by;
break;
}
}
// The normal is simply the rotated tangent:
@ -740,7 +743,7 @@ statics: {
* @bean
* @ignore
*/
}), Base.each(['getPoint', 'getTangent', 'getNormal'],
}), Base.each(['getPoint', 'getTangent', 'getNormal', 'getCurvature'],
// Note: Although Curve.getBounds() exists, we are using Path.getBounds() to
// determine the bounds of Curve objects with defined segment1 and segment2
// values Curve.getBounds() can be used directly on curve arrays, without
@ -822,7 +825,7 @@ statics: {
*/
/**
* Returns the tangent point on the curve at the specified position.
* Returns the tangent vector of the curve at the specified position.
*
* @name Curve#getTangentAt
* @function
@ -830,11 +833,11 @@ statics: {
* parameter if {@code isParameter} is {@code true}
* @param {Boolean} [isParameter=false] pass {@code true} if {@code offset}
* is a curve time parameter.
* @return {Point} the tangent to the curve at the specified offset.
* @return {Point} the tangent of the curve at the specified offset.
*/
/**
* Returns the normal point on the curve at the specified position.
* Returns the normal vector of the curve at the specified position.
*
* @name Curve#getNormalAt
* @function
@ -844,6 +847,18 @@ statics: {
* is a curve time parameter.
* @return {Point} the normal of the curve at the specified offset.
*/
/**
* Returns the curvature vector of the curve at the specified position.
*
* @name Curve#getCurvatureAt
* @function
* @param {Number} offset the offset on the curve, or the curve time
* parameter if {@code isParameter} is {@code true}
* @param {Boolean} [isParameter=false] pass {@code true} if {@code offset}
* is a curve time parameter.
* @return {Point} the curvature of the curve at the specified offset.
*/
}),
new function() { // Scope for methods that require numerical integration