diff --git a/src/path/Curve.js b/src/path/Curve.js
index 4d6392d4..d2c4df95 100644
--- a/src/path/Curve.js
+++ b/src/path/Curve.js
@@ -518,109 +518,6 @@ statics: {
return values;
},
- _evaluate: function(v, t, type, normalized) {
- // Do not produce results if parameter is out of range or invalid.
- if (t == null || t < 0 || t > 1)
- return null;
- var p1x = v[0], p1y = v[1],
- c1x = v[2], c1y = v[3],
- c2x = v[4], c2y = v[5],
- p2x = v[6], p2y = v[7],
- tolerance = /*#=*/Numerical.TOLERANCE,
- x, y;
-
- // Handle special case at beginning / end of curve
- if (type === 0 && (t < tolerance || t > 1 - tolerance)) {
- var isZero = t < tolerance;
- x = isZero ? p1x : p2x;
- y = isZero ? p1y : p2y;
- } else {
- // Calculate the polynomial coefficients.
- var cx = 3 * (c1x - p1x),
- bx = 3 * (c2x - c1x) - cx,
- ax = p2x - p1x - cx - bx,
-
- cy = 3 * (c1y - p1y),
- by = 3 * (c2y - c1y) - cy,
- ay = p2y - p1y - cy - by;
- if (type === 0) {
- // Calculate the curve point at parameter value t
- x = ((ax * t + bx) * t + cx) * t + p1x;
- y = ((ay * t + by) * t + cy) * t + p1y;
- } else {
- // 1: tangent, 1st derivative
- // 2: normal, 1st derivative
- // 3: curvature, 1st derivative & 2nd derivative
- // Simply use the derivation of the bezier function for both
- // the x and y coordinates:
- // Prevent tangents and normals of length 0:
- // http://stackoverflow.com/questions/10506868/
- if (t < tolerance) {
- x = cx;
- y = cy;
- } else if (t > 1 - tolerance) {
- x = 3 * (p2x - c2x);
- y = 3 * (p2y - c2y);
- } else {
- x = (3 * ax * t + 2 * bx) * t + cx;
- y = (3 * ay * t + 2 * by) * t + cy;
- }
- if (normalized) {
- // When the tangent at t is zero and we're at the beginning
- // or the end, we can use the vector between the handles,
- // but only when normalizing as its weighted length is 0.
- if (x === 0 && y === 0
- && (t < tolerance || t > 1 - tolerance)) {
- x = c2x - c1x;
- y = c2y - c1y;
- }
- // Now normalize x & y
- var len = Math.sqrt(x * x + y * y);
- x /= len;
- y /= len;
- }
- if (type === 3) {
- // Calculate 2nd derivative, and curvature from there:
- // http://cagd.cs.byu.edu/~557/text/ch2.pdf page#31
- // k = |dx * d2y - dy * d2x| / (( dx^2 + dy^2 )^(3/2))
- var x2 = 6 * ax * t + 2 * bx,
- y2 = 6 * ay * t + 2 * by,
- d = Math.pow(x * x + y * y, 3 / 2);
- // For JS optimizations we always return a Point, although
- // curvature is just a numeric value, stored in x:
- x = d !== 0 ? (x * y2 - y * x2) / d : 0;
- y = 0;
- }
- }
- }
- // The normal is simply the rotated tangent:
- return type === 2 ? new Point(y, -x) : new Point(x, y);
- },
-
- getPoint: function(v, t) {
- return Curve._evaluate(v, t, 0, false);
- },
-
- getTangent: function(v, t) {
- return Curve._evaluate(v, t, 1, true);
- },
-
- getWeightedTangent: function(v, t) {
- return Curve._evaluate(v, t, 1, false);
- },
-
- getNormal: function(v, t) {
- return Curve._evaluate(v, t, 2, true);
- },
-
- getWeightedNormal: function(v, t) {
- return Curve._evaluate(v, t, 2, false);
- },
-
- getCurvature: function(v, t) {
- return Curve._evaluate(v, t, 3, false).x;
- },
-
subdivide: function(v, t) {
var p1x = v[0], p1y = v[1],
c1x = v[2], c1y = v[3],
@@ -1074,7 +971,7 @@ statics: {
* @return {Number} the curvature of the curve at the given offset
*/
}),
-new function() { // Scope for methods that require numerical integration
+new function() { // Scope for methods that require private functions
function getLengthIntegrand(v) {
// Calculate the coefficients of a Bezier derivative.
@@ -1107,6 +1004,85 @@ new function() { // Scope for methods that require numerical integration
return Math.max(2, Math.min(16, Math.ceil(Math.abs(b - a) * 32)));
}
+ function evaluate(v, t, type, normalized) {
+ // Do not produce results if parameter is out of range or invalid.
+ if (t == null || t < 0 || t > 1)
+ return null;
+ var p1x = v[0], p1y = v[1],
+ c1x = v[2], c1y = v[3],
+ c2x = v[4], c2y = v[5],
+ p2x = v[6], p2y = v[7],
+ tolerance = /*#=*/Numerical.TOLERANCE,
+ x, y;
+
+ // Handle special case at beginning / end of curve
+ if (type === 0 && (t < tolerance || t > 1 - tolerance)) {
+ var isZero = t < tolerance;
+ x = isZero ? p1x : p2x;
+ y = isZero ? p1y : p2y;
+ } else {
+ // Calculate the polynomial coefficients.
+ var cx = 3 * (c1x - p1x),
+ bx = 3 * (c2x - c1x) - cx,
+ ax = p2x - p1x - cx - bx,
+
+ cy = 3 * (c1y - p1y),
+ by = 3 * (c2y - c1y) - cy,
+ ay = p2y - p1y - cy - by;
+ if (type === 0) {
+ // Calculate the curve point at parameter value t
+ x = ((ax * t + bx) * t + cx) * t + p1x;
+ y = ((ay * t + by) * t + cy) * t + p1y;
+ } else {
+ // 1: tangent, 1st derivative
+ // 2: normal, 1st derivative
+ // 3: curvature, 1st derivative & 2nd derivative
+ // Simply use the derivation of the bezier function for both
+ // the x and y coordinates:
+ // Prevent tangents and normals of length 0:
+ // http://stackoverflow.com/questions/10506868/
+ if (t < tolerance) {
+ x = cx;
+ y = cy;
+ } else if (t > 1 - tolerance) {
+ x = 3 * (p2x - c2x);
+ y = 3 * (p2y - c2y);
+ } else {
+ x = (3 * ax * t + 2 * bx) * t + cx;
+ y = (3 * ay * t + 2 * by) * t + cy;
+ }
+ if (normalized) {
+ // When the tangent at t is zero and we're at the beginning
+ // or the end, we can use the vector between the handles,
+ // but only when normalizing as its weighted length is 0.
+ if (x === 0 && y === 0
+ && (t < tolerance || t > 1 - tolerance)) {
+ x = c2x - c1x;
+ y = c2y - c1y;
+ }
+ // Now normalize x & y
+ var len = Math.sqrt(x * x + y * y);
+ x /= len;
+ y /= len;
+ }
+ if (type === 3) {
+ // Calculate 2nd derivative, and curvature from there:
+ // http://cagd.cs.byu.edu/~557/text/ch2.pdf page#31
+ // k = |dx * d2y - dy * d2x| / (( dx^2 + dy^2 )^(3/2))
+ var x2 = 6 * ax * t + 2 * bx,
+ y2 = 6 * ay * t + 2 * by,
+ d = Math.pow(x * x + y * y, 3 / 2);
+ // For JS optimizations we always return a Point, although
+ // curvature is just a numeric value, stored in x:
+ x = d !== 0 ? (x * y2 - y * x2) / d : 0;
+ y = 0;
+ }
+ }
+ }
+ // The normal is simply the rotated tangent:
+ return type === 2 ? new Point(y, -x) : new Point(x, y);
+ }
+
return {
statics: true,
@@ -1173,6 +1149,30 @@ new function() { // Scope for methods that require numerical integration
// NOTE: guess is a negative value when not looking forward.
return Numerical.findRoot(f, ds, start + guess, a, b, 16,
tolerance);
+ },
+
+ getPoint: function(v, t) {
+ return evaluate(v, t, 0, false);
+ },
+
+ getTangent: function(v, t) {
+ return evaluate(v, t, 1, true);
+ },
+
+ getWeightedTangent: function(v, t) {
+ return evaluate(v, t, 1, false);
+ },
+
+ getNormal: function(v, t) {
+ return evaluate(v, t, 2, true);
+ },
+
+ getWeightedNormal: function(v, t) {
+ return evaluate(v, t, 2, false);
+ },
+
+ getCurvature: function(v, t) {
+ return evaluate(v, t, 3, false).x;
}
};
}, new function() { // Scope for intersection using bezier fat-line clipping