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https://github.com/scratchfoundation/paper.js.git
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Move Curve evaluate() method to private scope.
This commit is contained in:
Jürg Lehni
parent
da82116501
commit
9fe93d1434
1 changed files with 104 additions and 104 deletions
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@ -518,109 +518,6 @@ statics: {
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return values;
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},
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_evaluate: function(v, t, type, normalized) {
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// Do not produce results if parameter is out of range or invalid.
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if (t == null || t < 0 || t > 1)
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return null;
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var p1x = v[0], p1y = v[1],
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c1x = v[2], c1y = v[3],
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c2x = v[4], c2y = v[5],
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p2x = v[6], p2y = v[7],
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tolerance = /*#=*/Numerical.TOLERANCE,
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x, y;
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// Handle special case at beginning / end of curve
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if (type === 0 && (t < tolerance || t > 1 - tolerance)) {
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var isZero = t < tolerance;
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x = isZero ? p1x : p2x;
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y = isZero ? p1y : p2y;
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} else {
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// Calculate the polynomial coefficients.
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var cx = 3 * (c1x - p1x),
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bx = 3 * (c2x - c1x) - cx,
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ax = p2x - p1x - cx - bx,
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cy = 3 * (c1y - p1y),
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by = 3 * (c2y - c1y) - cy,
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ay = p2y - p1y - cy - by;
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if (type === 0) {
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// Calculate the curve point at parameter value t
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x = ((ax * t + bx) * t + cx) * t + p1x;
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y = ((ay * t + by) * t + cy) * t + p1y;
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} else {
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// 1: tangent, 1st derivative
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// 2: normal, 1st derivative
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// 3: curvature, 1st derivative & 2nd derivative
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// Simply use the derivation of the bezier function for both
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// the x and y coordinates:
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// Prevent tangents and normals of length 0:
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// http://stackoverflow.com/questions/10506868/
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if (t < tolerance) {
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x = cx;
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y = cy;
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} else if (t > 1 - tolerance) {
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x = 3 * (p2x - c2x);
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y = 3 * (p2y - c2y);
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} else {
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x = (3 * ax * t + 2 * bx) * t + cx;
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y = (3 * ay * t + 2 * by) * t + cy;
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}
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if (normalized) {
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// When the tangent at t is zero and we're at the beginning
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// or the end, we can use the vector between the handles,
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// but only when normalizing as its weighted length is 0.
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if (x === 0 && y === 0
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&& (t < tolerance || t > 1 - tolerance)) {
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x = c2x - c1x;
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y = c2y - c1y;
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}
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// Now normalize x & y
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var len = Math.sqrt(x * x + y * y);
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x /= len;
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y /= len;
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}
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if (type === 3) {
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// Calculate 2nd derivative, and curvature from there:
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// http://cagd.cs.byu.edu/~557/text/ch2.pdf page#31
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// k = |dx * d2y - dy * d2x| / (( dx^2 + dy^2 )^(3/2))
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var x2 = 6 * ax * t + 2 * bx,
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y2 = 6 * ay * t + 2 * by,
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d = Math.pow(x * x + y * y, 3 / 2);
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// For JS optimizations we always return a Point, although
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// curvature is just a numeric value, stored in x:
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x = d !== 0 ? (x * y2 - y * x2) / d : 0;
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y = 0;
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}
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}
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}
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// The normal is simply the rotated tangent:
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return type === 2 ? new Point(y, -x) : new Point(x, y);
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},
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getPoint: function(v, t) {
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return Curve._evaluate(v, t, 0, false);
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},
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getTangent: function(v, t) {
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return Curve._evaluate(v, t, 1, true);
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},
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getWeightedTangent: function(v, t) {
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return Curve._evaluate(v, t, 1, false);
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},
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getNormal: function(v, t) {
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return Curve._evaluate(v, t, 2, true);
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},
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getWeightedNormal: function(v, t) {
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return Curve._evaluate(v, t, 2, false);
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},
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getCurvature: function(v, t) {
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return Curve._evaluate(v, t, 3, false).x;
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},
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subdivide: function(v, t) {
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var p1x = v[0], p1y = v[1],
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c1x = v[2], c1y = v[3],
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@ -1074,7 +971,7 @@ statics: {
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* @return {Number} the curvature of the curve at the given offset
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*/
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}),
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new function() { // Scope for methods that require numerical integration
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new function() { // Scope for methods that require private functions
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function getLengthIntegrand(v) {
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// Calculate the coefficients of a Bezier derivative.
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@ -1107,6 +1004,85 @@ new function() { // Scope for methods that require numerical integration
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return Math.max(2, Math.min(16, Math.ceil(Math.abs(b - a) * 32)));
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}
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function evaluate(v, t, type, normalized) {
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// Do not produce results if parameter is out of range or invalid.
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if (t == null || t < 0 || t > 1)
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return null;
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var p1x = v[0], p1y = v[1],
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c1x = v[2], c1y = v[3],
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c2x = v[4], c2y = v[5],
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p2x = v[6], p2y = v[7],
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tolerance = /*#=*/Numerical.TOLERANCE,
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x, y;
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// Handle special case at beginning / end of curve
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if (type === 0 && (t < tolerance || t > 1 - tolerance)) {
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var isZero = t < tolerance;
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x = isZero ? p1x : p2x;
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y = isZero ? p1y : p2y;
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} else {
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// Calculate the polynomial coefficients.
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var cx = 3 * (c1x - p1x),
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bx = 3 * (c2x - c1x) - cx,
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ax = p2x - p1x - cx - bx,
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cy = 3 * (c1y - p1y),
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by = 3 * (c2y - c1y) - cy,
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ay = p2y - p1y - cy - by;
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if (type === 0) {
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// Calculate the curve point at parameter value t
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x = ((ax * t + bx) * t + cx) * t + p1x;
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y = ((ay * t + by) * t + cy) * t + p1y;
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} else {
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// 1: tangent, 1st derivative
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// 2: normal, 1st derivative
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// 3: curvature, 1st derivative & 2nd derivative
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// Simply use the derivation of the bezier function for both
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// the x and y coordinates:
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// Prevent tangents and normals of length 0:
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// http://stackoverflow.com/questions/10506868/
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if (t < tolerance) {
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x = cx;
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y = cy;
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} else if (t > 1 - tolerance) {
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x = 3 * (p2x - c2x);
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y = 3 * (p2y - c2y);
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} else {
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x = (3 * ax * t + 2 * bx) * t + cx;
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y = (3 * ay * t + 2 * by) * t + cy;
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}
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if (normalized) {
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// When the tangent at t is zero and we're at the beginning
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// or the end, we can use the vector between the handles,
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// but only when normalizing as its weighted length is 0.
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if (x === 0 && y === 0
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&& (t < tolerance || t > 1 - tolerance)) {
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x = c2x - c1x;
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y = c2y - c1y;
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}
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// Now normalize x & y
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var len = Math.sqrt(x * x + y * y);
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x /= len;
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y /= len;
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}
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if (type === 3) {
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// Calculate 2nd derivative, and curvature from there:
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// http://cagd.cs.byu.edu/~557/text/ch2.pdf page#31
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// k = |dx * d2y - dy * d2x| / (( dx^2 + dy^2 )^(3/2))
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var x2 = 6 * ax * t + 2 * bx,
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y2 = 6 * ay * t + 2 * by,
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d = Math.pow(x * x + y * y, 3 / 2);
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// For JS optimizations we always return a Point, although
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// curvature is just a numeric value, stored in x:
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x = d !== 0 ? (x * y2 - y * x2) / d : 0;
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y = 0;
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}
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}
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}
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// The normal is simply the rotated tangent:
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return type === 2 ? new Point(y, -x) : new Point(x, y);
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}
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return {
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statics: true,
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@ -1173,6 +1149,30 @@ new function() { // Scope for methods that require numerical integration
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// NOTE: guess is a negative value when not looking forward.
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return Numerical.findRoot(f, ds, start + guess, a, b, 16,
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tolerance);
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},
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getPoint: function(v, t) {
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return evaluate(v, t, 0, false);
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},
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getTangent: function(v, t) {
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return evaluate(v, t, 1, true);
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},
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getWeightedTangent: function(v, t) {
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return evaluate(v, t, 1, false);
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},
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getNormal: function(v, t) {
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return evaluate(v, t, 2, true);
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},
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getWeightedNormal: function(v, t) {
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return evaluate(v, t, 2, false);
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},
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getCurvature: function(v, t) {
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return evaluate(v, t, 3, false).x;
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}
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};
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}, new function() { // Scope for intersection using bezier fat-line clipping
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