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Move private getPeaks() to Curve.getPeaks()

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It will be of use in the offsetting code as well.
This commit is contained in:
Jürg Lehni 2017-02-05 14:20:43 +01:00
parent 7fc029d98b
commit 1f768c69d2
2 changed files with 40 additions and 28 deletions
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37
src/path/Curve.js
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@ -1681,6 +1681,43 @@ new function() { // Scope for methods that require private functions
getCurvature: function(v, t) {
return evaluate(v, t, 3, false).x;
},
/**
* Returns the t values for the "peaks" of the curve. The peaks are
* calculated by finding the roots of the dot product of the first and
* second derivative.
*
* Peaks are locations sharing some qualities of curvature extrema but
* are cheaper to compute. They fulfill their purpose here quite well.
* See:
* http://math.stackexchange.com/questions/1954845/bezier-curvature-extrema
*
* @param {Number[]} v the curve values array
* @returns {Number[]} the roots of all found peaks
*/
getPeaks: function(v) {
var x0 = v[0], y0 = v[1],
x1 = v[2], y1 = v[3],
x2 = v[4], y2 = v[5],
x3 = v[6], y3 = v[7],
ax = -x0 + 3 * x1 - 3 * x2 + x3,
bx = 3 * x0 - 6 * x1 + 3 * x2,
cx = -3 * x0 + 3 * x1,
ay = -y0 + 3 * y1 - 3 * y2 + y3,
by = 3 * y0 - 6 * y1 + 3 * y2,
cy = -3 * y0 + 3 * y1,
tMin = /*#=*/Numerical.CURVETIME_EPSILON,
tMax = 1 - tMin,
roots = [];
Numerical.solveCubic(
9 * (ax * ax + ay * ay),
9 * (ax * bx + by * ay),
2 * (bx * bx + by * by) + 3 * (cx * ax + cy * ay),
(cx * bx + by * cy),
// Exclude 0 and 1 as we don't count them as peaks.
roots, tMin, tMax);
return roots.sort();
}
}};
},

31
src/path/CurveLocation.js
View file

@ -437,10 +437,10 @@ var CurveLocation = Base.extend(/** @lends CurveLocation# */{
var offsets = [];
function addOffsets(curve, end) {
// Find the largest offset of unambiguous direction on the curve by
// finding their inflections points and "peaks".
// Find the largest offset of unambiguous direction on the curve,
// taking their loops, cusps, inflections, and "peaks" into account.
var v = curve.getValues(),
roots = Curve.classify(v).roots || getPeaks(v),
roots = Curve.classify(v).roots || Curve.getPeaks(v),
count = roots.length,
t = end && count > 1 ? roots[count - 1]
: count > 0 ? roots[0]
@ -449,31 +449,6 @@ var CurveLocation = Base.extend(/** @lends CurveLocation# */{
offsets.push(Curve.getLength(v, end ? t : 0, end ? 1 : t) / 2);
}
// Peaks are locations sharing some qualities of curvature extrema but
// are cheaper to compute. They fulfill their purpose here quite well.
// See: http://math.stackexchange.com/questions/1954845/bezier-curvature-extrema
function getPeaks(v) {
var x0 = v[0], y0 = v[1],
x1 = v[2], y1 = v[3],
x2 = v[4], y2 = v[5],
x3 = v[6], y3 = v[7],
ax = -x0 + 3 * x1 - 3 * x2 + x3,
bx = 3 * x0 - 6 * x1 + 3 * x2,
cx = -3 * x0 + 3 * x1,
ay = -y0 + 3 * y1 - 3 * y2 + y3,
by = 3 * y0 - 6 * y1 + 3 * y2,
cy = -3 * y0 + 3 * y1,
roots = [];
Numerical.solveCubic(
9 * (ax * ax + ay * ay),
9 * (ax * bx + by * ay),
2 * (bx * bx + by * by) + 3 * (cx * ax + cy * ay),
(cx * bx + by * cy),
// Exclude 0 and 1 as we don't want to use them as peaks.
roots, tMin, tMax);
return roots.sort();
}
function isInRange(angle, min, max) {
return min < max
? angle > min && angle < max