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* Paper.js - The Swiss Army Knife of Vector Graphics Scripting.
* http://paperjs.org/
*
* Copyright (c) 2011 - 2020, Jürg Lehni & Jonathan Puckey
* http://juerglehni.com/ & https://puckey.studio/
*
* Distributed under the MIT license. See LICENSE file for details.
*
* All rights reserved.
*/
// TODO: remove eslint-disable comment and deal with errors over time
/* eslint-disable */
import { ref } from '~/globals';
import { Base } from '~/straps';
import { Numerical } from '~/util/Numerical';
import { Segment } from './Segment';
// An Algorithm for Automatically Fitting Digitized Curves
// by Philip J. Schneider
// from "Graphics Gems", Academic Press, 1990
// Modifications and optimizations of original algorithm by Jürg Lehni.
/**
* @name PathFitter
* @class
* @private
*/
export const PathFitter = Base.extend({
initialize: function (path) {
var points = (this.points = []),
segments = path._segments,
closed = path._closed;
// Copy over points from path and filter out adjacent duplicates.
for (var i = 0, prev, l = segments.length; i < l; i++) {
var point = segments[i].point;
if (!prev || !prev.equals(point)) {
points.push((prev = point.clone()));
}
}
// We need to duplicate the first and last segment when simplifying a
// closed path.
if (closed) {
points.unshift(points[points.length - 1]);
points.push(points[1]); // The point previously at index 0 is now 1.
}
this.closed = closed;
},
fit: function (error) {
var points = this.points,
length = points.length,
segments = null;
if (length > 0) {
// To support reducing paths with multiple points in the same place
// to one segment:
segments = [new Segment(points[0])];
if (length > 1) {
this.fitCubic(
segments,
error,
0,
length - 1,
// Left Tangent
points[1].subtract(points[0]),
// Right Tangent
points[length - 2].subtract(points[length - 1])
);
// Remove the duplicated segments for closed paths again.
if (this.closed) {
segments.shift();
segments.pop();
}
}
}
return segments;
},
// Fit a Bezier curve to a (sub)set of digitized points
fitCubic: function (segments, error, first, last, tan1, tan2) {
var points = this.points;
// Use heuristic if region only has two points in it
if (last - first === 1) {
var pt1 = points[first],
pt2 = points[last],
dist = pt1.getDistance(pt2) / 3;
this.addCurve(segments, [pt1, pt1.add(tan1.normalize(dist)), pt2.add(tan2.normalize(dist)), pt2]);
return;
}
// Parameterize points, and attempt to fit curve
var uPrime = this.chordLengthParameterize(first, last),
maxError = Math.max(error, error * error),
split,
parametersInOrder = true;
// Try 4 iterations
for (var i = 0; i <= 4; i++) {
var curve = this.generateBezier(first, last, uPrime, tan1, tan2);
// Find max deviation of points to fitted curve
var max = this.findMaxError(first, last, curve, uPrime);
if (max.error < error && parametersInOrder) {
this.addCurve(segments, curve);
return;
}
split = max.index;
// If error not too large, try reparameterization and iteration
if (max.error >= maxError) break;
parametersInOrder = this.reparameterize(first, last, uPrime, curve);
maxError = max.error;
}
// Fitting failed -- split at max error point and fit recursively
var tanCenter = points[split - 1].subtract(points[split + 1]);
this.fitCubic(segments, error, first, split, tan1, tanCenter);
this.fitCubic(segments, error, split, last, tanCenter.negate(), tan2);
},
addCurve: function (segments, curve) {
var prev = segments[segments.length - 1];
prev.setHandleOut(curve[1].subtract(curve[0]));
segments.push(new Segment(curve[3], curve[2].subtract(curve[3])));
},
// Use least-squares method to find Bezier control points for region.
generateBezier: function (first, last, uPrime, tan1, tan2) {
var epsilon = /*#=*/ Numerical.EPSILON,
abs = Math.abs,
points = this.points,
pt1 = points[first],
pt2 = points[last],
// Create the C and X matrices
C = [
[0, 0],
[0, 0],
],
X = [0, 0];
for (var i = 0, l = last - first + 1; i < l; i++) {
var u = uPrime[i],
t = 1 - u,
b = 3 * u * t,
b0 = t * t * t,
b1 = b * t,
b2 = b * u,
b3 = u * u * u,
a1 = tan1.normalize(b1),
a2 = tan2.normalize(b2),
tmp = points[first + i].subtract(pt1.multiply(b0 + b1)).subtract(pt2.multiply(b2 + b3));
C[0][0] += a1.dot(a1);
C[0][1] += a1.dot(a2);
// C[1][0] += a1.dot(a2);
C[1][0] = C[0][1];
C[1][1] += a2.dot(a2);
X[0] += a1.dot(tmp);
X[1] += a2.dot(tmp);
}
// Compute the determinants of C and X
var detC0C1 = C[0][0] * C[1][1] - C[1][0] * C[0][1],
alpha1,
alpha2;
if (abs(detC0C1) > epsilon) {
// Kramer's rule
var detC0X = C[0][0] * X[1] - C[1][0] * X[0],
detXC1 = X[0] * C[1][1] - X[1] * C[0][1];
// Derive alpha values
alpha1 = detXC1 / detC0C1;
alpha2 = detC0X / detC0C1;
} else {
// Matrix is under-determined, try assuming alpha1 == alpha2
var c0 = C[0][0] + C[0][1],
c1 = C[1][0] + C[1][1];
alpha1 = alpha2 = abs(c0) > epsilon ? X[0] / c0 : abs(c1) > epsilon ? X[1] / c1 : 0;
}
// If alpha negative, use the Wu/Barsky heuristic (see text)
// (if alpha is 0, you get coincident control points that lead to
// divide by zero in any subsequent NewtonRaphsonRootFind() call.
var segLength = pt2.getDistance(pt1),
eps = epsilon * segLength,
handle1,
handle2;
if (alpha1 < eps || alpha2 < eps) {
// fall back on standard (probably inaccurate) formula,
// and subdivide further if needed.
alpha1 = alpha2 = segLength / 3;
} else {
// Check if the found control points are in the right order when
// projected onto the line through pt1 and pt2.
var line = pt2.subtract(pt1);
// Control points 1 and 2 are positioned an alpha distance out
// on the tangent vectors, left and right, respectively
handle1 = tan1.normalize(alpha1);
handle2 = tan2.normalize(alpha2);
if (handle1.dot(line) - handle2.dot(line) > segLength * segLength) {
// Fall back to the Wu/Barsky heuristic above.
alpha1 = alpha2 = segLength / 3;
handle1 = handle2 = null; // Force recalculation
}
}
// First and last control points of the Bezier curve are
// positioned exactly at the first and last data points
return [pt1, pt1.add(handle1 || tan1.normalize(alpha1)), pt2.add(handle2 || tan2.normalize(alpha2)), pt2];
},
// Given set of points and their parameterization, try to find
// a better parameterization.
reparameterize: function (first, last, u, curve) {
for (var i = first; i <= last; i++) {
u[i - first] = this.findRoot(curve, this.points[i], u[i - first]);
}
// Detect if the new parameterization has reordered the points.
// In that case, we would fit the points of the path in the wrong order.
// @ts-expect-error = Subsequent variable declarations must have the same type
for (var i = 1, l = u.length; i < l; i++) {
if (u[i] <= u[i - 1]) return false;
}
return true;
},
// Use Newton-Raphson iteration to find better root.
findRoot: function (curve, point, u) {
var curve1 = [],
curve2 = [];
// Generate control vertices for Q'
for (var i = 0; i <= 2; i++) {
curve1[i] = curve[i + 1].subtract(curve[i]).multiply(3);
}
// Generate control vertices for Q''
for (var i = 0; i <= 1; i++) {
curve2[i] = curve1[i + 1].subtract(curve1[i]).multiply(2);
}
// Compute Q(u), Q'(u) and Q''(u)
var pt = this.evaluate(3, curve, u),
pt1 = this.evaluate(2, curve1, u),
pt2 = this.evaluate(1, curve2, u),
diff = pt.subtract(point),
df = pt1.dot(pt1) + diff.dot(pt2);
// u = u - f(u) / f'(u)
return Numerical.isMachineZero(df) ? u : u - diff.dot(pt1) / df;
},
// Evaluate a bezier curve at a particular parameter value
evaluate: function (degree, curve, t) {
// Copy array
var tmp = curve.slice();
// Triangle computation
for (var i = 1; i <= degree; i++) {
for (var j = 0; j <= degree - i; j++) {
tmp[j] = tmp[j].multiply(1 - t).add(tmp[j + 1].multiply(t));
}
}
return tmp[0];
},
// Assign parameter values to digitized points
// using relative distances between points.
chordLengthParameterize: function (first, last) {
var u = [0];
for (var i = first + 1; i <= last; i++) {
u[i - first] = u[i - first - 1] + this.points[i].getDistance(this.points[i - 1]);
}
// @ts-expect-error = Subsequent variable declarations must have the same type
for (var i = 1, m = last - first; i <= m; i++) {
u[i] /= u[m];
}
return u;
},
// Find the maximum squared distance of digitized points to fitted curve.
findMaxError: function (first, last, curve, u) {
var index = Math.floor((last - first + 1) / 2),
maxDist = 0;
for (var i = first + 1; i < last; i++) {
var P = this.evaluate(3, curve, u[i - first]);
var v = P.subtract(this.points[i]);
var dist = v.x * v.x + v.y * v.y; // squared
if (dist >= maxDist) {
maxDist = dist;
index = i;
}
}
return {
error: maxDist,
index: index,
};
},
});
ref.PathFitter = PathFitter;
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