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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 type { Path } from './Path';
import { ref } from '~/globals';
import { Base } from '~/straps';
import { Numerical } from '~/util/Numerical';
import { Formatter } from '~/util/Formatter';
import { Curve } from './Curve';
/**
* @name CurveLocation
*
* @class CurveLocation objects describe a location on {@link Curve} objects, as
* defined by the curve-time {@link #time}, a value between `0` (beginning
* of the curve) and `1` (end of the curve). If the curve is part of a
* {@link Path} item, its {@link #index} inside the {@link Path#curves}
* array is also provided.
*
* The class is in use in many places, such as
* {@link Path#getLocationAt(offset)},
* {@link Path#getLocationOf(point)},
* {@link PathItem#getNearestLocation(point)},
* {@link PathItem#getIntersections(path)},
* etc.
*/
export const CurveLocation = Base.extend(
/** @lends CurveLocation# */ {
_class: 'CurveLocation',
// DOCS: CurveLocation class description: add these back when the mentioned
// functioned have been added: {@link Path#split(location)}
/**
* Creates a new CurveLocation object.
*
* @param {Curve} curve
* @param {Number} time
* @param {Point} [point]
*/
initialize: function CurveLocation(curve, time, point, _overlap, _distance) {
// Merge intersections very close to the end of a curve with the
// beginning of the next curve.
if (time >= /*#=*/ 1 - Numerical.CURVETIME_EPSILON) {
var next = curve.getNext();
if (next) {
time = 0;
curve = next;
}
}
this._setCurve(curve);
this._time = time;
this._point = point || curve.getPointAtTime(time);
this._overlap = _overlap;
this._distance = _distance;
// Properties related to linked intersection locations
this._intersection = this._next = this._previous = null;
},
_setPath: function (path) {
// We only store the path to verify versions for cached values.
// To ensure we use the right path (e.g. after splitting), we shall
// always access the path on the result of getCurve().
this._path = path;
this._version = path ? path._version : 0;
},
_setCurve: function (curve) {
this._setPath(curve._path);
this._curve = curve;
this._segment = null; // To be determined, see #getSegment()
// Also store references to segment1 and segment2, in case path
// splitting / dividing is going to happen, in which case the segments
// can be used to determine the new curves, see #getCurve(true)
this._segment1 = curve._segment1;
this._segment2 = curve._segment2;
},
_setSegment: function (segment) {
var curve = segment.getCurve();
if (curve) {
this._setCurve(curve);
} else {
this._setPath(segment._path);
this._segment1 = segment;
this._segment2 = null;
}
this._segment = segment;
this._time = segment === this._segment1 ? 0 : 1;
// To avoid issues with imprecision in getCurve() / trySegment()
this._point = segment._point.clone();
},
/**
* The segment of the curve which is closer to the described location.
*
* @bean
* @type Segment
*/
getSegment: function () {
// Request curve first, so _segment gets invalidated if it's out of sync
var segment = this._segment;
if (!segment) {
var curve = this.getCurve(),
time = this.getTime();
if (time === 0) {
segment = curve._segment1;
} else if (time === 1) {
segment = curve._segment2;
} else if (time != null) {
// Determine the closest segment by comparing curve lengths
segment = curve.getPartLength(0, time) < curve.getPartLength(time, 1) ? curve._segment1 : curve._segment2;
}
this._segment = segment;
}
return segment;
},
/**
* The curve that this location belongs to.
*
* @bean
* @type Curve
*/
getCurve: function () {
var path = this._path,
that = this;
if (path && path._version !== this._version) {
// If the path's segments have changed, clear the cached time and
// offset values and force re-fetching of the correct curve.
this._time = this._offset = this._curveOffset = this._curve = null;
}
// If path is out of sync, access current curve objects through segment1
// / segment2. Since path splitting or dividing might have happened in
// the meantime, try segment1's curve, and see if _point lies on it
// still, otherwise assume it's the curve before segment2.
function trySegment(segment) {
var curve = segment && segment.getCurve();
if (curve && (that._time = curve.getTimeOf(that._point)) != null) {
// Fetch path again as it could be on a new one through split()
that._setCurve(curve);
return curve;
}
}
return (
this._curve ||
trySegment(this._segment) ||
trySegment(this._segment1) ||
trySegment(this._segment2.getPrevious())
);
},
/**
* The path that this locations is situated on.
*
* @bean
* @type Path
*/
getPath: function () {
var curve = this.getCurve();
return curve && curve._path;
},
/**
* The index of the {@link #curve} within the {@link Path#curves} list, if
* it is part of a {@link Path} item.
*
* @bean
* @type Number
*/
getIndex: function () {
var curve = this.getCurve();
return curve && curve.getIndex();
},
/**
* The curve-time parameter, as used by various bezier curve calculations.
* It is value between `0` (beginning of the curve) and `1` (end of the
* curve).
*
* @bean
* @type Number
*/
getTime: function () {
var curve = this.getCurve(),
time = this._time;
return curve && time == null ? (this._time = curve.getTimeOf(this._point)) : time;
},
/**
* @private
* @bean
* @deprecated use {@link #time} instead.
*/
getParameter: '#getTime',
/**
* The point which is defined by the {@link #curve} and
* {@link #time}.
*
* @bean
* @type Point
*/
getPoint: function () {
return this._point;
},
/**
* The length of the path from its beginning up to the location described
* by this object. If the curve is not part of a path, then the length
* within the curve is returned instead.
*
* @bean
* @type Number
*/
getOffset: function () {
var offset = this._offset;
if (offset == null) {
offset = 0;
var path = this.getPath(),
index = this.getIndex();
if (path && index != null) {
var curves = path.getCurves();
for (var i = 0; i < index; i++) offset += curves[i].getLength();
}
this._offset = offset += this.getCurveOffset();
}
return offset;
},
/**
* The length of the curve from its beginning up to the location described
* by this object.
*
* @bean
* @type Number
*/
getCurveOffset: function () {
var offset = this._curveOffset;
if (offset == null) {
var curve = this.getCurve(),
time = this.getTime();
this._curveOffset = offset = time != null && curve && curve.getPartLength(0, time);
}
return offset;
},
/**
* The curve location on the intersecting curve, if this location is the
* result of a call to {@link PathItem#getIntersections(path)} /
* {@link Curve#getIntersections(curve)}.
*
* @bean
* @type CurveLocation
*/
getIntersection: function () {
return this._intersection;
},
/**
* The tangential vector to the {@link #curve} at the given location.
*
* @name CurveLocation#getTangent
* @bean
* @type Point
*/
/**
* The normal vector to the {@link #curve} at the given location.
*
* @name CurveLocation#getNormal
* @bean
* @type Point
*/
/**
* The curvature of the {@link #curve} at the given location.
*
* @name CurveLocation#getCurvature
* @bean
* @type Number
*/
/**
* The distance from the queried point to the returned location.
*
* @bean
* @type Number
* @see Curve#getNearestLocation(point)
* @see PathItem#getNearestLocation(point)
*/
getDistance: function () {
return this._distance;
},
// DOCS: divide(), split()
divide: function () {
var curve = this.getCurve(),
res = curve && curve.divideAtTime(this.getTime());
// Change to the newly inserted segment, also adjusts _time.
if (res) {
this._setSegment(res._segment1);
}
return res;
},
split: function () {
var curve = this.getCurve(),
path = curve._path,
res = curve && curve.splitAtTime(this.getTime());
if (res) {
// Set the segment to the end-segment of the path after splitting.
this._setSegment(path.getLastSegment());
}
return res;
},
/**
* Checks whether tow CurveLocation objects are describing the same location
* on a path, by applying the same tolerances as elsewhere when dealing with
* curve-time parameters.
*
* @param {CurveLocation} location
* @return {Boolean} {@true if the locations are equal}
*/
equals: function (loc, _ignoreOther) {
var res = this === loc;
if (!res && loc instanceof CurveLocation) {
var c1 = this.getCurve(),
c2 = loc.getCurve(),
p1 = c1._path,
p2 = c2._path;
if (p1 === p2) {
// instead of comparing curve-time, compare the actual offsets
// of both locations to determine if they're in the same spot,
// taking into account the wrapping around path ends. This is
// necessary to avoid issues wit CURVETIME_EPSILON imprecisions.
var abs = Math.abs,
epsilon = /*#=*/ Numerical.GEOMETRIC_EPSILON,
diff = abs(this.getOffset() - loc.getOffset()),
i1 = !_ignoreOther && this._intersection,
i2 = !_ignoreOther && loc._intersection;
res =
(diff < epsilon || (p1 && abs(p1.getLength() - diff) < epsilon)) &&
// Compare the the other location, but prevent endless
// recursion by passing `true` for _ignoreOther.
((!i1 && !i2) || (i1 && i2 && i1.equals(i2, true)));
}
}
return res;
},
/**
* @return {String} a string representation of the curve location
*/
toString: function () {
var parts = [],
point = this.getPoint(),
f = Formatter.instance;
if (point) parts.push('point: ' + point);
var index = this.getIndex();
if (index != null) parts.push('index: ' + index);
var time = this.getTime();
if (time != null) parts.push('time: ' + f.number(time));
if (this._distance != null) parts.push('distance: ' + f.number(this._distance));
return '{ ' + parts.join(', ') + ' }';
},
/**
* {@grouptitle Tests}
* Checks if the location is an intersection with another curve and is
* merely touching the other curve, as opposed to crossing it.
*
* @return {Boolean} {@true if the location is an intersection that is
* merely touching another curve}
* @see #isCrossing()
*/
isTouching: function () {
var inter = this._intersection;
if (inter && this.getTangent().isCollinear(inter.getTangent())) {
// Only consider two straight curves as touching if their lines
// don't intersect.
var curve1 = this.getCurve(),
curve2 = inter.getCurve();
return !(curve1.isStraight() && curve2.isStraight() && curve1.getLine().intersect(curve2.getLine()));
}
return false;
},
/**
* Checks if the location is an intersection with another curve and is
* crossing the other curve, as opposed to just touching it.
*
* @return {Boolean} {@true if the location is an intersection that is
* crossing another curve}
* @see #isTouching()
*/
isCrossing: function () {
// Implementation loosely based on work by Andy Finnell:
// http://losingfight.com/blog/2011/07/09/how-to-implement-boolean-operations-on-bezier-paths-part-3/
// https://bitbucket.org/andyfinnell/vectorboolean
var inter = this._intersection;
if (!inter) return false;
var t1 = this.getTime(),
t2 = inter.getTime(),
tMin = /*#=*/ Numerical.CURVETIME_EPSILON,
tMax = 1 - tMin,
// t*Inside specifies if the found intersection is inside the curve.
t1Inside = t1 >= tMin && t1 <= tMax,
t2Inside = t2 >= tMin && t2 <= tMax;
// If the intersection is in the middle of both paths, it is either a
// tangent or a crossing, no need for the detailed corner check below:
if (t1Inside && t2Inside) return !this.isTouching();
// Now get the references to the 4 curves involved in the intersection:
// - c1 & c2 are the curves on the first intersecting path, left and
// right of the intersection.
// - c3 & c4 are the same for the second intersecting path.
// - If the intersection is in the middle of the curve (t*Inside), then
// both values point to the same curve, and the curve-time is to be
// handled accordingly further down.
var c2 = this.getCurve(),
c1 = c2 && t1 < tMin ? c2.getPrevious() : c2,
c4 = inter.getCurve(),
c3 = c4 && t2 < tMin ? c4.getPrevious() : c4;
// If t1 / t2 are at the end, then step to the next curve.
if (t1 > tMax) c2 = c2.getNext();
if (t2 > tMax) c4 = c4.getNext();
if (!c1 || !c2 || !c3 || !c4) return false;
// Calculate unambiguous angles for all 4 tangents at the intersection:
// - If the intersection is inside a curve (t1 / t2Inside), the tangent
// at t1 / t2 is unambiguous, because the curve is continuous.
// - If the intersection is on a segment, step away at equal offsets on
// each curve, to calculate unambiguous angles. The vector from the
// intersection to this new location is used to determine the angle.
var offsets = [];
function addOffsets(curve, end) {
// 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 || Curve.getPeaks(v),
count = roots.length,
offset = Curve.getLength(v, end && count ? roots[count - 1] : 0, !end && count ? roots[0] : 1);
// When no root was found, the full length was calculated. Use a
// fraction of it. By trial & error, 64 was determined to work well.
offsets.push(count ? offset : offset / 32);
}
function isInRange(angle, min, max) {
return min < max
? angle > min && angle < max
: // min > max: the range wraps around -180 / 180 degrees
angle > min || angle < max;
}
if (!t1Inside) {
addOffsets(c1, true);
addOffsets(c2, false);
}
if (!t2Inside) {
addOffsets(c3, true);
addOffsets(c4, false);
}
var pt = this.getPoint(),
// Determined the shared unambiguous offset by the taking the
// shortest offsets on all involved curves that are unambiguous.
offset = Math.min.apply(Math, offsets),
v2 = t1Inside ? c2.getTangentAtTime(t1) : c2.getPointAt(offset).subtract(pt),
v1 = t1Inside ? v2.negate() : c1.getPointAt(-offset).subtract(pt),
v4 = t2Inside ? c4.getTangentAtTime(t2) : c4.getPointAt(offset).subtract(pt),
v3 = t2Inside ? v4.negate() : c3.getPointAt(-offset).subtract(pt),
a1 = v1.getAngle(),
a2 = v2.getAngle(),
a3 = v3.getAngle(),
a4 = v4.getAngle();
// Count how many times curve2 angles appear between the curve1 angles.
// If each pair of angles split the other two, then the edges cross.
// Use t1Inside to decide which angle pair to check against.
// If t1 is inside the curve, check against a3 & a4, otherwise a1 & a2.
return !!(t1Inside
? // @ts-expect-error = The '^' operator is not allowed for boolean types
isInRange(a1, a3, a4) ^ isInRange(a2, a3, a4) &&
// @ts-expect-error = The '^' operator is not allowed for boolean types
isInRange(a1, a4, a3) ^ isInRange(a2, a4, a3)
: // @ts-expect-error = The '^' operator is not allowed for boolean types
isInRange(a3, a1, a2) ^ isInRange(a4, a1, a2) &&
// @ts-expect-error = The '^' operator is not allowed for boolean types
isInRange(a3, a2, a1) ^ isInRange(a4, a2, a1));
},
/**
* Checks if the location is an intersection with another curve and is
* part of an overlap between the two involved paths.
*
* @return {Boolean} {@true if the location is an intersection that is
* part of an overlap between the two involved paths}
* @see #isCrossing()
* @see #isTouching()
*/
hasOverlap: function () {
return !!this._overlap;
},
},
Base.each(
Curve._evaluateMethods,
function (name) {
// Produce getters for #getTangent() / #getNormal() / #getCurvature()
// NOTE: (For easier searching): This loop produces:
// getPointAt, getTangentAt, getNormalAt, getWeightedTangentAt,
// getWeightedNormalAt, getCurvatureAt
var get = name + 'At';
this[name] = function () {
var curve = this.getCurve(),
time = this.getTime();
return time != null && curve && curve[get](time, true);
};
},
{
// Do not override the existing #getPoint():
preserve: true,
}
),
// @ts-expect-error = 'new' expression, whose target lacks a construct signature
new (function () {
// Scope for statics
function insert(locations, loc, merge) {
// Insert-sort by path-id, curve, time so we can easily merge
// duplicates with calls to equals() after.
var length = locations.length,
l = 0,
r = length - 1;
function search(index, dir) {
// If we reach the beginning/end of the list, also compare with the
// location at the other end, as paths are circular lists.
// NOTE: When merging, the locations array will only contain
// locations on the same path, so it is fine that check for the end
// to address circularity. See PathItem#getIntersections()
for (var i = index + dir; i >= -1 && i <= length; i += dir) {
// Wrap the index around, to match the other ends:
var loc2 = locations[((i % length) + length) % length];
// Once we're outside the spot, we can stop searching.
if (!loc.getPoint().isClose(loc2.getPoint(), /*#=*/ Numerical.GEOMETRIC_EPSILON)) break;
if (loc.equals(loc2)) return loc2;
}
return null;
}
while (l <= r) {
var m = (l + r) >>> 1,
loc2 = locations[m],
found;
// See if the two locations are actually the same, and merge if
// they are. If they aren't check the other neighbors with search()
if (merge && (found = loc.equals(loc2) ? loc2 : search(m, -1) || search(m, 1))) {
// We're done, don't insert, merge with the found location
// instead, and carry over overlap:
if (loc._overlap) {
found._overlap = found._intersection._overlap = true;
}
return found;
}
var path1 = loc.getPath(),
path2 = loc2.getPath(),
// NOTE: equals() takes the intersection location into account,
// while this calculation of diff doesn't!
diff =
path1 !== path2
? // Sort by path id to group all locs on same path.
path1._id - path2._id
: // Sort by both index and time on the same path. The two values
// added together provides a convenient sorting index.
loc.getIndex() + loc.getTime() - (loc2.getIndex() + loc2.getTime());
if (diff < 0) {
r = m - 1;
} else {
l = m + 1;
}
}
// We didn't merge with a preexisting location, insert it now.
locations.splice(l, 0, loc);
return loc;
}
return {
statics: {
insert: insert,
expand: function (locations) {
// Create a copy since insert() keeps modifying the array and
// inserting at sorted indices.
var expanded = locations.slice();
for (var i = locations.length - 1; i >= 0; i--) {
insert(expanded, locations[i]._intersection, false);
}
return expanded;
},
},
};
})()
);
ref.CurveLocation = CurveLocation;
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