plotboilerplate
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A simple javascript plotting boilerplate for 2d stuff.
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JavaScript
/**
* @author Ikaros Kappler
* @date 2018-04-14
* @modified 2018-11-17 Added the containsVert function.
* @modified 2018-12-04 Added the toSVGString function.
* @modified 2019-03-20 Added JSDoc tags.
* @modified 2019-10-25 Added the scale function.
* @modified 2019-11-06 JSDoc update.
* @modified 2019-11-07 Added toCubicBezierPath(number) function.
* @modified 2019-11-22 Added the rotate(number,Vertex) function.
* @modified 2020-03-24 Ported this class from vanilla-JS to Typescript.
* @modified 2020-10-30 Added the `addVertex` function.
* @modified 2020-10-31 Added the `getVertexAt` function.
* @modified 2020-11-06 Added the `move` function.
* @modified 2020-11-10 Added the `getBounds` function.
* @modified 2020-11-11 Generalized `move(Vertex)` to `move(XYCoords)`.
* @modified 2021-01-20 Added UID.
* @modified 2021-01-29 Added the `signedArea` function (was global function in the demos before).
* @modified 2021-01-29 Added the `isClockwise` function.
* @modified 2021-01-29 Added the `area` function.
* @modified 2021-01-29 Changed the param type for `containsVert` from Vertex to XYCoords.
* @modified 2021-12-14 Added the `perimeter()` function.
* @modified 2021-12-16 Added the `getEvenDistributionPolygon()` function.
* @modified 2022-02-02 Added the `destroy` method.
* @modified 2022-02-02 Cleared the `Polygon.toSVGString` function (deprecated). Use `drawutilssvg` instead.
* @modified 2022-03-08 Added the `Polygon.clone()` function.
* @modified 2023-09-25 Added the `Polygon.getInterpolationPolygon(number)` function.
* @modified 2023-09-25 Added the `Polygon.lineIntersections(Line,boolean)` function.
* @modified 2023-09-29 Added the `Polygon.closestLineIntersection(Line,boolean)` function.
* @modified 2023-11-24 Added the `Polygon.containsPolygon(Polygon)' function.
* @modified 2024-10-12 Added the `getEdgeAt` method.
* @modified 2024-10-30 Added the `getEdges` method.
* @modified 2024-12-02 Added the `elimitateColinearEdges` method.
* @modified 2025-02-12 Added the `containsVerts` method to test multiple vertices for containment.
* @version 1.14.0
*
* @file Polygon
* @public
**/
import { BezierPath } from "./BezierPath";
import { Bounds } from "./Bounds";
import { Line } from "./Line";
import { Triangle } from "./Triangle";
import { UIDGenerator } from "./UIDGenerator";
import { Vertex } from "./Vertex";
import { geomutils } from "./geomutils";
/**
* @classdesc A polygon class. Any polygon consists of an array of vertices; polygons can be open or closed.
*
* @requires BezierPath
* @requires Bounds
* @requires SVGSerializabe
* @requires UID
* @requires UIDGenerator
* @requires Vertex
* @requires XYCoords
*/
export class Polygon {
/**
* The constructor.
*
* @constructor
* @name Polygon
* @param {Vertex[]} vertices - An array of 2d vertices that shape the polygon.
* @param {boolean} isOpen - Indicates if the polygon should be rendered as an open or closed shape.
**/
constructor(vertices, isOpen) {
/**
* Required to generate proper CSS classes and other class related IDs.
**/
this.className = "Polygon";
this.uid = UIDGenerator.next();
if (typeof vertices == "undefined") {
vertices = [];
}
this.vertices = vertices;
this.isOpen = isOpen || false;
}
/**
* Add a vertex to the end of the `vertices` array.
*
* @method addVertex
* @param {Vertex} vert - The vertex to add.
* @instance
* @memberof Polygon
**/
addVertex(vert) {
this.vertices.push(vert);
}
/**
* Add a vertex at a particular position of the `vertices` array.
*
* @method addVertexAt
* @param {Vertex} vert - The vertex to add.
* @param {number} index - The position to add the vertex at. Will be handled modulo.
* @instance
* @memberof Polygon
**/
addVertexAt(vert, index) {
// var moduloIndex = index % (this.vertices.length + 1);
this.vertices.splice(index, 0, vert);
}
/**
* Get a new instance of the line at the given start index. The returned line will consist
* of the vertex at `vertIndex` and `vertIndex+1` (will be handled modulo).
*
* @method getEdgeAt
* @param {number} vertIndex - The vertex index of the line to start.
* @instance
* @memberof Polygon
* @return {Line}
**/
getEdgeAt(vertIndex) {
return new Line(this.getVertexAt(vertIndex), this.getVertexAt(vertIndex + 1));
}
/**
* Converts this polygon into a sequence of lines. Please note that each time
* this method is called new lines are created. The underlying line vertices are no clones
* (instances).
*
* @method getEdges
* @instance
* @memberof Polygon
* @return {Array<Line>}
*/
getEdges() {
const lines = [];
for (var i = 0; i + 1 < this.vertices.length; i++) {
// var line = this.getLineAt(i).clone();
lines.push(this.getEdgeAt(i));
}
if (!this.isOpen && this.vertices.length > 0) {
lines.push(this.getEdgeAt(this.vertices.length - 1));
}
return lines;
}
/**
* Checks if the angle at the given polygon vertex (index) is acute. Please not that this is
* only working for clockwise polygons. If this polygon is not clockwise please use the
* `isClockwise` method and reverse polygon vertices if needed.
*
* @method isAngleAcute
* @instance
* @memberof Polygon
* @param {number} vertIndex - The index of the polygon vertex to check.
* @returns {boolean} `true` is angle is acute, `false` is obtuse.
*/
getInnerAngleAt(vertIndex) {
const p2 = this.vertices[vertIndex];
const p1 = this.vertices[(vertIndex + this.vertices.length - 1) % this.vertices.length].clone();
const p3 = this.vertices[(vertIndex + 1) % this.vertices.length].clone();
// See
// https://math.stackexchange.com/questions/149959/how-to-find-the-interior-angle-of-an-irregular-pentagon-or-polygon
// π−arccos((P2−P1)⋅(P3−P2)|P2−P1||P3−P2|)
// Check if triangle is acute (will be used later)
// Acute angles and obtuse angles need to be handled differently.
const isAcute = this.isAngleAcute(vertIndex);
// Differences
const zero = new Vertex(0, 0);
const p2mp1 = new Vertex(p2.x - p1.x, p2.y - p1.y);
const p3mp2 = new Vertex(p3.x - p2.x, p3.y - p2.y);
const p2mp1_len = zero.distance(p2mp1);
const p3mp2_len = zero.distance(p3mp2);
// Dot products
const dotProduct = geomutils.dotProduct(p2mp1, p3mp2);
const lengthProduct = p2mp1_len * p3mp2_len;
if (isAcute) {
return Math.PI - Math.acos(dotProduct / lengthProduct);
}
else {
return Math.PI + Math.acos(dotProduct / lengthProduct);
}
}
/**
* Checks if the angle at the given polygon vertex (index) is acute.
*
* @method isAngleAcute
* @instance
* @memberof Polygon
* @param {number} vertIndex - The index of the polygon vertex to check.
* @returns {boolean} `true` is angle is acute, `false` is obtuse.
*/
isAngleAcute(vertIndex) {
const A = this.vertices[(vertIndex + this.vertices.length - 1) % this.vertices.length].clone();
const B = this.vertices[vertIndex];
const C = this.vertices[(vertIndex + 1) % this.vertices.length].clone();
// Find local winding number for triangle A B C
const windingNumber = Triangle.utils.determinant(A, B, C);
// console.log("vertIndex", vertIndex, "windingNumber", windingNumber);
return windingNumber < 0;
}
/**
* Get the polygon vertex at the given position (index).
*
* The index may exceed the total vertex count, and will be wrapped around then (modulo).
*
* For k >= 0:
* - getVertexAt( vertices.length ) == getVertexAt( 0 )
* - getVertexAt( vertices.length + k ) == getVertexAt( k )
* - getVertexAt( -k ) == getVertexAt( vertices.length -k )
*
* @method getVertexAt
* @param {number} index - The index of the desired vertex.
* @instance
* @memberof Polygon
* @return {Vertex} At the given index.
**/
getVertexAt(index) {
if (index < 0) {
return this.vertices[this.vertices.length - (Math.abs(index) % this.vertices.length)];
}
else {
return this.vertices[index % this.vertices.length];
}
}
/**
* Move the polygon's vertices by the given amount.
*
* @method move
* @param {XYCoords} amount - The amount to move.
* @instance
* @memberof Polygon
* @return {Polygon} this for chaining
**/
move(amount) {
for (var i in this.vertices) {
this.vertices[i].add(amount);
}
return this;
}
/**
* Check if the given vertex is inside this polygon.<br>
* <br>
* Ray-casting algorithm found at<br>
* https://stackoverflow.com/questions/22521982/check-if-point-inside-a-polygon
*
* @method containsVert
* @param {XYCoords} vert - The vertex to check.
* @return {boolean} True if the passed vertex is inside this polygon. The polygon is considered closed.
* @instance
* @memberof Polygon
**/
containsVert(vert) {
// ray-casting algorithm based on
// http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/pnpoly.html
var inside = false;
for (var i = 0, j = this.vertices.length - 1; i < this.vertices.length; j = i++) {
let xi = this.vertices[i].x, yi = this.vertices[i].y;
let xj = this.vertices[j].x, yj = this.vertices[j].y;
var intersect = yi > vert.y != yj > vert.y && vert.x < ((xj - xi) * (vert.y - yi)) / (yj - yi) + xi;
if (intersect)
inside = !inside;
}
return inside;
}
/**
* Check if all given vertices are inside this polygon.<br>
* <br>
* This method just uses the `Polygon.containsVert` method.
*
* @method containsVerts
* @param {XYCoords[]} verts - The vertices to check.
* @return {boolean} True if all passed vertices are inside this polygon. The polygon is considered closed.
* @instance
* @memberof Polygon
**/
containsVerts(verts) {
return verts.every((vert) => this.containsVert(vert));
}
/**
* Check if the passed polygon is completly contained inside this polygon.
*
* This means:
* - all polygon's vertices must be inside this polygon.
* - the polygon has no edge intersections with this polygon.
*
* @param {Polygon} polygon - The polygon to check if contained.
* @return {boolean}
*/
containsPolygon(polygon) {
for (var i = 0; i < polygon.vertices.length; i++) {
if (!this.containsVert(polygon.vertices[i])) {
return false;
}
}
// All vertices are inside; check for intersections
const lineSegment = new Line(new Vertex(), new Vertex());
for (var i = 0; i < polygon.vertices.length; i++) {
lineSegment.a.set(polygon.vertices[i]);
lineSegment.b.set(polygon.vertices[(i + 1) % polygon.vertices.length]);
if (this.lineIntersections(lineSegment, true).length > 0) {
// Current segment has intersection(s) with this polygon.
return false;
}
}
return true;
}
/**
* Calculate the area of the given polygon (unsigned).
*
* Note that this does not work for self-intersecting polygons.
*
* @method area
* @instance
* @memberof Polygon
* @return {number}
*/
area() {
return Polygon.utils.area(this.vertices);
}
/**
* Calulate the signed polyon area by interpreting the polygon as a matrix
* and calculating its determinant.
*
* @method signedArea
* @instance
* @memberof Polygon
* @return {number}
*/
signedArea() {
return Polygon.utils.signedArea(this.vertices);
}
/**
* Get the winding order of this polgon: clockwise or counterclockwise.
*
* @method isClockwise
* @instance
* @memberof Polygon
* @return {boolean}
*/
isClockwise() {
// return Polygon.utils.signedArea(this.vertices) < 0;
return Polygon.utils.isClockwise(this.vertices);
}
/**
* Get the perimeter of this polygon.
* The perimeter is the absolute length of the outline.
*
* If this polygon is open then the last segment (connecting the first and the
* last vertex) will be skipped.
*
* @method perimeter
* @instance
* @memberof Polygon
* @return {number}
*/
perimeter() {
let length = 0;
for (var i = 1; i < this.vertices.length; i++) {
length += this.vertices[i - 1].distance(this.vertices[i]);
}
if (!this.isOpen && this.vertices.length > 1) {
length += this.vertices[0].distance(this.vertices[this.vertices.length - 1]);
}
return length;
}
/**
* Scale the polygon relative to the given center.
*
* @method scale
* @param {number} factor - The scale factor.
* @param {Vertex} center - The center of scaling.
* @return {Polygon} this, for chaining.
* @instance
* @memberof Polygon
**/
scale(factor, center) {
for (var i in this.vertices) {
if (typeof this.vertices[i].scale == "function")
this.vertices[i].scale(factor, center);
else
console.log("There seems to be a null vertex!", this.vertices[i]);
}
return this;
}
/**
* Rotate the polygon around the given center.
*
* @method rotate
* @param {number} angle - The rotation angle.
* @param {Vertex} center - The center of rotation.
* @instance
* @memberof Polygon
* @return {Polygon} this, for chaining.
**/
rotate(angle, center) {
for (var i in this.vertices) {
this.vertices[i].rotate(angle, center);
}
return this;
}
/**
* Get the mean `center` of this polygon by calculating the mean value of all vertices.
*
* Mean: (v[0] + v[1] + ... v[n-1]) / n
*
* @method getMeanCenter
* @instance
* @memberof Polygon
* @return {Vertex|null} `null` is no vertices are available.
*/
getMeanCenter() {
if (this.vertices.length === 0) {
return null;
}
const center = this.vertices[0].clone();
for (var i = 1; i < this.vertices.length; i++) {
center.add(this.vertices[i]);
}
center.x /= this.vertices.length;
center.y /= this.vertices.length;
return center;
}
/**
* Get all line intersections with this polygon.
*
* See demo `47-closest-vector-projection-on-polygon` for how it works.
*
* @param {VertTuple} line - The line to find intersections with.
* @param {boolean} inVectorBoundsOnly - If set to true only intersecion points on the passed vector are returned (located strictly between start and end vertex).
* @returns {Array<Vertex>} - An array of all intersections within the polygon bounds.
*/
lineIntersections(line, inVectorBoundsOnly = false) {
// Find the intersections of all lines inside the edge bounds
const intersectionPoints = [];
for (var i = 0; i < this.vertices.length; i++) {
const polyLine = new Line(this.vertices[i], this.vertices[(i + 1) % this.vertices.length]);
const intersection = polyLine.intersection(line);
// true => only inside bounds
// ignore last edge if open
if ((!this.isOpen || i + 1 !== this.vertices.length) &&
intersection !== null &&
polyLine.hasPoint(intersection, true) &&
(!inVectorBoundsOnly || line.hasPoint(intersection, inVectorBoundsOnly))) {
intersectionPoints.push(intersection);
}
}
return intersectionPoints;
}
/**
* Get the closest line-polygon-intersection point (closest the line point A).
*
* See demo `47-closest-vector-projection-on-polygon` for how it works.
*
* @param {VertTuple} line - The line to find intersections with.
* @param {boolean} inVectorBoundsOnly - If set to true only intersecion points on the passed vector are considered (located strictly between start and end vertex).
* @returns {Array<Vertex>} - An array of all intersections within the polygon bounds.
*/
closestLineIntersection(line, inVectorBoundsOnly = false) {
const allIntersections = this.lineIntersections(line, inVectorBoundsOnly);
if (allIntersections.length <= 0) {
// Empty polygon -> no intersections
return null;
}
// Find the closest intersection
let closestIntersection = new Vertex(Number.MAX_VALUE, Number.MAX_VALUE);
let curDist = Number.MAX_VALUE;
for (var i in allIntersections) {
const curVert = allIntersections[i];
const dist = curVert.distance(line.a);
if (dist < curDist) {
// && line.hasPoint(curVert)) {
curDist = dist;
closestIntersection = curVert;
}
}
return closestIntersection;
}
/**
* Construct a new polygon from this polygon with more vertices on each edge. The
* interpolation count determines the number of additional vertices on each edge.
* An interpolation count of `0` will return a polygon that equals the source
* polygon.
*
* @param {number} interpolationCount
* @returns {Polygon} A polygon with `interpolationCount` more vertices (as as factor).
*/
getInterpolationPolygon(interpolationCount) {
const verts = [];
for (var i = 0; i < this.vertices.length; i++) {
const curVert = this.vertices[i];
const nextVert = this.vertices[(i + 1) % this.vertices.length];
verts.push(curVert.clone());
// Add interpolation points
if (!this.isOpen || i + 1 !== this.vertices.length) {
const lerpAmount = 1.0 / (interpolationCount + 1);
for (var j = 1; j <= interpolationCount; j++) {
verts.push(curVert.clone().lerp(nextVert, lerpAmount * j));
}
}
}
return new Polygon(verts, this.isOpen);
}
/**
* Convert this polygon into a new polygon with n evenly distributed vertices.
*
* @param {number} pointCount - Must not be negative.
*/
getEvenDistributionPolygon(pointCount) {
if (pointCount <= 0) {
throw new Error("pointCount must be larger than zero; is " + pointCount + ".");
}
const result = new Polygon([], this.isOpen);
if (this.vertices.length === 0) {
return result;
}
// Fetch and add the start point from the source polygon
let polygonPoint = new Vertex(this.vertices[0]);
result.vertices.push(polygonPoint);
if (this.vertices.length === 1) {
return result;
}
const perimeter = this.perimeter();
const stepSize = perimeter / pointCount;
const n = this.vertices.length;
let polygonIndex = 1;
let nextPolygonPoint = new Vertex(this.vertices[1]);
let segmentLength = polygonPoint.distance(nextPolygonPoint);
let loopMax = this.isOpen ? n : n + 1;
let curSegmentU = stepSize;
var i = 1;
while (i < pointCount && polygonIndex < loopMax) {
// Check if next eq point is inside this segment
if (curSegmentU < segmentLength) {
let newPoint = polygonPoint.clone().lerpAbs(nextPolygonPoint, curSegmentU);
result.vertices.push(newPoint);
curSegmentU += stepSize;
i++;
}
else {
polygonIndex++;
polygonPoint = nextPolygonPoint;
nextPolygonPoint = new Vertex(this.vertices[polygonIndex % n]);
curSegmentU = curSegmentU - segmentLength;
segmentLength = polygonPoint.distance(nextPolygonPoint);
}
}
return result;
}
/**
* Get the bounding box (bounds) of this polygon.
*
* @method getBounds
* @instance
* @memberof Polygon
* @return {Bounds} The rectangular bounds of this polygon.
**/
getBounds() {
return Bounds.computeFromVertices(this.vertices);
}
/**
* Create a deep copy of this polygon.
*
* @method clone
* @instance
* @memberof Polygon
* @return {Polygon} The cloned polygon.
*/
clone() {
return new Polygon(this.vertices.map(vert => vert.clone()), this.isOpen);
}
/**
* Create a new polygon without colinear adjacent edges. This method does not midify the current polygon
* but creates a new one.
*
* Please note that this method does NOT create deep clones of the vertices. Use Polygon.clone() if you need to.
*
* Please also note that the `tolerance` may become really large here, as the denominator of two closely
* parallel lines is usually pretty large. See the demo `57-eliminate-colinear-polygon-edges` to get
* an impression of how denominators work.
*
* @method elimitateColinearEdges
* @instance
* @memberof Polygon
* @param {number?} tolerance - (default is 1.0) The epsilon to detect co-linear edges.
* @return {Polygon} A new polygon without co-linear adjacent edges – respective the given epsilon.
*/
elimitateColinearEdges(tolerance) {
const eps = typeof tolerance === "undefined" ? 1.0 : tolerance;
const verts = this.vertices.slice(); // Creates a shallow copy
let i = 0;
var lineA = new Line(new Vertex(), new Vertex());
var lineB = new Line(new Vertex(), new Vertex());
while (i + 1 < verts.length && verts.length > 2) {
const vertA = verts[i];
const vertB = verts[(i + 1) % verts.length];
lineA.a = vertA;
lineA.b = vertB;
lineB.a = vertB;
let areColinear = false;
let j = i + 2;
do {
let vertC = verts[j % verts.length];
lineB.b = vertC;
areColinear = lineA.colinear(lineB, eps);
// console.log("are colinear?", i, i + 1, j, areColinear);
if (areColinear) {
j++;
}
} while (areColinear);
// Now j points to the first vertex that's NOT colinear to the current lineA
// -> delete all vertices in between
if (j - i > 2) {
// Means: there have been 'colinear vertices' in between
// console.log("Splice", "i", i, "j", j, i + 1, j - i - 1);
verts.splice(i + 1, j - i - 2);
}
i++;
}
return new Polygon(verts, this.isOpen);
}
/**
* Convert this polygon to a sequence of quadratic Bézier curves.<br>
* <br>
* The first vertex in the returned array is the start point.<br>
* The following sequence are pairs of control-point-and-end-point:
* <pre>startPoint, controlPoint0, pathPoint1, controlPoint1, pathPoint2, controlPoint2, ..., endPoint</pre>
*
* @method toQuadraticBezierData
* @return {Vertex[]} An array of 2d vertices that shape the quadratic Bézier curve.
* @instance
* @memberof Polygon
**/
toQuadraticBezierData() {
if (this.vertices.length < 3)
return [];
var qbezier = [];
var cc0 = this.vertices[0];
var cc1 = this.vertices[1];
var edgeCenter = new Vertex(cc0.x + (cc1.x - cc0.x) / 2, cc0.y + (cc1.y - cc0.y) / 2);
qbezier.push(edgeCenter);
var limit = this.isOpen ? this.vertices.length : this.vertices.length + 1;
for (var t = 1; t < limit; t++) {
cc0 = this.vertices[t % this.vertices.length];
cc1 = this.vertices[(t + 1) % this.vertices.length];
var edgeCenter = new Vertex(cc0.x + (cc1.x - cc0.x) / 2, cc0.y + (cc1.y - cc0.y) / 2);
qbezier.push(cc0);
qbezier.push(edgeCenter);
cc0 = cc1;
}
return qbezier;
}
/**
* Convert this polygon to a quadratic bezier curve, represented as an SVG data string.
*
* @method toQuadraticBezierSVGString
* @return {string} The 'd' part for an SVG 'path' element.
* @instance
* @memberof Polygon
**/
toQuadraticBezierSVGString() {
var qdata = this.toQuadraticBezierData();
if (qdata.length == 0)
return "";
var buffer = ["M " + qdata[0].x + " " + qdata[0].y];
for (var i = 1; i < qdata.length; i += 2) {
buffer.push("Q " + qdata[i].x + " " + qdata[i].y + ", " + qdata[i + 1].x + " " + qdata[i + 1].y);
}
return buffer.join(" ");
}
/**
* Convert this polygon to a sequence of cubic Bézier curves.<br>
* <br>
* The first vertex in the returned array is the start point.<br>
* The following sequence are triplets of (first-control-point, secnond-control-point, end-point):<br>
* <pre>startPoint, controlPoint0_0, controlPoint1_1, pathPoint1, controlPoint1_0, controlPoint1_1, ..., endPoint</pre>
*
* @method toCubicBezierData
* @param {number=} threshold - An optional threshold (default=1.0) how strong the curve segments
* should over-/under-drive. Should be between 0.0 and 1.0 for best
* results but other values are allowed.
* @return {Vertex[]} An array of 2d vertices that shape the cubic Bézier curve.
* @instance
* @memberof Polygon
**/
toCubicBezierData(threshold) {
if (typeof threshold == "undefined")
threshold = 1.0;
if (this.vertices.length < 3)
return [];
var cbezier = [];
var a = this.vertices[0];
var b = this.vertices[1];
var edgeCenter = new Vertex(a.x + (b.x - a.x) / 2, a.y + (b.y - a.y) / 2);
cbezier.push(edgeCenter);
var limit = this.isOpen ? this.vertices.length - 1 : this.vertices.length;
for (var t = 0; t < limit; t++) {
var a = this.vertices[t % this.vertices.length];
var b = this.vertices[(t + 1) % this.vertices.length];
var c = this.vertices[(t + 2) % this.vertices.length];
var aCenter = new Vertex(a.x + (b.x - a.x) / 2, a.y + (b.y - a.y) / 2);
var bCenter = new Vertex(b.x + (c.x - b.x) / 2, b.y + (c.y - b.y) / 2);
var a2 = new Vertex(aCenter.x + (b.x - aCenter.x) * threshold, aCenter.y + (b.y - aCenter.y) * threshold);
var b0 = new Vertex(bCenter.x + (b.x - bCenter.x) * threshold, bCenter.y + (b.y - bCenter.y) * threshold);
cbezier.push(a2);
cbezier.push(b0);
cbezier.push(bCenter);
}
return cbezier;
}
/**
* Convert this polygon to a cubic bezier curve, represented as an SVG data string.
*
* @method toCubicBezierSVGString
* @return {string} The 'd' part for an SVG 'path' element.
* @instance
* @memberof Polygon
**/
toCubicBezierSVGString(threshold) {
var qdata = this.toCubicBezierData(threshold);
if (qdata.length == 0) {
return "";
}
var buffer = ["M " + qdata[0].x + " " + qdata[0].y];
for (var i = 1; i < qdata.length; i += 3) {
buffer.push("C " +
qdata[i].x +
" " +
qdata[i].y +
", " +
qdata[i + 1].x +
" " +
qdata[i + 1].y +
", " +
qdata[i + 2].x +
" " +
qdata[i + 2].y);
}
return buffer.join(" ");
}
/**
* Convert this polygon to a cubic bezier path instance.
*
* @method toCubicBezierPath
* @param {number} threshold - The threshold, usually from 0.0 to 1.0.
* @return {BezierPath} - A bezier path instance.
* @instance
* @memberof Polygon
**/
toCubicBezierPath(threshold) {
var qdata = this.toCubicBezierData(threshold);
// Conver the linear path vertices to a two-dimensional path array
var pathdata = [];
for (var i = 0; i + 3 < qdata.length; i += 3) {
pathdata.push([qdata[i], qdata[i + 3], qdata[i + 1], qdata[i + 2]]);
}
return BezierPath.fromArray(pathdata);
}
/**
* This function should invalidate any installed listeners and invalidate this object.
* After calling this function the object might not hold valid data any more and
* should not be used.
*/
destroy() {
for (var i = 0; i < this.vertices.length; i++) {
this.vertices[i].destroy();
}
this.isDestroyed = true;
}
}
Polygon.utils = {
/**
* Calculate the area of the given polygon (unsigned).
*
* Note that this does not work for self-intersecting polygons.
*
* @name area
* @return {number}
*/
area(vertices) {
// Found at:
// https://stackoverflow.com/questions/16285134/calculating-polygon-area
let total = 0.0;
for (var i = 0, l = vertices.length; i < l; i++) {
const addX = vertices[i].x;
const addY = vertices[(i + 1) % l].y;
const subX = vertices[(i + 1) % l].x;
const subY = vertices[i].y;
total += addX * addY * 0.5;
total -= subX * subY * 0.5;
}
return Math.abs(total);
},
isClockwise(vertices) {
return Polygon.utils.signedArea(vertices) < 0;
},
/**
* Calulate the signed polyon area by interpreting the polygon as a matrix
* and calculating its determinant.
*
* @name signedArea
* @return {number}
*/
signedArea(vertices) {
let sum = 0;
const n = vertices.length;
for (var i = 0; i < n; i++) {
const j = (i + 1) % n;
sum += (vertices[j].x - vertices[i].x) * (vertices[i].y + vertices[j].y);
}
return sum;
}
};
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