@flatten-js/core
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Javascript library for 2d geometry
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JavaScript
/**
* Created by Alex Bol on 3/15/2017.
*/
;
import Flatten from '../flatten';
import {ray_shoot} from "../algorithms/ray_shooting";
import * as Intersection from "../algorithms/intersection";
import * as Relations from "../algorithms/relation";
import {
addToIntPoints, calculateInclusionFlags, filterDuplicatedIntersections,
getSortedArray, initializeInclusionFlags, insertBetweenIntPoints,
splitByIntersections
} from "../data_structures/smart_intersections";
import {Multiline} from "./multiline";
import {intersectEdge2Edge, intersectMultiline2Polygon} from "../algorithms/intersection";
import {INSIDE, BOUNDARY} from "../utils/constants";
import {convertToString} from "../utils/attributes";
import {Matrix} from "./matrix";
/**
* Class representing a polygon.<br/>
* Polygon in FlattenJS is a multipolygon comprised from a set of [faces]{@link Flatten.Face}. <br/>
* Face, in turn, is a closed loop of [edges]{@link Flatten.Edge}, where edge may be segment or circular arc<br/>
* @type {Polygon}
*/
export class Polygon {
/**
* Constructor creates new instance of polygon. With no arguments new polygon is empty.<br/>
* Constructor accepts as argument array that define loop of shapes
* or array of arrays in case of multi polygon <br/>
* Loop may be defined in different ways: <br/>
* - array of shapes of type Segment or Arc <br/>
* - array of points (Flatten.Point) <br/>
* - array of numeric pairs which represent points <br/>
* - box or circle object <br/>
* Alternatively, it is possible to use polygon.addFace method
* @param {args} - array of shapes or array of arrays
*/
constructor() {
/**
* Container of faces (closed loops), may be empty
* @type {PlanarSet}
*/
this.faces = new Flatten.PlanarSet();
/**
* Container of edges
* @type {PlanarSet}
*/
this.edges = new Flatten.PlanarSet();
/* It may be array of something that may represent one loop (face) or
array of arrays that represent multiple loops
*/
let args = [...arguments];
if (args.length === 1 &&
((args[0] instanceof Array && args[0].length > 0) ||
args[0] instanceof Flatten.Circle || args[0] instanceof Flatten.Box)) {
let argsArray = args[0];
if (args[0] instanceof Array && args[0].every((loop) => {
return loop instanceof Array
})) {
if (argsArray.every(el => {
return el instanceof Array && el.length === 2 && typeof (el[0]) === "number" && typeof (el[1]) === "number"
})) {
this.faces.add(new Flatten.Face(this, argsArray)); // one-loop polygon as array of pairs of numbers
} else {
for (let loop of argsArray) { // multi-loop polygon
/* Check extra level of nesting for GeoJSON-style multi polygons */
if (loop instanceof Array && loop[0] instanceof Array &&
loop[0].every(el => {
return el instanceof Array && el.length === 2 && typeof (el[0]) === "number" && typeof (el[1]) === "number"
})) {
for (let loop1 of loop) {
this.faces.add(new Flatten.Face(this, loop1));
}
} else {
this.faces.add(new Flatten.Face(this, loop));
}
}
}
} else {
this.faces.add(new Flatten.Face(this, argsArray)); // one-loop polygon
}
}
}
/**
* (Getter) Returns bounding box of the polygon
* @returns {Box}
*/
get box() {
return [...this.faces].reduce((acc, face) => acc.merge(face.box), new Flatten.Box());
}
/**
* (Getter) Returns array of vertices
* @returns {Array}
*/
get vertices() {
return [...this.edges].map(edge => edge.start);
}
/**
* Create new cloned instance of the polygon
* @returns {Polygon}
*/
clone() {
let polygon = new Polygon();
for (let face of this.faces) {
polygon.addFace(face.shapes);
}
return polygon;
}
/**
* Return true is polygon has no edges
* @returns {boolean}
*/
isEmpty() {
return this.edges.size === 0;
}
/**
* Return true if polygon is valid for boolean operations
* Polygon is valid if <br/>
* 1. All faces are simple polygons (there are no self-intersected polygons) <br/>
* 2. All faces are orientable and there is no island inside island or hole inside hole - TODO <br/>
* 3. There is no intersections between faces (excluding touching) - TODO <br/>
* @returns {boolean}
*/
isValid() {
let valid = true;
// 1. Polygon is invalid if at least one face is not simple
for (let face of this.faces) {
if (!face.isSimple(this.edges)) {
valid = false;
break;
}
}
// 2. TODO: check if no island inside island and no hole inside hole
// 3. TODO: check the there is no intersection between faces
return valid;
}
/**
* Returns area of the polygon. Area of an island will be added, area of a hole will be subtracted
* @returns {number}
*/
area() {
let signedArea = [...this.faces].reduce((acc, face) => acc + face.signedArea(), 0);
return Math.abs(signedArea);
}
/**
* Add new face to polygon. Returns added face
* @param {Point[]|Segment[]|Arc[]|Circle|Box} args - new face may be create with one of the following ways: <br/>
* 1) array of points that describe closed path (edges are segments) <br/>
* 2) array of shapes (segments and arcs) which describe closed path <br/>
* 3) circle - will be added as counterclockwise arc <br/>
* 4) box - will be added as counterclockwise rectangle <br/>
* You can chain method face.reverse() is you need to change direction of the creates face
* @returns {Face}
*/
addFace(...args) {
let face = new Flatten.Face(this, ...args);
this.faces.add(face);
return face;
}
/**
* Delete existing face from polygon
* @param {Face} face Face to be deleted
* @returns {boolean}
*/
deleteFace(face) {
for (let edge of face) {
this.edges.delete(edge);
}
return this.faces.delete(face);
}
/**
* Clear all faces and create new faces from edges
*/
recreateFaces() {
// Remove all faces
this.faces.clear();
for (let edge of this.edges) {
edge.face = null;
}
// Restore faces
let first;
let unassignedEdgeFound = true;
while (unassignedEdgeFound) {
unassignedEdgeFound = false;
for (let edge of this.edges) {
if (edge.face === null) {
first = edge;
unassignedEdgeFound = true;
break;
}
}
if (unassignedEdgeFound) {
let last = first;
do {
last = last.next;
} while (last.next !== first)
this.addFace(first, last);
}
}
}
/**
* Delete chain of edges from the face.
* @param {Face} face Face to remove chain
* @param {Edge} edgeFrom Start of the chain of edges to be removed
* @param {Edge} edgeTo End of the chain of edges to be removed
*/
removeChain(face, edgeFrom, edgeTo) {
// Special case: all edges removed
if (edgeTo.next === edgeFrom) {
this.deleteFace(face);
return;
}
for (let edge = edgeFrom; edge !== edgeTo.next; edge = edge.next) {
face.remove(edge);
this.edges.delete(edge); // delete from PlanarSet of edges and update index
if (face.isEmpty()) {
this.deleteFace(face); // delete from PlanarSet of faces and update index
break;
}
}
}
/**
* Add point as a new vertex and split edge. Point supposed to belong to an edge.
* When edge is split, new edge created from the start of the edge to the new vertex
* and inserted before current edge.
* Current edge is trimmed and updated.
* Method returns new edge added. If no edge added, it returns edge before vertex
* @param {Point} pt Point to be added as a new vertex
* @param {Edge} edge Edge to be split with new vertex and then trimmed from start
* @returns {Edge}
*/
addVertex(pt, edge) {
let shapes = edge.shape.split(pt);
// if (shapes.length < 2) return;
if (shapes[0] === null) // point incident to edge start vertex, return previous edge
return edge.prev;
if (shapes[1] === null) // point incident to edge end vertex, return edge itself
return edge;
let newEdge = new Flatten.Edge(shapes[0]);
let edgeBefore = edge.prev;
/* Insert first split edge into linked list after edgeBefore */
edge.face.insert(newEdge, edgeBefore);
// Remove old edge from edges container and 2d index
this.edges.delete(edge);
// Insert new edge to the edges container and 2d index
this.edges.add(newEdge);
// Update edge shape with second split edge keeping links
edge.shape = shapes[1];
// Add updated edge to the edges container and 2d index
this.edges.add(edge);
return newEdge;
}
/**
* Merge given edge with next edge and remove vertex between them
* @param {Edge} edge
*/
removeEndVertex(edge) {
const edge_next = edge.next
if (edge_next === edge) return
edge.face.merge_with_next_edge(edge)
this.edges.delete(edge_next)
}
/**
* Cut polygon with multiline and return a new polygon
* @param {Multiline} multiline
* @returns {Polygon}
*/
cut(multiline) {
let newPoly = this.clone()
// smart intersections
let intersections = {
int_points1: [],
int_points2: [],
int_points1_sorted: [],
int_points2_sorted: []
};
// intersect each edge of multiline with each edge of the polygon
// and create smart intersections
for (let edge1 of multiline.edges) {
for (let edge2 of newPoly.edges) {
let ip = intersectEdge2Edge(edge1, edge2);
// for each intersection point
for (let pt of ip) {
addToIntPoints(edge1, pt, intersections.int_points1);
addToIntPoints(edge2, pt, intersections.int_points2);
}
}
}
// No intersections - return a copy of the original polygon
if (intersections.int_points1.length === 0)
return newPoly;
// sort smart intersections
intersections.int_points1_sorted = getSortedArray(intersections.int_points1);
intersections.int_points2_sorted = getSortedArray(intersections.int_points2);
// split by intersection points
splitByIntersections(multiline, intersections.int_points1_sorted);
splitByIntersections(newPoly, intersections.int_points2_sorted);
// filter duplicated intersection points
filterDuplicatedIntersections(intersections);
// sort intersection points again after filtering
intersections.int_points1_sorted = getSortedArray(intersections.int_points1);
intersections.int_points2_sorted = getSortedArray(intersections.int_points2);
// initialize inclusion flags for edges of multiline incident to intersections
initializeInclusionFlags(intersections.int_points1);
// calculate inclusion flag for edges of multiline incident to intersections
calculateInclusionFlags(intersections.int_points1, newPoly);
// filter intersections between two edges that got same inclusion flag
for (let int_point1 of intersections.int_points1_sorted) {
if (int_point1.edge_before && int_point1.edge_after &&
int_point1.edge_before.bv === int_point1.edge_after.bv) {
intersections.int_points2[int_point1.id] = -1; // to be filtered out
int_point1.id = -1; // to be filtered out
}
}
intersections.int_points1 = intersections.int_points1.filter( int_point => int_point.id >= 0);
intersections.int_points2 = intersections.int_points2.filter( int_point => int_point.id >= 0);
intersections.int_points1.forEach((int_point, index) => { int_point.id = index });
intersections.int_points2.forEach((int_point, index) => { int_point.id = index });
// No intersections left after filtering - return a copy of the original polygon
if (intersections.int_points1.length === 0)
return newPoly;
// sort intersection points 3d time after filtering
intersections.int_points1_sorted = getSortedArray(intersections.int_points1);
intersections.int_points2_sorted = getSortedArray(intersections.int_points2);
// Add new inner edges between intersection points
let int_point1_prev
let int_point1_curr;
for (let i = 1; i < intersections.int_points1_sorted.length; i++) {
int_point1_curr = intersections.int_points1_sorted[i]
int_point1_prev = intersections.int_points1_sorted[i-1];
if (int_point1_curr.edge_before && int_point1_curr.edge_before.bv === INSIDE) {
let edgeFrom = int_point1_prev.edge_after
let edgeTo = int_point1_curr.edge_before
let newEdges = multiline.getChain(edgeFrom, edgeTo)
insertBetweenIntPoints(intersections.int_points2[int_point1_prev.id], intersections.int_points2[int_point1_curr.id], newEdges);
newEdges.forEach(edge => newPoly.edges.add(edge))
newEdges = newEdges.reverse().map(edge => new Flatten.Edge(edge.shape.reverse()))
for (let k=0; k < newEdges.length-1; k++) {
newEdges[k].next = newEdges[k+1]
newEdges[k+1].prev = newEdges[k]
}
insertBetweenIntPoints(intersections.int_points2[int_point1_curr.id], intersections.int_points2[int_point1_prev.id], newEdges);
newEdges.forEach(edge => newPoly.edges.add(edge));
}
}
// Recreate faces
newPoly.recreateFaces();
return newPoly
}
/**
* A special case of cut() function
* The return is a polygon cut with line
* @param {Line} line - cutting line
* @returns {Polygon} newPoly - resulted polygon
*/
cutWithLine(line) {
let multiline = new Multiline([line]);
return this.cut(multiline);
}
/**
* Returns the first found edge of polygon that contains given point
* If point is a vertex, return the edge where the point is an end vertex, not a start one
* @param {Point} pt
* @returns {Edge}
*/
findEdgeByPoint(pt) {
let edge;
for (let face of this.faces) {
edge = face.findEdgeByPoint(pt);
if (edge !== undefined)
break;
}
return edge;
}
/**
* Split polygon into array of polygons, where each polygon is an outer face with all
* containing inner faces
* @returns {Flatten.Polygon[]}
*/
splitToIslands() {
if (this.isEmpty()) return []; // return empty array if polygon is empty
let polygons = this.toArray(); // split into array of one-loop polygons
/* Sort polygons by area in descending order */
polygons.sort((polygon1, polygon2) => polygon2.area() - polygon1.area());
/* define orientation of the island by orientation of the first polygon in array */
let orientation = [...polygons[0].faces][0].orientation();
/* Create output array from polygons with same orientation as a first polygon (array of islands) */
let newPolygons = polygons.filter(polygon => [...polygon.faces][0].orientation() === orientation);
for (let polygon of polygons) {
let face = [...polygon.faces][0];
if (face.orientation() === orientation) continue; // skip same orientation
/* Proceed with opposite orientation */
/* Look if any of island polygons contains tested polygon as a hole */
for (let islandPolygon of newPolygons) {
if (face.shapes.every(shape => islandPolygon.contains(shape))) {
islandPolygon.addFace(face.shapes); // add polygon as a hole in islandPolygon
break;
}
}
}
// TODO: assert if not all polygons added into output
return newPolygons;
}
/**
* Reverse orientation of all faces to opposite
* @returns {Polygon}
*/
reverse() {
for (let face of this.faces) {
face.reverse();
}
return this;
}
/**
* Returns true if polygon contains shape: no point of shape lay outside of the polygon,
* false otherwise
* @param {Shape} shape - test shape
* @returns {boolean}
*/
contains(shape) {
if (shape instanceof Flatten.Point) {
let rel = ray_shoot(this, shape);
return rel === INSIDE || rel === BOUNDARY;
} else {
return Relations.cover(this, shape);
}
}
/**
* Return distance and shortest segment between polygon and other shape as array [distance, shortest_segment]
* @param {Shape} shape Shape of one of the types Point, Circle, Line, Segment, Arc or Polygon
* @returns {Number | Segment}
*/
distanceTo(shape) {
// let {Distance} = Flatten;
if (shape instanceof Flatten.Point) {
let [dist, shortest_segment] = Flatten.Distance.point2polygon(shape, this);
shortest_segment = shortest_segment.reverse();
return [dist, shortest_segment];
}
if (shape instanceof Flatten.Circle ||
shape instanceof Flatten.Line ||
shape instanceof Flatten.Segment ||
shape instanceof Flatten.Arc) {
let [dist, shortest_segment] = Flatten.Distance.shape2polygon(shape, this);
shortest_segment = shortest_segment.reverse();
return [dist, shortest_segment];
}
/* this method is bit faster */
if (shape instanceof Flatten.Polygon) {
let min_dist_and_segment = [Number.POSITIVE_INFINITY, new Flatten.Segment()];
let dist, shortest_segment;
for (let edge of this.edges) {
// let [dist, shortest_segment] = Distance.shape2polygon(edge.shape, shape);
let min_stop = min_dist_and_segment[0];
[dist, shortest_segment] = Flatten.Distance.shape2planarSet(edge.shape, shape.edges, min_stop);
if (Flatten.Utils.LT(dist, min_stop)) {
min_dist_and_segment = [dist, shortest_segment];
}
}
return min_dist_and_segment;
}
}
/**
* Return array of intersection points between polygon and other shape
* @param shape Shape of the one of supported types <br/>
* @returns {Point[]}
*/
intersect(shape) {
if (shape instanceof Flatten.Point) {
return this.contains(shape) ? [shape] : [];
}
if (shape instanceof Flatten.Line) {
return Intersection.intersectLine2Polygon(shape, this);
}
if (shape instanceof Flatten.Ray) {
return Intersection.intersectRay2Polygon(shape, this);
}
if (shape instanceof Flatten.Circle) {
return Intersection.intersectCircle2Polygon(shape, this);
}
if (shape instanceof Flatten.Segment) {
return Intersection.intersectSegment2Polygon(shape, this);
}
if (shape instanceof Flatten.Arc) {
return Intersection.intersectArc2Polygon(shape, this);
}
if (shape instanceof Flatten.Polygon) {
return Intersection.intersectPolygon2Polygon(shape, this);
}
if (shape instanceof Flatten.Multiline) {
return Intersection.intersectMultiline2Polygon(shape, this);
}
}
/**
* Returns new polygon translated by vector vec
* @param {Vector} vec
* @returns {Polygon}
*/
translate(vec) {
let newPolygon = new Polygon();
for (let face of this.faces) {
newPolygon.addFace(face.shapes.map(shape => shape.translate(vec)));
}
return newPolygon;
}
/**
* Return new polygon rotated by given angle around given point
* If point omitted, rotate around origin (0,0)
* Positive value of angle defines rotation counterclockwise, negative - clockwise
* @param {number} angle - rotation angle in radians
* @param {Point} center - rotation center, default is (0,0)
* @returns {Polygon} - new rotated polygon
*/
rotate(angle = 0, center = new Flatten.Point()) {
let newPolygon = new Polygon();
for (let face of this.faces) {
newPolygon.addFace(face.shapes.map(shape => shape.rotate(angle, center)));
}
return newPolygon;
}
/**
* Return new polygon with coordinates multiplied by scaling factor
* @param {number} sx - x-axis scaling factor
* @param {number} sy - y-axis scaling factor
* @returns {Polygon}
*/
scale(sx, sy) {
let newPolygon = new Polygon();
for (let face of this.faces) {
newPolygon.addFace(face.shapes.map(shape => shape.scale(sx, sy)));
}
return newPolygon;
}
/**
* Return new polygon transformed using affine transformation matrix
* @param {Matrix} matrix - affine transformation matrix
* @returns {Polygon} - new polygon
*/
transform(matrix = new Flatten.Matrix()) {
let newPolygon = new Polygon();
for (let face of this.faces) {
newPolygon.addFace(face.shapes.map(shape => shape.transform(matrix)));
}
return newPolygon;
}
/**
* This method returns an object that defines how data will be
* serialized when called JSON.stringify() method
* @returns {Object}
*/
toJSON() {
return [...this.faces].map(face => face.toJSON());
}
/**
* Transform all faces into array of polygons
* @returns {Flatten.Polygon[]}
*/
toArray() {
return [...this.faces].map(face => face.toPolygon());
}
/**
* Return string to be assigned to 'd' attribute of <path> element
* @returns {*}
*/
dpath() {
return [...this.faces].reduce((acc, face) => acc + face.svg(), "")
}
/**
* Return string to draw polygon in svg
* @param attrs - an object with attributes for svg path element
* @returns {string}
*/
svg(attrs = {}) {
let svgStr = `\n<path ${convertToString({fillRule: "evenodd", fill: "lightcyan", ...attrs})} d="`;
for (let face of this.faces) {
svgStr += `\n${face.svg()}` ;
}
svgStr += `" >\n</path>`;
return svgStr;
}
}
Flatten.Polygon = Polygon;
/**
* Shortcut method to create new polygon
*/
export const polygon = (...args) => new Flatten.Polygon(...args);
Flatten.polygon = polygon;