romgrk-2d-geometry
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Javascript library for 2d geometry
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text/typescript
import { PIx2, CCW } from '../utils/constants';
import * as Distance from '../algorithms/distance';
import { PlanarSet } from '../data_structures/PlanarSet';
import * as Utils from '../utils/utils'
import * as Intersection from '../algorithms/intersection';
import {convertToString} from '../utils/attributes';
import * as geom from './index'
import {Point} from './Point';
import {Shape} from './Shape';
/**
* Class representing a circular arc
*/
export class Arc extends Shape<Arc> {
static EMPTY = Object.freeze(new Arc(Point.EMPTY, 0, 0, 0, CCW));
/**
* Arc center
*/
pc: Point
/**
* Arc radius
*/
r: number
/**
* Arc start angle in radians
*/
startAngle: number
/**
* Arc end angle in radians
*/
endAngle: number
/**
* Arc orientation
*/
counterClockwise: boolean
/**
* @param {Point} pc - arc center
* @param {number} r - arc radius
* @param {number} startAngle - start angle in radians from 0 to 2*PI
* @param {number} endAngle - end angle in radians from 0 to 2*PI
* @param {boolean} counterClockwise - arc direction, true - clockwise, false - counterclockwise
*/
constructor(...args) {
super()
/**
* Arc center
* @type {Point}
*/
this.pc = new Point();
/**
* Arc radius
* @type {number}
*/
this.r = 1;
/**
* Arc start angle in radians
* @type {number}
*/
this.startAngle = 0;
/**
* Arc end angle in radians
* @type {number}
*/
this.endAngle = 2 * Math.PI;
/**
* Arc orientation
* @type {boolean}
*/
this.counterClockwise = CCW;
if (args.length === 0)
return;
if (args.length === 1 && args[0] instanceof Object && args[0].name === "arc") {
let {pc, r, startAngle, endAngle, counterClockwise} = args[0];
this.pc = new Point(pc.x, pc.y);
this.r = r;
this.startAngle = startAngle;
this.endAngle = endAngle;
this.counterClockwise = counterClockwise;
} else {
let [pc, r, startAngle, endAngle, counterClockwise] = [...args];
if (pc && pc instanceof Point) this.pc = pc.clone();
if (r !== undefined) this.r = r;
if (startAngle !== undefined) this.startAngle = startAngle;
if (endAngle !== undefined) this.endAngle = endAngle;
if (counterClockwise !== undefined) this.counterClockwise = counterClockwise;
}
// throw geom.Errors.ILLEGAL_PARAMETERS; unreachable code
}
/**
* Return new cloned instance of arc
* @returns {Arc}
*/
clone() {
return new geom.Arc(this.pc.clone(), this.r, this.startAngle, this.endAngle, this.counterClockwise);
}
/**
* Get sweep angle in radians. Sweep angle is non-negative number from 0 to 2*PI
* @returns {number}
*/
get sweep() {
if (Utils.EQ(this.startAngle, this.endAngle))
return 0.0;
if (Utils.EQ(Math.abs(this.startAngle - this.endAngle), PIx2)) {
return PIx2;
}
let sweep;
if (this.counterClockwise) {
sweep = Utils.GT(this.endAngle, this.startAngle) ?
this.endAngle - this.startAngle : this.endAngle - this.startAngle + PIx2;
} else {
sweep = Utils.GT(this.startAngle, this.endAngle) ?
this.startAngle - this.endAngle : this.startAngle - this.endAngle + PIx2;
}
if (Utils.GT(sweep, PIx2)) {
sweep -= PIx2;
}
if (Utils.LT(sweep, 0)) {
sweep += PIx2;
}
return sweep;
}
/**
* Get start point of arc
*/
get start(): Point {
let p0 = new Point(this.pc.x + this.r, this.pc.y);
return p0.rotate(this.startAngle, this.pc) as Point;
}
/**
* Get end point of arc
*/
get end() {
let p0 = new Point(this.pc.x + this.r, this.pc.y);
return p0.rotate(this.endAngle, this.pc) as Point;
}
/**
* Get center of arc
* @returns {Point}
*/
get center() {
return this.pc.clone();
}
get vertices() {
return [this.start.clone(), this.end.clone()];
}
/**
* Get arc length
*/
get length() {
return Math.abs(this.sweep * this.r);
}
/**
* Get bounding box of the arc
* @returns {Box}
*/
get box() {
let func_arcs = this.breakToFunctional();
let box = func_arcs.reduce((acc, arc) => acc.merge(arc.start.box), new geom.Box());
box = box.merge(this.end.box);
return box;
}
/**
* Returns true if arc contains point, false otherwise
* @param {Point} pt - point to test
* @returns {boolean}
*/
contains(pt) {
// first check if point on circle (pc,r)
if (!Utils.EQ(this.pc.distanceTo(pt)[0], this.r))
return false;
// point on circle
if (pt.equalTo(this.start))
return true;
let angle = new geom.Vector(this.pc, pt).slope;
let test_arc = new geom.Arc(this.pc, this.r, this.startAngle, angle, this.counterClockwise);
return Utils.LE(test_arc.length, this.length);
}
/**
* When given point belongs to arc, return array of two arcs split by this point. If points is incident
* to start or end point of the arc, return clone of the arc. If point does not belong to the arcs, return
* empty array.
* @param {Point} pt Query point
* @returns {Arc[]}
*/
split(pt) {
if (this.start.equalTo(pt))
return [null, this.clone()];
if (this.end.equalTo(pt))
return [this.clone(), null];
let angle = new geom.Vector(this.pc, pt).slope;
return [
new geom.Arc(this.pc, this.r, this.startAngle, angle, this.counterClockwise),
new geom.Arc(this.pc, this.r, angle, this.endAngle, this.counterClockwise)
]
}
/**
* Return middle point of the arc
* @returns {Point}
*/
middle() {
let endAngle = this.counterClockwise ? this.startAngle + this.sweep / 2 : this.startAngle - this.sweep / 2;
let arc = new geom.Arc(this.pc, this.r, this.startAngle, endAngle, this.counterClockwise);
return arc.end;
}
/**
* Get point at given length
* @param length - The length along the arc
*/
pointAtLength(length: number) {
if (length > this.length || length < 0) return null;
if (length === 0) return this.start;
if (length === this.length) return this.end;
let factor = length / this.length;
let endAngle = this.counterClockwise ? this.startAngle + this.sweep * factor : this.startAngle - this.sweep * factor;
let arc = new geom.Arc(this.pc, this.r, this.startAngle, endAngle, this.counterClockwise);
return arc.end;
}
/**
* Returns chord height ("sagitta") of the arc
* @returns {number}
*/
chordHeight() {
return (1.0 - Math.cos(Math.abs(this.sweep / 2.0))) * this.r;
}
/**
* Returns array of intersection points between arc and other shape
* @param {Shape} shape Shape of the one of supported types <br/>
* @returns {Point[]}
*/
intersect(shape) {
if (shape instanceof Point) {
return this.contains(shape) ? [shape] : [];
}
if (shape instanceof geom.Line) {
return Intersection.intersectLine2Arc(shape, this);
}
if (shape instanceof geom.Ray) {
return Intersection.intersectRay2Arc(shape, this);
}
if (shape instanceof geom.Circle) {
return Intersection.intersectArc2Circle(this, shape);
}
if (shape instanceof geom.Segment) {
return Intersection.intersectSegment2Arc(shape, this);
}
if (shape instanceof geom.Box) {
return Intersection.intersectArc2Box(this, shape);
}
if (shape instanceof geom.Arc) {
return Intersection.intersectArc2Arc(this, shape);
}
if (shape instanceof geom.Polygon) {
return Intersection.intersectArc2Polygon(this, shape);
}
}
/**
* Calculate distance and shortest segment from arc to shape and return array [distance, shortest segment]
* @param {Shape} shape Shape of the one of supported types Point, Line, Circle, Segment, Arc, Polygon or Planar Set
* @returns {number} distance from arc to shape
* @returns {Segment} shortest segment between arc and shape (started at arc, ended at shape)
*/
distanceTo(shape) {
if (shape instanceof geom.Point) {
let [dist, shortest_segment] = Distance.point2arc(shape, this);
shortest_segment = shortest_segment.reverse();
return [dist, shortest_segment];
}
if (shape instanceof geom.Circle) {
let [dist, shortest_segment] = Distance.arc2circle(this, shape);
return [dist, shortest_segment];
}
if (shape instanceof geom.Line) {
let [dist, shortest_segment] = Distance.arc2line(this, shape);
return [dist, shortest_segment];
}
if (shape instanceof geom.Segment) {
let [dist, shortest_segment] = Distance.segment2arc(shape, this);
shortest_segment = shortest_segment.reverse();
return [dist, shortest_segment];
}
if (shape instanceof geom.Arc) {
let [dist, shortest_segment] = Distance.arc2arc(this, shape);
return [dist, shortest_segment];
}
if (shape instanceof geom.Polygon) {
let [dist, shortest_segment] = Distance.shape2polygon(this, shape);
return [dist, shortest_segment];
}
if (shape instanceof PlanarSet) {
let [dist, shortest_segment] = Distance.shape2planarSet(this, shape);
return [dist, shortest_segment];
}
}
/**
* Breaks arc in extreme point 0, pi/2, pi, 3*pi/2 and returns array of sub-arcs
*/
breakToFunctional() {
let func_arcs_array = [] as Arc[];
let angles = [0, Math.PI / 2, 2 * Math.PI / 2, 3 * Math.PI / 2];
let pts = [
this.pc.translate(this.r, 0),
this.pc.translate(0, this.r),
this.pc.translate(-this.r, 0),
this.pc.translate(0, -this.r)
];
// If arc contains extreme point,
// create test arc started at start point and ended at this extreme point
let test_arcs = [];
for (let i = 0; i < 4; i++) {
if (pts[i].on(this)) {
test_arcs.push(new geom.Arc(this.pc, this.r, this.startAngle, angles[i], this.counterClockwise));
}
}
if (test_arcs.length === 0) { // arc does contain any extreme point
func_arcs_array.push(this.clone());
} else { // arc passes extreme point
// sort these arcs by length
test_arcs.sort((arc1, arc2) => arc1.length - arc2.length);
for (let i = 0; i < test_arcs.length; i++) {
let prev_arc = func_arcs_array.length > 0 ? func_arcs_array[func_arcs_array.length - 1] : undefined;
let new_arc;
if (prev_arc) {
new_arc = new geom.Arc(this.pc, this.r, prev_arc.endAngle, test_arcs[i].endAngle, this.counterClockwise);
} else {
new_arc = new geom.Arc(this.pc, this.r, this.startAngle, test_arcs[i].endAngle, this.counterClockwise);
}
if (!Utils.EQ_0(new_arc.length)) {
func_arcs_array.push(new_arc.clone());
}
}
// add last sub arc
let prev_arc = func_arcs_array.length > 0 ? func_arcs_array[func_arcs_array.length - 1] : undefined;
let new_arc;
if (prev_arc) {
new_arc = new geom.Arc(this.pc, this.r, prev_arc.endAngle, this.endAngle, this.counterClockwise);
} else {
new_arc = new geom.Arc(this.pc, this.r, this.startAngle, this.endAngle, this.counterClockwise);
}
// It could be 2*PI when occasionally start = 0 and end = 2*PI but this is not valid for breakToFunctional
if (!Utils.EQ_0(new_arc.length) && !Utils.EQ(new_arc.sweep, 2*Math.PI)) {
func_arcs_array.push(new_arc.clone());
}
}
return func_arcs_array;
}
/**
* Return tangent unit vector in the start point in the direction from start to end
* @returns {Vector}
*/
tangentInStart() {
let vec = new geom.Vector(this.pc, this.start);
let angle = this.counterClockwise ? Math.PI / 2. : -Math.PI / 2.;
return vec.rotate(angle).normalize();
}
/**
* Return tangent unit vector in the end point in the direction from end to start
* @returns {Vector}
*/
tangentInEnd() {
let vec = new geom.Vector(this.pc, this.end);
let angle = this.counterClockwise ? -Math.PI / 2. : Math.PI / 2.;
return vec.rotate(angle).normalize();
}
/**
* Returns new arc with swapped start and end angles and reversed direction
* @returns {Arc}
*/
reverse() {
return new geom.Arc(this.pc, this.r, this.endAngle, this.startAngle, !this.counterClockwise);
}
/**
* Return new arc transformed using affine transformation matrix <br/>
*/
transform(matrix = new geom.Matrix()) {
let newStart = this.start.transform(matrix);
let newEnd = this.end.transform(matrix);
let newCenter = this.pc.transform(matrix);
let newDirection = this.counterClockwise;
if (matrix.a * matrix.d < 0) {
newDirection = !newDirection;
}
return geom.Arc.arcSE(newCenter, newStart, newEnd, newDirection);
}
static arcSE(center, start, end, counterClockwise) {
let {vector} = geom;
let startAngle = vector(center, start).slope;
let endAngle = vector(center, end).slope;
if (Utils.EQ(startAngle, endAngle)) {
endAngle += 2 * Math.PI;
counterClockwise = true;
}
let r = vector(center, start).length;
return new geom.Arc(center, r, startAngle, endAngle, counterClockwise);
}
definiteIntegral(ymin = 0) {
let f_arcs = this.breakToFunctional();
let area = f_arcs.reduce((acc, arc) => acc + arc.circularSegmentDefiniteIntegral(ymin), 0.0);
return area;
}
circularSegmentDefiniteIntegral(ymin) {
let line = new geom.Line(this.start, this.end);
let onLeftSide = this.pc.leftTo(line);
let segment = new geom.Segment(this.start, this.end);
let areaTrapez = segment.definiteIntegral(ymin);
let areaCircularSegment = this.circularSegmentArea();
let area = onLeftSide ? areaTrapez - areaCircularSegment : areaTrapez + areaCircularSegment;
return area;
}
circularSegmentArea() {
return (0.5 * this.r * this.r * (this.sweep - Math.sin(this.sweep)))
}
/**
* Sort given array of points from arc start to end, assuming all points lay on the arc
* @param {Point[]} pts array of points
* @returns {Point[]} new array sorted
*/
sortPoints(pts) {
let {vector} = geom;
return pts.slice().sort( (pt1, pt2) => {
let slope1 = vector(this.pc, pt1).slope;
let slope2 = vector(this.pc, pt2).slope;
if (slope1 < slope2) {
return -1;
}
if (slope1 > slope2) {
return 1;
}
return 0;
})
}
get name() {
return "arc"
}
/**
* Return string to draw arc in svg
* @param {Object} attrs - an object with attributes of svg path element
* @returns {string}
*/
svg(attrs = {}) {
let largeArcFlag = this.sweep <= Math.PI ? "0" : "1";
let sweepFlag = this.counterClockwise ? "1" : "0";
if (Utils.EQ(this.sweep, 2 * Math.PI)) {
let circle = new geom.Circle(this.pc, this.r);
return circle.svg(attrs);
} else {
return `\n<path d="M${(this.start as any).x},${this.start.y}
A${this.r},${this.r} 0 ${largeArcFlag},${sweepFlag} ${this.end.x},${this.end.y}"
${convertToString({fill: "none", ...attrs})} />`
}
}
}
/**
* Function to create arc equivalent to "new" constructor
* @param args
*/
export const arc = (...args) => new geom.Arc(...args);