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Algebra.ts
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Algebra.ts
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import { Engine } from './Engine';
import * as Util from './Util/Util';
import { Clonable } from './Interfaces/Clonable';
import { obsolete } from './Util/Decorators';
/**
* A 2D vector on a plane.
*/
export class Vector implements Clonable<Vector> {
/**
* A (0, 0) vector
*/
public static get Zero() {
return new Vector(0, 0);
}
/**
* A (1, 1) vector
*/
public static get One() {
return new Vector(1, 1);
}
/**
* A (0.5, 0.5) vector
*/
public static get Half() {
return new Vector(0.5, 0.5);
}
/**
* A unit vector pointing up (0, -1)
*/
public static get Up() {
return new Vector(0, -1);
}
/**
* A unit vector pointing down (0, 1)
*/
public static get Down() {
return new Vector(0, 1);
}
/**
* A unit vector pointing left (-1, 0)
*/
public static get Left() {
return new Vector(-1, 0);
}
/**
* A unit vector pointing right (1, 0)
*/
public static get Right() {
return new Vector(1, 0);
}
/**
* Returns a vector of unit length in the direction of the specified angle in Radians.
* @param angle The angle to generate the vector
*/
public static fromAngle(angle: number) {
return new Vector(Math.cos(angle), Math.sin(angle));
}
/**
* Checks if vector is not null, undefined, or if any of its components are NaN or Infinity.
*/
public static isValid(vec: Vector) {
if (vec === null || vec === undefined) {
return false;
}
if (isNaN(vec.x) || isNaN(vec.y)) {
return false;
}
if (vec.x === Infinity || vec.y === Infinity || vec.x === -Infinity || vec.y === -Infinity) {
return false;
}
return true;
}
/**
* Calculates distance between two Vectors
* @param vec1
* @param vec2
*/
public static distance(vec1: Vector, vec2: Vector) {
return Math.sqrt(Math.pow(vec1.x - vec2.x, 2) + Math.pow(vec1.y - vec2.y, 2));
}
/**
* @param x X component of the Vector
* @param y Y component of the Vector
*/
constructor(public x: number, public y: number) {}
/**
* Sets the x and y components at once
*/
public setTo(x: number, y: number) {
this.x = x;
this.y = y;
}
/**
* Compares this point against another and tests for equality
* @param point The other point to compare to
*/
public equals(vector: Vector, tolerance: number = 0.001): boolean {
return Math.abs(this.x - vector.x) <= tolerance && Math.abs(this.y - vector.y) <= tolerance;
}
/**
* The distance to another vector. If no other Vector is specified, this will return the [[magnitude]].
* @param v The other vector. Leave blank to use origin vector.
*/
public distance(v?: Vector): number {
if (!v) {
v = Vector.Zero;
}
return Math.sqrt(Math.pow(this.x - v.x, 2) + Math.pow(this.y - v.y, 2));
}
/**
* The magnitude (size) of the Vector
* @obsolete magnitude will be removed in favour of '.size' in version 0.25.0
*/
@obsolete({ message: 'will be removed in favour of `.size` in version 0.25.0' })
public magnitude(): number {
return this.distance();
}
/**
* The size(magnitude) of the Vector
*/
public get size(): number {
return this.distance();
}
public set size(newLength: number) {
const v = this.normalize().scale(newLength);
this.x = v.x;
this.y = v.y;
}
/**
* Normalizes a vector to have a magnitude of 1.
*/
public normalize(): Vector {
const d = this.distance();
if (d > 0) {
return new Vector(this.x / d, this.y / d);
} else {
return new Vector(0, 1);
}
}
/**
* Returns the average (midpoint) between the current point and the specified
*/
public average(vec: Vector): Vector {
return this.add(vec).scale(0.5);
}
/**
* Scales a vector's by a factor of size
* @param size The factor to scale the magnitude by
*/
public scale(scale: Vector): Vector;
public scale(size: number): Vector;
public scale(sizeOrScale: number | Vector): Vector {
if (sizeOrScale instanceof Vector) {
return new Vector(this.x * sizeOrScale.x, this.y * sizeOrScale.y);
} else {
return new Vector(this.x * sizeOrScale, this.y * sizeOrScale);
}
}
/**
* Adds one vector to another
* @param v The vector to add
*/
public add(v: Vector): Vector {
return new Vector(this.x + v.x, this.y + v.y);
}
/**
* Subtracts a vector from another, if you subtract vector `B.sub(A)` the resulting vector points from A -> B
* @param v The vector to subtract
*/
public sub(v: Vector): Vector {
return new Vector(this.x - v.x, this.y - v.y);
}
/**
* Adds one vector to this one modifying the original
* @param v The vector to add
*/
public addEqual(v: Vector): Vector {
this.x += v.x;
this.y += v.y;
return this;
}
/**
* Subtracts a vector from this one modifying the original
* @parallel v The vector to subtract
*/
public subEqual(v: Vector): Vector {
this.x -= v.x;
this.y -= v.y;
return this;
}
/**
* Scales this vector by a factor of size and modifies the original
*/
public scaleEqual(size: number): Vector {
this.x *= size;
this.y *= size;
return this;
}
/**
* Performs a dot product with another vector
* @param v The vector to dot
*/
public dot(v: Vector): number {
return this.x * v.x + this.y * v.y;
}
/**
* Performs a 2D cross product with scalar. 2D cross products with a scalar return a vector.
* @param v The scalar to cross
*/
public cross(v: number): Vector;
/**
* Performs a 2D cross product with another vector. 2D cross products return a scalar value not a vector.
* @param v The vector to cross
*/
public cross(v: Vector): number;
public cross(v: any): any {
if (v instanceof Vector) {
return this.x * v.y - this.y * v.x;
} else if (typeof v === 'number') {
return new Vector(v * this.y, -v * this.x);
}
}
/**
* Returns the perpendicular vector to this one
*/
public perpendicular(): Vector {
return new Vector(this.y, -this.x);
}
/**
* Returns the normal vector to this one, same as the perpendicular of length 1
*/
public normal(): Vector {
return this.perpendicular().normalize();
}
/**
* Negate the current vector
*/
public negate(): Vector {
return this.scale(-1);
}
/**
* Returns the angle of this vector.
*/
public toAngle(): number {
return Math.atan2(this.y, this.x);
}
/**
* Rotates the current vector around a point by a certain number of
* degrees in radians
*/
public rotate(angle: number, anchor?: Vector): Vector {
if (!anchor) {
anchor = new Vector(0, 0);
}
const sinAngle = Math.sin(angle);
const cosAngle = Math.cos(angle);
const x = cosAngle * (this.x - anchor.x) - sinAngle * (this.y - anchor.y) + anchor.x;
const y = sinAngle * (this.x - anchor.x) + cosAngle * (this.y - anchor.y) + anchor.y;
return new Vector(x, y);
}
/**
* Creates new vector that has the same values as the previous.
*/
public clone(): Vector {
return new Vector(this.x, this.y);
}
/**
* Returns a string representation of the vector.
*/
public toString(): string {
return `(${this.x}, ${this.y})`;
}
}
/**
* A 2D ray that can be cast into the scene to do collision detection
*/
export class Ray {
public pos: Vector;
public dir: Vector;
/**
* @param pos The starting position for the ray
* @param dir The vector indicating the direction of the ray
*/
constructor(pos: Vector, dir: Vector) {
this.pos = pos;
this.dir = dir.normalize();
}
/**
* Tests a whether this ray intersects with a line segment. Returns a number greater than or equal to 0 on success.
* This number indicates the mathematical intersection time.
* @param line The line to test
*/
public intersect(line: Line): number {
const numerator = line.begin.sub(this.pos);
// Test is line and ray are parallel and non intersecting
if (this.dir.cross(line.getSlope()) === 0 && numerator.cross(this.dir) !== 0) {
return -1;
}
// Lines are parallel
const divisor = this.dir.cross(line.getSlope());
if (divisor === 0) {
return -1;
}
const t = numerator.cross(line.getSlope()) / divisor;
if (t >= 0) {
const u = numerator.cross(this.dir) / divisor / line.getLength();
if (u >= 0 && u <= 1) {
return t;
}
}
return -1;
}
/**
* Returns the point of intersection given the intersection time
*/
public getPoint(time: number): Vector {
return this.pos.add(this.dir.scale(time));
}
}
/**
* A 2D line segment
*/
export class Line {
/**
* @param begin The starting point of the line segment
* @param end The ending point of the line segment
*/
constructor(public begin: Vector, public end: Vector) {}
/**
* Gets the raw slope (m) of the line. Will return (+/-)Infinity for vertical lines.
*/
public get slope() {
return (this.end.y - this.begin.y) / (this.end.x - this.begin.x);
}
/**
* Gets the Y-intercept (b) of the line. Will return (+/-)Infinity if there is no intercept.
*/
public get intercept() {
return this.begin.y - this.slope * this.begin.x;
}
/**
* Gets the normal of the line
*/
public normal(): Vector {
return this.end.sub(this.begin).normal();
}
/**
* Returns the slope of the line in the form of a vector of length 1
*/
public getSlope(): Vector {
const begin = this.begin;
const end = this.end;
const distance = begin.distance(end);
return end.sub(begin).scale(1 / distance);
}
/**
* Returns the edge of the line as vector, the length of the vector is the length of the edge
*/
public getEdge(): Vector {
const begin = this.begin;
const end = this.end;
return end.sub(begin);
}
/**
* Returns the length of the line segment in pixels
*/
public getLength(): number {
const begin = this.begin;
const end = this.end;
const distance = begin.distance(end);
return distance;
}
/**
* Returns the midpoint of the edge
*/
public get midpoint(): Vector {
return this.begin.add(this.end).scale(0.5);
}
/**
* Flips the direction of the line segment
*/
public flip(): Line {
return new Line(this.end, this.begin);
}
/**
* Find the perpendicular distance from the line to a point
* https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line
* @param point
*/
public distanceToPoint(point: Vector) {
const x0 = point.x;
const y0 = point.y;
const l = this.getLength();
const dy = this.end.y - this.begin.y;
const dx = this.end.x - this.begin.x;
const distance = Math.abs(dy * x0 - dx * y0 + this.end.x * this.begin.y - this.end.y * this.begin.x) / l;
return distance;
}
/**
* Find the perpendicular line from the line to a point
* https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line
* (a - p) - ((a - p) * n)n
* a is a point on the line
* p is the arbitrary point above the line
* n is a unit vector in direction of the line
* @param point
*/
public findVectorToPoint(point: Vector): Vector {
const aMinusP = this.begin.sub(point);
const n = this.getSlope();
return aMinusP.sub(n.scale(aMinusP.dot(n)));
}
/**
* Finds a point on the line given only an X or a Y value. Given an X value, the function returns
* a new point with the calculated Y value and vice-versa.
*
* @param x The known X value of the target point
* @param y The known Y value of the target point
* @returns A new point with the other calculated axis value
*/
public findPoint(x: number = null, y: number = null): Vector {
const m = this.slope;
const b = this.intercept;
if (x !== null) {
return new Vector(x, m * x + b);
} else if (y !== null) {
return new Vector((y - b) / m, y);
} else {
throw new Error('You must provide an X or a Y value');
}
}
/**
* Whether or not the given point lies on this line. This method is precise by default
* meaning the point must lie exactly on the line. Adjust threshold to
* loosen the strictness of the check for floating-point calculations.
*/
public hasPoint(x: number, y: number, threshold?: number): boolean;
/**
* Whether or not the given point lies on this line. This method is precise by default
* meaning the point must lie exactly on the line. Adjust threshold to
* loosen the strictness of the check for floating-point calculations.
*/
public hasPoint(v: Vector, threshold?: number): boolean;
/**
* @see http://stackoverflow.com/a/11908158/109458
*/
public hasPoint(): boolean {
let currPoint: Vector;
let threshold = 0;
if (typeof arguments[0] === 'number' && typeof arguments[1] === 'number') {
currPoint = new Vector(arguments[0], arguments[1]);
threshold = arguments[2] || 0;
} else if (arguments[0] instanceof Vector) {
currPoint = arguments[0];
threshold = arguments[1] || 0;
} else {
throw 'Could not determine the arguments for Vector.hasPoint';
}
const dxc = currPoint.x - this.begin.x;
const dyc = currPoint.y - this.begin.y;
const dx1 = this.end.x - this.begin.x;
const dy1 = this.end.y - this.begin.y;
const cross = dxc * dy1 - dyc * dx1;
// check whether point lines on the line
if (Math.abs(cross) > threshold) {
return false;
}
// check whether point lies in-between start and end
if (Math.abs(dx1) >= Math.abs(dy1)) {
return dx1 > 0 ? this.begin.x <= currPoint.x && currPoint.x <= this.end.x : this.end.x <= currPoint.x && currPoint.x <= this.begin.x;
} else {
return dy1 > 0 ? this.begin.y <= currPoint.y && currPoint.y <= this.end.y : this.end.y <= currPoint.y && currPoint.y <= this.begin.y;
}
}
}
/**
* A 1 dimensional projection on an axis, used to test overlaps
*/
export class Projection {
constructor(public min: number, public max: number) {}
public overlaps(projection: Projection): boolean {
return this.max > projection.min && projection.max > this.min;
}
public getOverlap(projection: Projection): number {
if (this.overlaps(projection)) {
if (this.max > projection.max) {
return projection.max - this.min;
} else {
return this.max - projection.min;
}
}
return 0;
}
}
export class GlobalCoordinates {
public static fromPagePosition(x: number, y: number, engine: Engine): GlobalCoordinates;
public static fromPagePosition(pos: Vector, engine: Engine): GlobalCoordinates;
public static fromPagePosition(xOrPos: number | Vector, yOrEngine: number | Engine, engineOrUndefined?: Engine): GlobalCoordinates {
let pageX: number;
let pageY: number;
let pagePos: Vector;
let engine: Engine;
if (arguments.length === 3) {
pageX = <number>xOrPos;
pageY = <number>yOrEngine;
pagePos = new Vector(pageX, pageY);
engine = engineOrUndefined;
} else {
pagePos = <Vector>xOrPos;
pageX = pagePos.x;
pageY = pagePos.y;
engine = <Engine>yOrEngine;
}
const screenX: number = pageX - Util.getPosition(engine.canvas).x;
const screenY: number = pageY - Util.getPosition(engine.canvas).y;
const screenPos = new Vector(screenX, screenY);
const worldPos = engine.screenToWorldCoordinates(screenPos);
return new GlobalCoordinates(worldPos, pagePos, screenPos);
}
constructor(public worldPos: Vector, public pagePos: Vector, public screenPos: Vector) {}
}
/**
* Shorthand for creating new Vectors - returns a new Vector instance with the
* provided X and Y components.
*
* @param x X component of the Vector
* @param y Y component of the Vector
*/
export function vec(x: number, y: number): Vector {
return new Vector(x, y);
}