p5.Vector.js

/**
 * @module Math
 * @submodule Vector
 * @requires constants
 */

import p5 from '../core/main';
import * as constants from '../core/constants';


/**
 * A class to describe a two or three-dimensional vector.
 *
 * A vector can be thought of in different ways. In one view, a vector is like
 * an arrow pointing in space. Vectors have both magnitude (length) and
 * direction.
 *
 * `p5.Vector` objects are often used to program motion because they simplify
 * the math. For example, a moving ball has a position and a velocity.
 * Position describes where the ball is in space. The ball's position vector
 * extends from the origin to the ball's center. Velocity describes the ball's
 * speed and the direction it's moving. If the ball is moving straight up, its
 * velocity vector points straight up. Adding the ball's velocity vector to
 * its position vector moves it, as in `pos.add(vel)`. Vector math relies on
 * methods inside the `p5.Vector` class.
 *
 * Note: <a href="#/p5/createVector">createVector()</a> is the recommended way
 * to make an instance of this class.
 *
 * @class p5.Vector
 * @constructor
 * @param {Number} [x] x component of the vector.
 * @param {Number} [y] y component of the vector.
 * @param {Number} [z] z component of the vector.
 * @example
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Create p5.Vector objects.
 *   let p1 = createVector(25, 25);
 *   let p2 = createVector(75, 75);
 *
 *   // Style the points.
 *   strokeWeight(5);
 *
 *   // Draw the first point using a p5.Vector.
 *   point(p1);
 *
 *   // Draw the second point using a p5.Vector's components.
 *   point(p2.x, p2.y);
 *
 *   describe('Two black dots on a gray square, one at the top left and the other at the bottom right.');
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * let pos;
 * let vel;
 *
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   // Create p5.Vector objects.
 *   pos = createVector(50, 100);
 *   vel = createVector(0, -1);
 *
 *   describe('A black dot moves from bottom to top on a gray square. The dot reappears at the bottom when it reaches the top.');
 * }
 *
 * function draw() {
 *   background(200);
 *
 *   // Add velocity to position.
 *   pos.add(vel);
 *
 *   // If the dot reaches the top of the canvas,
 *   // restart from the bottom.
 *   if (pos.y < 0) {
 *     pos.y = 100;
 *   }
 *
 *   // Draw the dot.
 *   strokeWeight(5);
 *   point(pos);
 * }
 * </code>
 * </div>
 */
p5.Vector = class {
  // This is how it comes in with createVector()
  // This check if the first argument is a function
  constructor(...args) {
    let x, y, z;
    if (typeof args[0] === 'function') {
      this.isPInst = true;
      this._fromRadians = args[0];
      this._toRadians = args[1];
      x = args[2] || 0;
      y = args[3] || 0;
      z = args[4] || 0;
      // This is what we'll get with new p5.Vector()
    } else {
      x = args[0] || 0;
      y = args[1] || 0;
      z = args[2] || 0;
    }
    /**
     * The x component of the vector
     * @type {Number}
     * @property x
     * @name x
     */
    this.x = x;
    /**
     * The y component of the vector
     * @type {Number}
     * @property y
     * @name y
     */
    this.y = y;
    /**
     * The z component of the vector
     * @type {Number}
     * @property z
     * @name z
     */
    this.z = z;
  }

  /**
 * Returns a string representation of a vector.
 *
 * Calling `toString()` is useful for printing vectors to the console while
 * debugging.
 *
 * @method  toString
 * @return {String} string representation of the vector.
 *
 * @example
 * <div class = "norender">
 * <code>
 * function setup() {
 *   let v = createVector(20, 30);
 *
 *   // Prints 'p5.Vector Object : [20, 30, 0]'.
 *   print(v.toString());
 * }
 * </code>
 * </div>
 */
  toString() {
    return `p5.Vector Object : [${this.x}, ${this.y}, ${this.z}]`;
  }

  /**
 * Sets the vector's `x`, `y`, and `z` components.
 *
 * `set()` can use separate numbers, as in `v.set(1, 2, 3)`, a
 * <a href="#/p5.Vector">p5.Vector</a> object, as in `v.set(v2)`, or an
 * array of numbers, as in `v.set([1, 2, 3])`.
 *
 * If a value isn't provided for a component, it will be set to 0. For
 * example, `v.set(4, 5)` sets `v.x` to 4, `v.y` to 5, and `v.z` to 0.
 * Calling `set()` with no arguments, as in `v.set()`, sets all the vector's
 * components to 0.
 *
 * @method set
 * @param {Number} [x] x component of the vector.
 * @param {Number} [y] y component of the vector.
 * @param {Number} [z] z component of the vector.
 * @chainable
 * @example
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Style the points.
 *   strokeWeight(5);
 *
 *   // Top left.
 *   let pos = createVector(25, 25);
 *   point(pos);
 *
 *   // Top right.
 *   // set() with numbers.
 *   pos.set(75, 25);
 *   point(pos);
 *
 *   // Bottom right.
 *   // set() with a p5.Vector.
 *   let p2 = createVector(75, 75);
 *   pos.set(p2);
 *   point(pos);
 *
 *   // Bottom left.
 *   // set() with an array.
 *   let arr = [25, 75];
 *   pos.set(arr);
 *   point(pos);
 *
 *   describe('Four black dots arranged in a square on a gray background.');
 * }
 * </code>
 * </div>
 */
  /**
 * @method set
 * @param {p5.Vector|Number[]} value vector to set.
 * @chainable
 */
  set (x, y, z) {
    if (x instanceof p5.Vector) {
      this.x = x.x || 0;
      this.y = x.y || 0;
      this.z = x.z || 0;
      return this;
    }
    if (Array.isArray(x)) {
      this.x = x[0] || 0;
      this.y = x[1] || 0;
      this.z = x[2] || 0;
      return this;
    }
    this.x = x || 0;
    this.y = y || 0;
    this.z = z || 0;
    return this;
  }

  /**
 * Returns a copy of the <a href="#/p5.Vector">p5.Vector</a> object.
 *
 * @method copy
 * @return {p5.Vector} copy of the <a href="#/p5.Vector">p5.Vector</a> object.
 *
 * @example
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100 ,100);
 *
 *   background(200);
 *
 *   // Create a p5.Vector object.
 *   let pos = createVector(50, 50);
 *
 *   // Make a copy.
 *   let pc = pos.copy();
 *
 *   // Draw the point.
 *   strokeWeight(5);
 *   point(pc);
 *
 *   describe('A black point drawn in the middle of a gray square.');
 * }
 * </code>
 * </div>
 */
  copy () {
    if (this.isPInst) {
      return new p5.Vector(
        this._fromRadians,
        this._toRadians,
        this.x,
        this.y,
        this.z
      );
    } else {
      return new p5.Vector(this.x, this.y, this.z);
    }
  }

  /**
 * Adds to a vector's `x`, `y`, and `z` components.
 *
 * `add()` can use separate numbers, as in `v.add(1, 2, 3)`,
 * another <a href="#/p5.Vector">p5.Vector</a> object, as in `v.add(v2)`, or
 * an array of numbers, as in `v.add([1, 2, 3])`.
 *
 * If a value isn't provided for a component, it won't change. For
 * example, `v.add(4, 5)` adds 4 to `v.x`, 5 to `v.y`, and 0 to `v.z`.
 * Calling `add()` with no arguments, as in `v.add()`, has no effect.
 *
 * The static version of `add()`, as in `p5.Vector.add(v2, v1)`, returns a new
 * <a href="#/p5.Vector">p5.Vector</a> object and doesn't change the
 * originals.
 *
 * @method add
 * @param  {Number} x   x component of the vector to be added.
 * @param  {Number} [y] y component of the vector to be added.
 * @param  {Number} [z] z component of the vector to be added.
 * @chainable
 *
 * @example
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Style the points.
 *   strokeWeight(5);
 *
 *   // Top left.
 *   let pos = createVector(25, 25);
 *   point(pos);
 *
 *   // Top right.
 *   // Add numbers.
 *   pos.add(50, 0);
 *   point(pos);
 *
 *   // Bottom right.
 *   // Add a p5.Vector.
 *   let p2 = createVector(0, 50);
 *   pos.add(p2);
 *   point(pos);
 *
 *   // Bottom left.
 *   // Add an array.
 *   let arr = [-50, 0];
 *   pos.add(arr);
 *   point(pos);
 *
 *   describe('Four black dots arranged in a square on a gray background.');
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Top left.
 *   let p1 = createVector(25, 25);
 *
 *   // Center.
 *   let p2 = createVector(50, 50);
 *
 *   // Bottom right.
 *   // Add p1 and p2.
 *   let p3 = p5.Vector.add(p1, p2);
 *
 *   // Draw the points.
 *   strokeWeight(5);
 *   point(p1);
 *   point(p2);
 *   point(p3);
 *
 *   describe('Three black dots in a diagonal line from top left to bottom right.');
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   describe('Three arrows drawn on a gray square. A red arrow extends from the top left corner to the center. A blue arrow extends from the tip of the red arrow. A purple arrow extends from the origin to the tip of the blue arrow.');
 * }
 *
 * function draw() {
 *   background(200);
 *
 *   let origin = createVector(0, 0);
 *
 *   // Draw the red arrow.
 *   let v1 = createVector(50, 50);
 *   drawArrow(origin, v1, 'red');
 *
 *   // Draw the blue arrow.
 *   let v2 = createVector(-30, 20);
 *   drawArrow(v1, v2, 'blue');
 *
 *   // Purple arrow.
 *   let v3 = p5.Vector.add(v1, v2);
 *   drawArrow(origin, v3, 'purple');
 * }
 *
 * // Draws an arrow between two vectors.
 * function drawArrow(base, vec, myColor) {
 *   push();
 *   stroke(myColor);
 *   strokeWeight(3);
 *   fill(myColor);
 *   translate(base.x, base.y);
 *   line(0, 0, vec.x, vec.y);
 *   rotate(vec.heading());
 *   let arrowSize = 7;
 *   translate(vec.mag() - arrowSize, 0);
 *   triangle(0, arrowSize / 2, 0, -arrowSize / 2, arrowSize, 0);
 *   pop();
 * }
 * </code>
 * </div>
 */
  /**
 * @method add
 * @param  {p5.Vector|Number[]} value The vector to add
 * @chainable
 */
  add (x, y, z) {
    if (x instanceof p5.Vector) {
      this.x += x.x || 0;
      this.y += x.y || 0;
      this.z += x.z || 0;
      return this;
    }
    if (Array.isArray(x)) {
      this.x += x[0] || 0;
      this.y += x[1] || 0;
      this.z += x[2] || 0;
      return this;
    }
    this.x += x || 0;
    this.y += y || 0;
    this.z += z || 0;
    return this;
  }

  /**
   * @private
   * @chainable
   */
  calculateRemainder2D (xComponent, yComponent) {
    if (xComponent !== 0) {
      this.x = this.x % xComponent;
    }
    if (yComponent !== 0) {
      this.y = this.y % yComponent;
    }
    return this;
  }

  /**
   * @private
   * @chainable
   */
  calculateRemainder3D (xComponent, yComponent, zComponent) {
    if (xComponent !== 0) {
      this.x = this.x % xComponent;
    }
    if (yComponent !== 0) {
      this.y = this.y % yComponent;
    }
    if (zComponent !== 0) {
      this.z = this.z % zComponent;
    }
    return this;
  }

  /**
   * Performs modulo (remainder) division with a vector's `x`, `y`, and `z`
   * components.
   *
   * `rem()` can use separate numbers, as in `v.rem(1, 2, 3)`,
   * another <a href="#/p5.Vector">p5.Vector</a> object, as in `v.rem(v2)`, or
   * an array of numbers, as in `v.rem([1, 2, 3])`.
   *
   * If only one value is provided, as in `v.rem(2)`, then all the components
   * will be set to their values modulo 2. If two values are provided, as in
   * `v.rem(2, 3)`, then `v.z` won't change. Calling `rem()` with no
   * arguments, as in `v.rem()`, has no effect.
   *
   * The static version of `rem()`, as in `p5.Vector.rem(v2, v1)`, returns a
   * new <a href="#/p5.Vector">p5.Vector</a> object and doesn't change the
   * originals.
   *
   * @method rem
   * @param {Number} x x component of divisor vector.
   * @param {Number} y y component of divisor vector.
   * @param {Number} z z component of divisor vector.
   * @chainable
   *
   * @example
   * <div class='norender'>
   * <code>
   * function setup() {
   *   // Create a p5.Vector object.
   *   let v = createVector(3, 4, 5);
   *
   *   // Divide numbers.
   *   v.rem(2);
   *
   *   // Prints 'p5.Vector Object : [1, 0, 1]'.
   *   print(v.toString());
   * }
   * </code>
   * </div>
   *
   * <div class='norender'>
   * <code>
   * function setup() {
   *   // Create a p5.Vector object.
   *   let v = createVector(3, 4, 5);
   *
   *   // Divide numbers.
   *   v.rem(2, 3);
   *
   *   // Prints 'p5.Vector Object : [1, 1, 5]'.
   *   print(v.toString());
   * }
   * </code>
   * </div>
   *
   * <div class='norender'>
   * <code>
   * function setup() {
   *   // Create a p5.Vector object.
   *   let v = createVector(3, 4, 5);
   *
   *   // Divide numbers.
   *   v.rem(2, 3, 4);
   *
   *   // Prints 'p5.Vector Object : [1, 1, 1]'.
   *   print(v.toString());
   * }
   * </code>
   * </div>
   *
   * <div class='norender'>
   * <code>
   * function setup() {
   *   // Create p5.Vector objects.
   *   let v1 = createVector(3, 4, 5);
   *   let v2 = createVector(2, 3, 4);
   *
   *   // Divide a p5.Vector.
   *   v1.rem(v2);
   *
   *   // Prints 'p5.Vector Object : [1, 1, 1]'.
   *   print(v1.toString());
   * }
   * </code>
   * </div>
   *
   * <div class='norender'>
   * <code>
   * function setup() {
   *   // Create a p5.Vector object.
   *   let v = createVector(3, 4, 5);
   *
   *   // Divide an array.
   *   let arr = [2, 3, 4];
   *   v.rem(arr);
   *
   *   // Prints 'p5.Vector Object : [1, 1, 1]'.
   *   print(v.toString());
   * }
   * </code>
   * </div>
   *
   * <div class="norender">
   * <code>
   * function setup() {
   *   // Create p5.Vector objects.
   *   let v1 = createVector(3, 4, 5);
   *   let v2 = createVector(2, 3, 4);
   *
   *   // Divide without modifying the original vectors.
   *   let v3 = p5.Vector.rem(v1, v2);
   *
   *   // Prints 'p5.Vector Object : [1, 1, 1]'.
   *   print(v3.toString());
   * }
   * </code>
   * </div>
   */
  /**
   * @method rem
   * @param {p5.Vector | Number[]}  value  divisor vector.
   * @chainable
   */
  rem (...args) {
    let [x, y, z] = args;
    if (x instanceof p5.Vector) {
      if ([x.x,x.y,x.z].every(Number.isFinite)) {
        const xComponent = parseFloat(x.x);
        const yComponent = parseFloat(x.y);
        const zComponent = parseFloat(x.z);
        return this.calculateRemainder3D(
          xComponent,
          yComponent,
          zComponent
        );
      }
    } else if (Array.isArray(x)) {
      if (x.every(Number.isFinite)) {
        if (x.length === 2) {
          return this.calculateRemainder2D(x[0], x[1]);
        }
        if (x.length === 3) {
          return this.calculateRemainder3D(x[0], x[1], x[2]);
        }
      }
    } else if (args.length === 1) {
      if (Number.isFinite(x) && x !== 0) {
        this.x = this.x % x;
        this.y = this.y % x;
        this.z = this.z % x;
        return this;
      }
    } else if (args.length === 2) {
      if (args.every(Number.isFinite)) {
        return this.calculateRemainder2D(
          x,
          y
        );
      }
    } else if (args.length === 3) {
      if (args.every(Number.isFinite)) {
        return this.calculateRemainder3D(
          x,
          y,
          z
        );
      }
    }
  }

  /**
 * Subtracts from a vector's `x`, `y`, and `z` components.
 *
 * `sub()` can use separate numbers, as in `v.sub(1, 2, 3)`, another
 * <a href="#/p5.Vector">p5.Vector</a> object, as in `v.sub(v2)`, or an array
 * of numbers, as in `v.sub([1, 2, 3])`.
 *
 * If a value isn't provided for a component, it won't change. For
 * example, `v.sub(4, 5)` subtracts 4 from `v.x`, 5 from `v.y`, and 0 from `v.z`.
 * Calling `sub()` with no arguments, as in `v.sub()`, has no effect.
 *
 * The static version of `sub()`, as in `p5.Vector.sub(v2, v1)`, returns a new
 * <a href="#/p5.Vector">p5.Vector</a> object and doesn't change the
 * originals.
 *
 * @method sub
 * @param  {Number} x   x component of the vector to subtract.
 * @param  {Number} [y] y component of the vector to subtract.
 * @param  {Number} [z] z component of the vector to subtract.
 * @chainable
 *
 * @example
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Style the points.
 *   strokeWeight(5);
 *
 *   // Bottom right.
 *   let pos = createVector(75, 75);
 *   point(pos);
 *
 *   // Top right.
 *   // Subtract numbers.
 *   pos.sub(0, 50);
 *   point(pos);
 *
 *   // Top left.
 *   // Subtract a p5.Vector.
 *   let p2 = createVector(50, 0);
 *   pos.sub(p2);
 *   point(pos);
 *
 *   // Bottom left.
 *   // Subtract an array.
 *   let arr = [0, -50];
 *   pos.sub(arr);
 *   point(pos);
 *
 *   describe('Four black dots arranged in a square on a gray background.');
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Create p5.Vector objects.
 *   let p1 = createVector(75, 75);
 *   let p2 = createVector(50, 50);
 *
 *   // Subtract with modifying the original vectors.
 *   let p3 = p5.Vector.sub(p1, p2);
 *
 *   // Draw the points.
 *   strokeWeight(5);
 *   point(p1);
 *   point(p2);
 *   point(p3);
 *
 *   describe('Three black dots in a diagonal line from top left to bottom right.');
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   describe('Three arrows drawn on a gray square. A red and a blue arrow extend from the top left. A purple arrow extends from the tip of the red arrow to the tip of the blue arrow.');
 * }
 *
 * function draw() {
 *   background(200);
 *
 *   let origin = createVector(0, 0);
 *
 *   // Draw the red arrow.
 *   let v1 = createVector(50, 50);
 *   drawArrow(origin, v1, 'red');
 *
 *   // Draw the blue arrow.
 *   let v2 = createVector(20, 70);
 *   drawArrow(origin, v2, 'blue');
 *
 *   // Purple arrow.
 *   let v3 = p5.Vector.sub(v2, v1);
 *   drawArrow(v1, v3, 'purple');
 * }
 *
 * // Draws an arrow between two vectors.
 * function drawArrow(base, vec, myColor) {
 *   push();
 *   stroke(myColor);
 *   strokeWeight(3);
 *   fill(myColor);
 *   translate(base.x, base.y);
 *   line(0, 0, vec.x, vec.y);
 *   rotate(vec.heading());
 *   let arrowSize = 7;
 *   translate(vec.mag() - arrowSize, 0);
 *   triangle(0, arrowSize / 2, 0, -arrowSize / 2, arrowSize, 0);
 *   pop();
 * }
 * </code>
 * </div>
 */
  /**
 * @method sub
 * @param  {p5.Vector|Number[]} value the vector to subtract
 * @chainable
 */
  sub(x, y, z) {
    if (x instanceof p5.Vector) {
      this.x -= x.x || 0;
      this.y -= x.y || 0;
      this.z -= x.z || 0;
      return this;
    }
    if (Array.isArray(x)) {
      this.x -= x[0] || 0;
      this.y -= x[1] || 0;
      this.z -= x[2] || 0;
      return this;
    }
    this.x -= x || 0;
    this.y -= y || 0;
    this.z -= z || 0;
    return this;
  }

  /**
 * Multiplies a vector's `x`, `y`, and `z` components.
 *
 * `mult()` can use separate numbers, as in `v.mult(1, 2, 3)`, another
 * <a href="#/p5.Vector">p5.Vector</a> object, as in `v.mult(v2)`, or an array
 * of numbers, as in `v.mult([1, 2, 3])`.
 *
 * If only one value is provided, as in `v.mult(2)`, then all the components
 * will be multiplied by 2. If a value isn't provided for a component, it
 * won't change. For example, `v.mult(4, 5)` multiplies `v.x` by, `v.y` by 5,
 * and `v.z` by 1. Calling `mult()` with no arguments, as in `v.mult()`, has
 * no effect.
 *
 * The static version of `mult()`, as in `p5.Vector.mult(v, 2)`, returns a new
 * <a href="#/p5.Vector">p5.Vector</a> object and doesn't change the
 * originals.
 *
 * @method mult
 * @param  {Number} n The number to multiply with the vector
 * @chainable
 * @example
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Style the points.
 *   strokeWeight(5);
 *
 *   // Top-left.
 *   let p = createVector(25, 25);
 *   point(p);
 *
 *   // Center.
 *   // Multiply all components by 2.
 *   p.mult(2);
 *   point(p);
 *
 *   describe('Two black dots drawn on a gray square. One dot is in the top left corner and the other is in the center.');
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   strokeWeight(5);
 *
 *   // Top-left.
 *   let p = createVector(25, 25);
 *   point(p);
 *
 *   // Bottom-right.
 *   // Multiply p.x * 2 and p.y * 3
 *   p.mult(2, 3);
 *   point(p);
 *
 *   describe('Two black dots drawn on a gray square. One dot is in the top left corner and the other is in the bottom center.');
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Style the points.
 *   strokeWeight(5);
 *
 *   // Top-left.
 *   let p = createVector(25, 25);
 *   point(p);
 *
 *   // Bottom-right.
 *   // Multiply p.x * 2 and p.y * 3
 *   let arr = [2, 3];
 *   p.mult(arr);
 *   point(p);
 *
 *   describe('Two black dots drawn on a gray square. One dot is in the top left corner and the other is in the bottom center.');
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Style the points.
 *   strokeWeight(5);
 *
 *   // Top-left.
 *   let p = createVector(25, 25);
 *   point(p);
 *
 *   // Bottom-right.
 *   // Multiply p.x * p2.x and p.y * p2.y
 *   let p2 = createVector(2, 3);
 *   p.mult(p2);
 *   point(p);
 *
 *   describe('Two black dots drawn on a gray square. One dot is in the top left corner and the other is in the bottom center.');
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Style the points.
 *   strokeWeight(5);
 *
 *   // Top-left.
 *   let p = createVector(25, 25);
 *   point(p);
 *
 *   // Bottom-right.
 *   // Create a new p5.Vector with
 *   // p3.x = p.x * p2.x
 *   // p3.y = p.y * p2.y
 *   let p2 = createVector(2, 3);
 *   let p3 = p5.Vector.mult(p, p2);
 *   point(p3);
 *
 *   describe('Two black dots drawn on a gray square. One dot is in the top left corner and the other is in the bottom center.');
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   describe('Two arrows extending from the top left corner. The blue arrow is twice the length of the red arrow.');
 * }
 * function draw() {
 *   background(200);
 *
 *   let origin = createVector(0, 0);
 *
 *   // Draw the red arrow.
 *   let v1 = createVector(25, 25);
 *   drawArrow(origin, v1, 'red');
 *
 *   // Draw the blue arrow.
 *   let v2 = p5.Vector.mult(v1, 2);
 *   drawArrow(origin, v2, 'blue');
 * }
 *
 * // Draws an arrow between two vectors.
 * function drawArrow(base, vec, myColor) {
 *   push();
 *   stroke(myColor);
 *   strokeWeight(3);
 *   fill(myColor);
 *   translate(base.x, base.y);
 *   line(0, 0, vec.x, vec.y);
 *   rotate(vec.heading());
 *   let arrowSize = 7;
 *   translate(vec.mag() - arrowSize, 0);
 *   triangle(0, arrowSize / 2, 0, -arrowSize / 2, arrowSize, 0);
 *   pop();
 * }
 * </code>
 * </div>
 */

  /**
 * @method mult
 * @param  {Number} x number to multiply with the x component of the vector.
 * @param  {Number} y number to multiply with the y component of the vector.
 * @param  {Number} [z] number to multiply with the z component of the vector.
 * @chainable
 */

  /**
 * @method mult
 * @param  {Number[]} arr array to multiply with the components of the vector.
 * @chainable
 */

  /**
 * @method mult
 * @param  {p5.Vector} v vector to multiply with the components of the original vector.
 * @chainable
 */

  mult(...args) {
    let [x, y, z] = args;
    if (x instanceof p5.Vector) {
    // new p5.Vector will check that values are valid upon construction but it's possible
    // that someone could change the value of a component after creation, which is why we still
    // perform this check
      if (
        Number.isFinite(x.x) &&
      Number.isFinite(x.y) &&
      Number.isFinite(x.z) &&
      typeof x.x === 'number' &&
      typeof x.y === 'number' &&
      typeof x.z === 'number'
      ) {
        this.x *= x.x;
        this.y *= x.y;
        this.z *= x.z;
      } else {
        console.warn(
          'p5.Vector.prototype.mult:',
          'x contains components that are either undefined or not finite numbers'
        );
      }
      return this;
    }
    if (Array.isArray(x)) {
      if (
        x.every(element => Number.isFinite(element)) &&
      x.every(element => typeof element === 'number')
      ) {
        if (x.length === 1) {
          this.x *= x[0];
          this.y *= x[0];
          this.z *= x[0];
        } else if (x.length === 2) {
          this.x *= x[0];
          this.y *= x[1];
        } else if (x.length === 3) {
          this.x *= x[0];
          this.y *= x[1];
          this.z *= x[2];
        }
      } else {
        console.warn(
          'p5.Vector.prototype.mult:',
          'x contains elements that are either undefined or not finite numbers'
        );
      }
      return this;
    }

    const vectorComponents = args;
    if (
      vectorComponents.every(element => Number.isFinite(element)) &&
    vectorComponents.every(element => typeof element === 'number')
    ) {
      if (args.length === 1) {
        this.x *= x;
        this.y *= x;
        this.z *= x;
      }
      if (args.length === 2) {
        this.x *= x;
        this.y *= y;
      }
      if (args.length === 3) {
        this.x *= x;
        this.y *= y;
        this.z *= z;
      }
    } else {
      console.warn(
        'p5.Vector.prototype.mult:',
        'x, y, or z arguments are either undefined or not a finite number'
      );
    }

    return this;
  }

  /**
 * Divides a vector's `x`, `y`, and `z` components.
 *
 * `div()` can use separate numbers, as in `v.div(1, 2, 3)`, another
 * <a href="#/p5.Vector">p5.Vector</a> object, as in `v.div(v2)`, or an array
 * of numbers, as in `v.div([1, 2, 3])`.
 *
 * If only one value is provided, as in `v.div(2)`, then all the components
 * will be divided by 2. If a value isn't provided for a component, it
 * won't change. For example, `v.div(4, 5)` divides `v.x` by, `v.y` by 5,
 * and `v.z` by 1. Calling `div()` with no arguments, as in `v.div()`, has
 * no effect.
 *
 * The static version of `div()`, as in `p5.Vector.div(v, 2)`, returns a new
 * <a href="#/p5.Vector">p5.Vector</a> object and doesn't change the
 * originals.
 *
 * @method div
 * @param  {number}    n The number to divide the vector by
 * @chainable
 * @example
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Style the points.
 *   strokeWeight(5);
 *
 *   // Center.
 *   let p = createVector(50, 50);
 *   point(p);
 *
 *   // Top-left.
 *   // Divide p.x / 2 and p.y / 2
 *   p.div(2);
 *   point(p);
 *
 *   describe('Two black dots drawn on a gray square. One dot is in the top left corner and the other is in the center.');
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Style the points.
 *   strokeWeight(5);
 *
 *   // Bottom-right.
 *   let p = createVector(50, 75);
 *   point(p);
 *
 *   // Top-left.
 *   // Divide p.x / 2 and p.y / 3
 *   p.div(2, 3);
 *   point(p);
 *
 *   describe('Two black dots drawn on a gray square. One dot is in the top left corner and the other is in the bottom center.');
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Style the points.
 *   strokeWeight(5);
 *
 *   // Bottom-right.
 *   let p = createVector(50, 75);
 *   point(p);
 *
 *   // Top-left.
 *   // Divide p.x / 2 and p.y / 3
 *   let arr = [2, 3];
 *   p.div(arr);
 *   point(p);
 *
 *   describe('Two black dots drawn on a gray square. One dot is in the top left corner and the other is in the bottom center.');
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Style the points.
 *   strokeWeight(5);
 *
 *   // Bottom-right.
 *   let p = createVector(50, 75);
 *   point(p);
 *
 *   // Top-left.
 *   // Divide p.x / 2 and p.y / 3
 *   let p2 = createVector(2, 3);
 *   p.div(p2);
 *   point(p);
 *
 *   describe('Two black dots drawn on a gray square. One dot is in the top left corner and the other is in the bottom center.');
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Style the points.
 *   strokeWeight(5);
 *
 *   // Bottom-right.
 *   let p = createVector(50, 75);
 *   point(p);
 *
 *   // Top-left.
 *   // Create a new p5.Vector with
 *   // p3.x = p.x / p2.x
 *   // p3.y = p.y / p2.y
 *   let p2 = createVector(2, 3);
 *   let p3 = p5.Vector.div(p, p2);
 *   point(p3);
 *
 *   describe('Two black dots drawn on a gray square. One dot is in the top left corner and the other is in the bottom center.');
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function draw() {
 *   background(200);
 *
 *   let origin = createVector(0, 0);
 *
 *   // Draw the red arrow.
 *   let v1 = createVector(50, 50);
 *   drawArrow(origin, v1, 'red');
 *
 *   // Draw the blue arrow.
 *   let v2 = p5.Vector.div(v1, 2);
 *   drawArrow(origin, v2, 'blue');
 *
 *   describe('Two arrows extending from the top left corner. The blue arrow is half the length of the red arrow.');
 * }
 *
 * // Draws an arrow between two vectors.
 * function drawArrow(base, vec, myColor) {
 *   push();
 *   stroke(myColor);
 *   strokeWeight(3);
 *   fill(myColor);
 *   translate(base.x, base.y);
 *   line(0, 0, vec.x, vec.y);
 *   rotate(vec.heading());
 *   let arrowSize = 7;
 *   translate(vec.mag() - arrowSize, 0);
 *   triangle(0, arrowSize / 2, 0, -arrowSize / 2, arrowSize, 0);
 *   pop();
 * }
 * </code>
 * </div>
 */

  /**
 * @method div
 * @param  {Number} x number to divide with the x component of the vector.
 * @param  {Number} y number to divide with the y component of the vector.
 * @param  {Number} [z] number to divide with the z component of the vector.
 * @chainable
 */

  /**
 * @method div
 * @param  {Number[]} arr array to divide the components of the vector by.
 * @chainable
 */

  /**
 * @method div
 * @param  {p5.Vector} v vector to divide the components of the original vector by.
 * @chainable
 */
  div(...args) {
    let [x, y, z] = args;
    if (x instanceof p5.Vector) {
    // new p5.Vector will check that values are valid upon construction but it's possible
    // that someone could change the value of a component after creation, which is why we still
    // perform this check
      if (
        Number.isFinite(x.x) &&
      Number.isFinite(x.y) &&
      Number.isFinite(x.z) &&
      typeof x.x === 'number' &&
      typeof x.y === 'number' &&
      typeof x.z === 'number'
      ) {
        const isLikely2D = x.z === 0 && this.z === 0;
        if (x.x === 0 || x.y === 0 || (!isLikely2D && x.z === 0)) {
          console.warn('p5.Vector.prototype.div:', 'divide by 0');
          return this;
        }
        this.x /= x.x;
        this.y /= x.y;
        if (!isLikely2D) {
          this.z /= x.z;
        }
      } else {
        console.warn(
          'p5.Vector.prototype.div:',
          'x contains components that are either undefined or not finite numbers'
        );
      }
      return this;
    }
    if (Array.isArray(x)) {
      if (
        x.every(Number.isFinite) &&
      x.every(element => typeof element === 'number')
      ) {
        if (x.some(element => element === 0)) {
          console.warn('p5.Vector.prototype.div:', 'divide by 0');
          return this;
        }

        if (x.length === 1) {
          this.x /= x[0];
          this.y /= x[0];
          this.z /= x[0];
        } else if (x.length === 2) {
          this.x /= x[0];
          this.y /= x[1];
        } else if (x.length === 3) {
          this.x /= x[0];
          this.y /= x[1];
          this.z /= x[2];
        }
      } else {
        console.warn(
          'p5.Vector.prototype.div:',
          'x contains components that are either undefined or not finite numbers'
        );
      }

      return this;
    }

    if (
      args.every(Number.isFinite) &&
    args.every(element => typeof element === 'number')
    ) {
      if (args.some(element => element === 0)) {
        console.warn('p5.Vector.prototype.div:', 'divide by 0');
        return this;
      }

      if (args.length === 1) {
        this.x /= x;
        this.y /= x;
        this.z /= x;
      }
      if (args.length === 2) {
        this.x /= x;
        this.y /= y;
      }
      if (args.length === 3) {
        this.x /= x;
        this.y /= y;
        this.z /= z;
      }
    } else {
      console.warn(
        'p5.Vector.prototype.div:',
        'x, y, or z arguments are either undefined or not a finite number'
      );
    }

    return this;
  }
  /**
 * Calculates the magnitude (length) of the vector.
 *
 * Use <a href="#/p5/mag">mag()</a> to calculate the magnitude of a 2D vector
 * using components as in `mag(x, y)`.
 *
 * @method mag
 * @return {Number} magnitude of the vector.
 *
 * @example
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Create a p5.Vector object.
 *   let p = createVector(30, 40);
 *
 *   // Draw a line from the origin.
 *   line(0, 0, p.x, p.y);
 *
 *   // Style the text.
 *   textAlign(CENTER);
 *   textSize(16);
 *
 *   // Display the vector's magnitude.
 *   let m = p.mag();
 *   text(m, p.x, p.y);
 *
 *   describe('A diagonal black line extends from the top left corner of a gray square. The number 50 is written at the end of the line.');
 * }
 * </code>
 * </div>
 */
  mag() {
    return Math.sqrt(this.magSq());
  }

  /**
 * Calculates the magnitude (length) of the vector squared.
 *
 * @method magSq
 * @return {number} squared magnitude of the vector.
 * @example
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Create a p5.Vector object.
 *   let p = createVector(30, 40);
 *
 *   // Draw a line from the origin.
 *   line(0, 0, p.x, p.y);
 *
 *   // Style the text.
 *   textAlign(CENTER);
 *   textSize(16);
 *
 *   // Display the vector's magnitude squared.
 *   let m = p.magSq();
 *   text(m, p.x, p.y);
 *
 *   describe('A diagonal black line extends from the top left corner of a gray square. The number 2500 is written at the end of the line.');
 * }
 * </code>
 * </div>
 */
  magSq() {
    const x = this.x;
    const y = this.y;
    const z = this.z;
    return x * x + y * y + z * z;
  }

  /**
 * Calculates the dot product of two vectors.
 *
 * The dot product is a number that describes the overlap between two vectors.
 * Visually, the dot product can be thought of as the "shadow" one vector
 * casts on another. The dot product's magnitude is largest when two vectors
 * point in the same or opposite directions. Its magnitude is 0 when two
 * vectors form a right angle.
 *
 * The version of `dot()` with one parameter interprets it as another
 * <a href="#/p5.Vector">p5.Vector</a> object.
 *
 * The version of `dot()` with multiple parameters interprets them as the
 * `x`, `y`, and `z` components of another vector.
 *
 * The static version of `dot()`, as in `p5.Vector.dot(v1, v2)`, is the same
 * as calling `v1.dot(v2)`.
 *
 * @method dot
 * @param  {Number} x   x component of the vector.
 * @param  {Number} [y] y component of the vector.
 * @param  {Number} [z] z component of the vector.
 * @return {Number}     dot product.
 *
 * @example
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create p5.Vector objects.
 *   let v1 = createVector(3, 4);
 *   let v2 = createVector(3, 0);
 *
 *   // Calculate the dot product.
 *   let dp = v1.dot(v2);
 *
 *   // Prints "9" to the console.
 *   print(dp);
 * }
 * </code>
 * </div>
 *
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create p5.Vector objects.
 *   let v1 = createVector(1, 0);
 *   let v2 = createVector(0, 1);
 *
 *   // Calculate the dot product.
 *   let dp = p5.Vector.dot(v1, v2);
 *
 *   // Prints "0" to the console.
 *   print(dp);
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   describe('Two arrows drawn on a gray square. A black arrow points to the right and a red arrow follows the mouse. The text "v1 • v2 = something" changes as the mouse moves.');
 * }
 *
 * function draw() {
 *   background(200);
 *
 *   // Center.
 *   let v0 = createVector(50, 50);
 *
 *   // Draw the black arrow.
 *   let v1 = createVector(30, 0);
 *   drawArrow(v0, v1, 'black');
 *
 *   // Draw the red arrow.
 *   let v2 = createVector(mouseX - 50, mouseY - 50);
 *   drawArrow(v0, v2, 'red');
 *
 *   // Display the dot product.
 *   let dp = v2.dot(v1);
 *   text(`v2 • v1 = ${dp}`, 10, 20);
 * }
 *
 * // Draws an arrow between two vectors.
 * function drawArrow(base, vec, myColor) {
 *   push();
 *   stroke(myColor);
 *   strokeWeight(3);
 *   fill(myColor);
 *   translate(base.x, base.y);
 *   line(0, 0, vec.x, vec.y);
 *   rotate(vec.heading());
 *   let arrowSize = 7;
 *   translate(vec.mag() - arrowSize, 0);
 *   triangle(0, arrowSize / 2, 0, -arrowSize / 2, arrowSize, 0);
 *   pop();
 * }
 * </code>
 * </div>
 */
  /**
 * @method dot
 * @param  {p5.Vector} v <a href="#/p5.Vector">p5.Vector</a> to be dotted.
 * @return {Number}
 */
  dot(x, y, z) {
    if (x instanceof p5.Vector) {
      return this.dot(x.x, x.y, x.z);
    }
    return this.x * (x || 0) + this.y * (y || 0) + this.z * (z || 0);
  }

  /**
 * Calculates the cross product of two vectors.
 *
 * The cross product is a vector that points straight out of the plane created
 * by two vectors. The cross product's magnitude is the area of the parallelogram
 * formed by the original two vectors.
 *
 * The static version of `cross()`, as in `p5.Vector.cross(v1, v2)`, is the same
 * as calling `v1.cross(v2)`.
 *
 * @method cross
 * @param  {p5.Vector} v <a href="#/p5.Vector">p5.Vector</a> to be crossed.
 * @return {p5.Vector}   cross product as a <a href="#/p5.Vector">p5.Vector</a>.
 *
 * @example
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create p5.Vector objects.
 *   let v1 = createVector(1, 0);
 *   let v2 = createVector(3, 4);
 *
 *   // Calculate the cross product.
 *   let cp = v1.cross(v2);
 *
 *   // Prints "p5.Vector Object : [0, 0, 4]" to the console.
 *   print(cp.toString());
 * }
 * </code>
 * </div>
 *
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create p5.Vector objects.
 *   let v1 = createVector(1, 0);
 *   let v2 = createVector(3, 4);
 *
 *   // Calculate the cross product.
 *   let cp = p5.Vector.cross(v1, v2);
 *
 *   // Prints "p5.Vector Object : [0, 0, 4]" to the console.
 *   print(cp.toString());
 * }
 * </code>
 * </div>
 */
  cross(v) {
    const x = this.y * v.z - this.z * v.y;
    const y = this.z * v.x - this.x * v.z;
    const z = this.x * v.y - this.y * v.x;
    if (this.isPInst) {
      return new p5.Vector(this._fromRadians, this._toRadians, x, y, z);
    } else {
      return new p5.Vector(x, y, z);
    }
  }

  /**
 * Calculates the distance between two points represented by vectors.
 *
 * A point's coordinates can be represented by the components of a vector
 * that extends from the origin to the point.
 *
 * The static version of `dist()`, as in `p5.Vector.dist(v1, v2)`, is the same
 * as calling `v1.dist(v2)`.
 *
 * Use <a href="#/p5/dist">dist()</a> to calculate the distance between points
 * using coordinates as in `dist(x1, y1, x2, y2)`.
 *
 * @method dist
 * @param  {p5.Vector} v x, y, and z coordinates of a <a href="#/p5.Vector">p5.Vector</a>.
 * @return {Number}      distance.
 *
 * @example
 * <div class="norender">
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Create p5.Vector objects.
 *   let v1 = createVector(1, 0);
 *   let v2 = createVector(0, 1);
 *
 *   // Calculate the distance between them.
 *   let d = v1.dist(v2);
 *
 *   // Prints "1.414..." to the console.
 *   print(d);
 * }
 * </code>
 * </div>
 *
 * <div class="norender">
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Create p5.Vector objects.
 *   let v1 = createVector(1, 0);
 *   let v2 = createVector(0, 1);
 *
 *   // Calculate the distance between them.
 *   let d = p5.Vector.dist(v1, v2);
 *
 *   // Prints "1.414..." to the console.
 *   print(d);
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   describe('Three arrows drawn on a gray square. A red and a blue arrow extend from the top left. A purple arrow extends from the tip of the red arrow to the tip of the blue arrow. The number 36 is written in black near the purple arrow.');
 * }
 *
 * function draw() {
 *   background(200);
 *
 *   let origin = createVector(0, 0);
 *
 *   // Draw the red arrow.
 *   let v1 = createVector(50, 50);
 *   drawArrow(origin, v1, 'red');
 *
 *   // Draw the blue arrow.
 *   let v2 = createVector(20, 70);
 *   drawArrow(origin, v2, 'blue');
 *
 *   // Purple arrow.
 *   let v3 = p5.Vector.sub(v2, v1);
 *   drawArrow(v1, v3, 'purple');
 *
 *   // Style the text.
 *   textAlign(CENTER);
 *
 *   // Display the magnitude.
 *   let m = floor(v3.mag());
 *   text(m, 50, 75);
 * }
 *
 * // Draws an arrow between two vectors.
 * function drawArrow(base, vec, myColor) {
 *   push();
 *   stroke(myColor);
 *   strokeWeight(3);
 *   fill(myColor);
 *   translate(base.x, base.y);
 *   line(0, 0, vec.x, vec.y);
 *   rotate(vec.heading());
 *   let arrowSize = 7;
 *   translate(vec.mag() - arrowSize, 0);
 *   triangle(0, arrowSize / 2, 0, -arrowSize / 2, arrowSize, 0);
 *   pop();
 * }
 * </code>
 * </div>
 */
  dist(v) {
    return v
      .copy()
      .sub(this)
      .mag();
  }

  /**
 * Scales the components of a <a href="#/p5.Vector">p5.Vector</a> object so
 * that its magnitude is 1.
 *
 * The static version of `normalize()`,  as in `p5.Vector.normalize(v)`,
 * returns a new <a href="#/p5.Vector">p5.Vector</a> object and doesn't change
 * the original.
 *
 * @method normalize
 * @return {p5.Vector} normalized <a href="#/p5.Vector">p5.Vector</a>.
 *
 * @example
 * <div class="norender">
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Create a p5.Vector.
 *   let v = createVector(10, 20, 2);
 *
 *   // Normalize.
 *   v.normalize();
 *
 *   // Prints "p5.Vector Object : [0.445..., 0.890..., 0.089...]" to the console.
 *   print(v.toString());
 * }
 * </code>
 * </div>
 *
 * <div class="norender">
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   background(200);
 *
 *   // Create a p5.Vector.
 *   let v0 = createVector(10, 20, 2);
 *
 *   // Create a normalized copy.
 *   let v1 = p5.Vector.normalize(v0);
 *
 *   // Prints "p5.Vector Object : [10, 20, 2]" to the console.
 *   print(v0.toString());
 *   // Prints "p5.Vector Object : [0.445..., 0.890..., 0.089...]" to the console.
 *   print(v1.toString());
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   describe("A red and blue arrow extend from the center of a circle. Both arrows follow the mouse, but the blue arrow's length is fixed to the circle's radius.");
 * }
 *
 * function draw() {
 *   background(240);
 *
 *   // Vector to the center.
 *   let v0 = createVector(50, 50);
 *
 *   // Vector from the center to the mouse.
 *   let v1 = createVector(mouseX - 50, mouseY - 50);
 *
 *   // Circle's radius.
 *   let r = 25;
 *
 *   // Draw the red arrow.
 *   drawArrow(v0, v1, 'red');
 *
 *   // Draw the blue arrow.
 *   v1.normalize();
 *   drawArrow(v0, v1.mult(r), 'blue');
 *
 *   // Draw the circle.
 *   noFill();
 *   circle(50, 50, r * 2);
 * }
 *
 * // Draws an arrow between two vectors.
 * function drawArrow(base, vec, myColor) {
 *   push();
 *   stroke(myColor);
 *   strokeWeight(3);
 *   fill(myColor);
 *   translate(base.x, base.y);
 *   line(0, 0, vec.x, vec.y);
 *   rotate(vec.heading());
 *   let arrowSize = 7;
 *   translate(vec.mag() - arrowSize, 0);
 *   triangle(0, arrowSize / 2, 0, -arrowSize / 2, arrowSize, 0);
 *   pop();
 * }
 * </code>
 * </div>
 */
  normalize() {
    const len = this.mag();
    // here we multiply by the reciprocal instead of calling 'div()'
    // since div duplicates this zero check.
    if (len !== 0) this.mult(1 / len);
    return this;
  }

  /**
 * Limits a vector's magnitude to a maximum value.
 *
 * The static version of `limit()`, as in `p5.Vector.limit(v, 5)`, returns a
 * new <a href="#/p5.Vector">p5.Vector</a> object and doesn't change the
 * original.
 *
 * @method limit
 * @param  {Number}    max maximum magnitude for the vector.
 * @chainable
 *
 * @example
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create a p5.Vector object.
 *   let v = createVector(10, 20, 2);
 *
 *   // Limit its magnitude.
 *   v.limit(5);
 *
 *   // Prints "p5.Vector Object : [2.227..., 4.454..., 0.445...]" to the console.
 *   print(v.toString());
 * }
 * </code>
 * </div>
 *
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create a p5.Vector object.
 *   let v0 = createVector(10, 20, 2);
 *
 *   // Create a copy an limit its magintude.
 *   let v1 = p5.Vector.limit(v0, 5);
 *
 *   // Prints "p5.Vector Object : [2.227..., 4.454..., 0.445...]" to the console.
 *   print(v1.toString());
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   describe("A red and blue arrow extend from the center of a circle. Both arrows follow the mouse, but the blue arrow never crosses the circle's edge.");
 * }
 * function draw() {
 *   background(240);
 *
 *   // Vector to the center.
 *   let v0 = createVector(50, 50);
 *
 *   // Vector from the center to the mouse.
 *   let v1 = createVector(mouseX - 50, mouseY - 50);
 *
 *   // Circle's radius.
 *   let r = 25;
 *
 *   // Draw the red arrow.
 *   drawArrow(v0, v1, 'red');
 *
 *   // Draw the blue arrow.
 *   drawArrow(v0, v1.limit(r), 'blue');
 *
 *   // Draw the circle.
 *   noFill();
 *   circle(50, 50, r * 2);
 * }
 *
 * // Draws an arrow between two vectors.
 * function drawArrow(base, vec, myColor) {
 *   push();
 *   stroke(myColor);
 *   strokeWeight(3);
 *   fill(myColor);
 *   translate(base.x, base.y);
 *   line(0, 0, vec.x, vec.y);
 *   rotate(vec.heading());
 *   let arrowSize = 7;
 *   translate(vec.mag() - arrowSize, 0);
 *   triangle(0, arrowSize / 2, 0, -arrowSize / 2, arrowSize, 0);
 *   pop();
 * }
 * </code>
 * </div>
 */
  limit(max) {
    const mSq = this.magSq();
    if (mSq > max * max) {
      this.div(Math.sqrt(mSq)) //normalize it
        .mult(max);
    }
    return this;
  }

  /**
 * Sets a vector's magnitude to a given value.
 *
 * The static version of `setMag()`, as in `p5.Vector.setMag(v, 10)`, returns
 * a new <a href="#/p5.Vector">p5.Vector</a> object and doesn't change the
 * original.
 *
 * @method setMag
 * @param  {number}    len new length for this vector.
 * @chainable
 *
 * @example
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create a p5.Vector object.
 *   let v = createVector(3, 4, 0);
 *
 *   // Prints "5" to the console.
 *   print(v.mag());
 *
 *   // Set its magnitude to 10.
 *   v.setMag(10);
 *
 *   // Prints "p5.Vector Object : [6, 8, 0]" to the console.
 *   print(v.toString());
 * }
 * </code>
 * </div>
 *
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create a p5.Vector object.
 *   let v0 = createVector(3, 4, 0);
 *
 *   // Create a copy with a magnitude of 10.
 *   let v1 = p5.Vector.setMag(v0, 10);
 *
 *   // Prints "5" to the console.
 *   print(v0.mag());
 *
 *   // Prints "p5.Vector Object : [6, 8, 0]" to the console.
 *   print(v1.toString());
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   describe('Two arrows extend from the top left corner of a square toward its center. The red arrow reaches the center and the blue arrow only extends part of the way.');
 * }
 *
 * function draw() {
 *   background(240);
 *
 *   let origin = createVector(0, 0);
 *   let v = createVector(50, 50);
 *
 *   // Draw the red arrow.
 *   drawArrow(origin, v, 'red');
 *
 *   // Set v's magnitude to 30.
 *   v.setMag(30);
 *
 *   // Draw the blue arrow.
 *   drawArrow(origin, v, 'blue');
 * }
 *
 * // Draws an arrow between two vectors.
 * function drawArrow(base, vec, myColor) {
 *   push();
 *   stroke(myColor);
 *   strokeWeight(3);
 *   fill(myColor);
 *   translate(base.x, base.y);
 *   line(0, 0, vec.x, vec.y);
 *   rotate(vec.heading());
 *   let arrowSize = 7;
 *   translate(vec.mag() - arrowSize, 0);
 *   triangle(0, arrowSize / 2, 0, -arrowSize / 2, arrowSize, 0);
 *   pop();
 * }
 * </code>
 * </div>
 */
  setMag(n) {
    return this.normalize().mult(n);
  }

  /**
 * Calculates the angle a 2D vector makes with the positive x-axis.
 *
 * By convention, the positive x-axis has an angle of 0. Angles increase in
 * the clockwise direction.
 *
 * If the vector was created with
 * <a href="#/p5/createVector">createVector()</a>, `heading()` returns angles
 * in the units of the current <a href="#/p5/angleMode">angleMode()</a>.
 *
 * The static version of `heading()`, as in `p5.Vector.heading(v)`, works the
 * same way.
 *
 * @method heading
 * @return {Number} angle of rotation.
 *
 * @example
 * <div class = "norender">
 * <code>
 * function setup() {
 *   // Create a p5.Vector object.
 *   let v = createVector(1, 1);
 *
 *   // Prints "0.785..." to the console.
 *   print(v.heading());
 *
 *   // Use degrees.
 *   angleMode(DEGREES);
 *
 *   // Prints "45" to the console.
 *   print(v.heading());
 * }
 * </code>
 * </div>
 *
 * <div class = "norender">
 * <code>
 * function setup() {
 *   // Create a p5.Vector object.
 *   let v = createVector(1, 1);
 *
 *   // Prints "0.785..." to the console.
 *   print(p5.Vector.heading(v));
 *
 *   // Use degrees.
 *   angleMode(DEGREES);
 *
 *   // Prints "45" to the console.
 *   print(p5.Vector.heading(v));
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   describe('A black arrow extends from the top left of a square to its center. The text "Radians: 0.79" and "Degrees: 45" is written near the tip of the arrow.');
 * }
 *
 * function draw() {
 *   background(200);
 *
 *   let origin = createVector(0, 0);
 *   let v = createVector(50, 50);
 *
 *   // Draw the black arrow.
 *   drawArrow(origin, v, 'black');
 *
 *   // Use radians.
 *   angleMode(RADIANS);
 *
 *   // Display the heading in radians.
 *   let h = round(v.heading(), 2);
 *   text(`Radians: ${h}`, 20, 70);
 *
 *   // Use degrees.
 *   angleMode(DEGREES);
 *
 *   // Display the heading in degrees.
 *   h = v.heading();
 *   text(`Degrees: ${h}`, 20, 85);
 * }
 *
 * // Draws an arrow between two vectors.
 * function drawArrow(base, vec, myColor) {
 *   push();
 *   stroke(myColor);
 *   strokeWeight(3);
 *   fill(myColor);
 *   translate(base.x, base.y);
 *   line(0, 0, vec.x, vec.y);
 *   rotate(vec.heading());
 *   let arrowSize = 7;
 *   translate(vec.mag() - arrowSize, 0);
 *   triangle(0, arrowSize / 2, 0, -arrowSize / 2, arrowSize, 0);
 *   pop();
 * }
 * </code>
 * </div>
 */
  heading() {
    const h = Math.atan2(this.y, this.x);
    if (this.isPInst) return this._fromRadians(h);
    return h;
  }

  /**
 * Rotates a 2D vector to a specific angle without changing its magnitude.
 *
 * By convention, the positive x-axis has an angle of 0. Angles increase in
 * the clockwise direction.
 *
 * If the vector was created with
 * <a href="#/p5/createVector">createVector()</a>, `setHeading()` uses
 * the units of the current <a href="#/p5/angleMode">angleMode()</a>.
 *
 * @method setHeading
 * @param  {number}    angle angle of rotation.
 * @chainable
 * @example
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create a p5.Vector object.
 *   let v = createVector(0, 1);
 *
 *   // Prints "1.570..." to the console.
 *   print(v.heading());
 *
 *   // Point to the left.
 *   v.setHeading(PI);
 *
 *   // Prints "3.141..." to the console.
 *   print(v.heading());
 * }
 * </code>
 * </div>
 *
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Use degrees.
 *   angleMode(DEGREES);
 *
 *   // Create a p5.Vector object.
 *   let v = createVector(0, 1);
 *
 *   // Prints "90" to the console.
 *   print(v.heading());
 *
 *   // Point to the left.
 *   v.setHeading(180);
 *
 *   // Prints "180" to the console.
 *   print(v.heading());
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   describe('Two arrows extend from the center of a gray square. The red arrow points to the right and the blue arrow points down.');
 * }
 *
 * function draw() {
 *   background(200);
 *
 *   // Create p5.Vector objects.
 *   let v0 = createVector(50, 50);
 *   let v1 = createVector(30, 0);
 *
 *   // Draw the red arrow.
 *   drawArrow(v0, v1, 'red');
 *
 *   // Point down.
 *   v1.setHeading(HALF_PI);
 *
 *   // Draw the blue arrow.
 *   drawArrow(v0, v1, 'blue');
 * }
 *
 * // Draws an arrow between two vectors.
 * function drawArrow(base, vec, myColor) {
 *   push();
 *   stroke(myColor);
 *   strokeWeight(3);
 *   fill(myColor);
 *   translate(base.x, base.y);
 *   line(0, 0, vec.x, vec.y);
 *   rotate(vec.heading());
 *   let arrowSize = 7;
 *   translate(vec.mag() - arrowSize, 0);
 *   triangle(0, arrowSize / 2, 0, -arrowSize / 2, arrowSize, 0);
 *   pop();
 * }
 * </code>
 * </div>
 */

  setHeading(a) {
    if (this.isPInst) a = this._toRadians(a);
    let m = this.mag();
    this.x = m * Math.cos(a);
    this.y = m * Math.sin(a);
    return this;
  }

  /**
 * Rotates a 2D vector by an angle without changing its magnitude.
 *
 * By convention, the positive x-axis has an angle of 0. Angles increase in
 * the clockwise direction.
 *
 * If the vector was created with
 * <a href="#/p5/createVector">createVector()</a>, `rotate()` uses
 * the units of the current <a href="#/p5/angleMode">angleMode()</a>.
 *
 * The static version of `rotate()`, as in `p5.Vector.rotate(v, PI)`,
 * returns a new <a href="#/p5.Vector">p5.Vector</a> object and doesn't change
 * the original.
 *
 * @method rotate
 * @param  {number}    angle angle of rotation.
 * @chainable
 * @example
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create a p5.Vector object.
 *   let v = createVector(1, 0);
 *
 *   // Prints "p5.Vector Object : [1, 0, 0]" to the console.
 *   print(v.toString());
 *
 *   // Rotate a quarter turn.
 *   v.rotate(HALF_PI);
 *
 *   // Prints "p5.Vector Object : [0, 1, 0]" to the console.
 *   print(v.toString());
 * }
 * </code>
 * </div>
 *
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Use degrees.
 *   angleMode(DEGREES);
 *
 *   // Create a p5.Vector object.
 *   let v = createVector(1, 0);
 *
 *   // Prints "p5.Vector Object : [1, 0, 0]" to the console.
 *   print(v.toString());
 *
 *   // Rotate a quarter turn.
 *   v.rotate(90);
 *
 *   // Prints "p5.Vector Object : [0, 1, 0]" to the console.
 *   print(v.toString());
 * }
 * </code>
 * </div>
 *
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create a p5.Vector object.
 *   let v0 = createVector(1, 0);
 *
 *   // Create a rotated copy.
 *   let v1 = p5.Vector.rotate(v0, HALF_PI);
 *
 *   // Prints "p5.Vector Object : [1, 0, 0]" to the console.
 *   print(v0.toString());
 *   // Prints "p5.Vector Object : [0, 1, 0]" to the console.
 *   print(v1.toString());
 * }
 * </code>
 * </div>
 *
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Use degrees.
 *   angleMode(DEGREES);
 *
 *   // Create a p5.Vector object.
 *   let v0 = createVector(1, 0);
 *
 *   // Create a rotated copy.
 *   let v1 = p5.Vector.rotate(v0, 90);
 *
 *   // Prints "p5.Vector Object : [1, 0, 0]" to the console.
 *   print(v0.toString());
 *
 *   // Prints "p5.Vector Object : [0, 1, 0]" to the console.
 *   print(v1.toString());
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * let v0;
 * let v1;
 *
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   // Create p5.Vector objects.
 *   v0 = createVector(50, 50);
 *   v1 = createVector(30, 0);
 *
 *   describe('A black arrow extends from the center of a gray square. The arrow rotates clockwise.');
 * }
 *
 * function draw() {
 *   background(240);
 *
 *   // Rotate v1.
 *   v1.rotate(0.01);
 *
 *   // Draw the black arrow.
 *   drawArrow(v0, v1, 'black');
 * }
 *
 * // Draws an arrow between two vectors.
 * function drawArrow(base, vec, myColor) {
 *   push();
 *   stroke(myColor);
 *   strokeWeight(3);
 *   fill(myColor);
 *   translate(base.x, base.y);
 *   line(0, 0, vec.x, vec.y);
 *   rotate(vec.heading());
 *   let arrowSize = 7;
 *   translate(vec.mag() - arrowSize, 0);
 *   triangle(0, arrowSize / 2, 0, -arrowSize / 2, arrowSize, 0);
 *   pop();
 * }
 * </code>
 * </div>
 */
  rotate(a) {
    let newHeading = this.heading() + a;
    if (this.isPInst) newHeading = this._toRadians(newHeading);
    const mag = this.mag();
    this.x = Math.cos(newHeading) * mag;
    this.y = Math.sin(newHeading) * mag;
    return this;
  }

  /**
 * Calculates the angle between two vectors.
 *
 * The angles returned are signed, which means that
 * `v1.angleBetween(v2) === -v2.angleBetween(v1)`.
 *
 * If the vector was created with
 * <a href="#/p5/createVector">createVector()</a>, `angleBetween()` returns
 * angles in the units of the current
 * <a href="#/p5/angleMode">angleMode()</a>.
 *
 * @method angleBetween
 * @param  {p5.Vector}    value x, y, and z components of a <a href="#/p5.Vector">p5.Vector</a>.
 * @return {Number}       angle between the vectors.
 * @example
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create p5.Vector objects.
 *   let v0 = createVector(1, 0);
 *   let v1 = createVector(0, 1);
 *
 *   // Prints "1.570..." to the console.
 *   print(v0.angleBetween(v1));
 *
 *   // Prints "-1.570..." to the console.
 *   print(v1.angleBetween(v0));
 * }
 * </code>
 * </div>
 *
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Use degrees.
 *   angleMode(DEGREES);
 *   // Create p5.Vector objects.
 *   let v0 = createVector(1, 0);
 *   let v1 = createVector(0, 1);
 *
 *   // Prints "90" to the console.
 *   print(v0.angleBetween(v1));
 *
 *   // Prints "-90" to the console.
 *   print(v1.angleBetween(v0));
 * }
 * </code>
 * </div>
 *
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create p5.Vector objects.
 *   let v0 = createVector(1, 0);
 *   let v1 = createVector(0, 1);
 *
 *   // Prints "1.570..." to the console.
 *   print(p5.Vector.angleBetween(v0, v1));
 *
 *   // Prints "-1.570..." to the console.
 *   print(p5.Vector.angleBetween(v1, v0));
 * }
 * </code>
 * </div>
 *
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Use degrees.
 *   angleMode(DEGREES);
 *
 *   // Create p5.Vector objects.
 *   let v0 = createVector(1, 0);
 *   let v1 = createVector(0, 1);
 *
 *   // Prints "90" to the console.
 *   print(p5.Vector.angleBetween(v0, v1));
 *
 *   // Prints "-90" to the console.
 *   print(p5.Vector.angleBetween(v1, v0));
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   describe('Two arrows extend from the center of a gray square. A red arrow points to the right and a blue arrow points down. The text "Radians: 1.57" and "Degrees: 90" is written above the arrows.');
 * }
 * function draw() {
 *   background(200);
 *
 *   // Create p5.Vector objects.
 *   let v0 = createVector(50, 50);
 *   let v1 = createVector(30, 0);
 *   let v2 = createVector(0, 30);
 *
 *   // Draw the red arrow.
 *   drawArrow(v0, v1, 'red');
 *
 *   // Draw the blue arrow.
 *   drawArrow(v0, v2, 'blue');
 *
 *   // Use radians.
 *   angleMode(RADIANS);
 *
 *   // Display the angle in radians.
 *   let angle = round(v1.angleBetween(v2), 2);
 *   text(`Radians: ${angle}`, 20, 20);
 *
 *   // Use degrees.
 *   angleMode(DEGREES);
 *
 *   // Display the angle in degrees.
 *   angle = round(v1.angleBetween(v2), 2);
 *   text(`Degrees: ${angle}`, 20, 35);
 * }
 *
 * // Draws an arrow between two vectors.
 * function drawArrow(base, vec, myColor) {
 *   push();
 *   stroke(myColor);
 *   strokeWeight(3);
 *   fill(myColor);
 *   translate(base.x, base.y);
 *   line(0, 0, vec.x, vec.y);
 *   rotate(vec.heading());
 *   let arrowSize = 7;
 *   translate(vec.mag() - arrowSize, 0);
 *   triangle(0, arrowSize / 2, 0, -arrowSize / 2, arrowSize, 0);
 *   pop();
 * }
 * </code>
 * </div>
 */
  angleBetween(v) {
    const magSqMult = this.magSq() * v.magSq();
    // Returns NaN if either vector is the zero vector.
    if (magSqMult === 0) {
      return NaN;
    }
    const u = this.cross(v);
    // The dot product computes the cos value, and the cross product computes
    // the sin value. Find the angle based on them. In addition, in the case of
    // 2D vectors, a sign is added according to the direction of the vector.
    let angle = Math.atan2(u.mag(), this.dot(v)) * Math.sign(u.z || 1);
    if (this.isPInst) {
      angle = this._fromRadians(angle);
    }
    return angle;
  }

  /**
 * Calculates new `x`, `y`, and `z` components that are proportionally the
 * same distance between two vectors.
 *
 * The `amt` parameter is the amount to interpolate between the old vector and
 * the new vector. 0.0 keeps all components equal to the old vector's, 0.5 is
 * halfway between, and 1.0 sets all components equal to the new vector's.
 *
 * The static version of `lerp()`, as in `p5.Vector.lerp(v0, v1, 0.5)`,
 * returns a new <a href="#/p5.Vector">p5.Vector</a> object and doesn't change
 * the original.
 *
 * @method lerp
 * @param  {Number}    x   x component.
 * @param  {Number}    y   y component.
 * @param  {Number}    z   z component.
 * @param  {Number}    amt amount of interpolation between 0.0 (old vector)
 *                         and 1.0 (new vector). 0.5 is halfway between.
 * @chainable
 *
 * @example
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create a p5.Vector object.
 *   let v0 = createVector(1, 1, 1);
 *   let v1 = createVector(3, 3, 3);
 *
 *   // Interpolate.
 *   v0.lerp(v1, 0.5);
 *
 *   // Prints "p5.Vector Object : [2, 2, 2]" to the console.
 *   print(v0.toString());
 * }
 * </code>
 * </div>
 *
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create a p5.Vector object.
 *   let v = createVector(1, 1, 1);
 *
 *   // Interpolate.
 *   v.lerp(3, 3, 3, 0.5);
 *
 *   // Prints "p5.Vector Object : [2, 2, 2]" to the console.
 *   print(v.toString());
 * }
 * </code>
 * </div>
 *
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create p5.Vector objects.
 *   let v0 = createVector(1, 1, 1);
 *   let v1 = createVector(3, 3, 3);
 *
 *   // Interpolate.
 *   let v2 = p5.Vector.lerp(v0, v1, 0.5);
 *
 *   // Prints "p5.Vector Object : [2, 2, 2]" to the console.
 *   print(v2.toString());
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   describe('Three arrows extend from the center of a gray square. A red arrow points to the right, a blue arrow points down, and a purple arrow points to the bottom right.');
 * }
 * function draw() {
 *   background(200);
 *
 *   // Create p5.Vector objects.
 *   let v0 = createVector(50, 50);
 *   let v1 = createVector(30, 0);
 *   let v2 = createVector(0, 30);
 *
 *   // Interpolate.
 *   let v3 = p5.Vector.lerp(v1, v2, 0.5);
 *
 *   // Draw the red arrow.
 *   drawArrow(v0, v1, 'red');
 *
 *   // Draw the blue arrow.
 *   drawArrow(v0, v2, 'blue');
 *
 *   // Draw the purple arrow.
 *   drawArrow(v0, v3, 'purple');
 * }
 *
 * // Draws an arrow between two vectors.
 * function drawArrow(base, vec, myColor) {
 *   push();
 *   stroke(myColor);
 *   strokeWeight(3);
 *   fill(myColor);
 *   translate(base.x, base.y);
 *   line(0, 0, vec.x, vec.y);
 *   rotate(vec.heading());
 *   let arrowSize = 7;
 *   translate(vec.mag() - arrowSize, 0);
 *   triangle(0, arrowSize / 2, 0, -arrowSize / 2, arrowSize, 0);
 *   pop();
 * }
 * </code>
 * </div>
 */
  /**
 * @method lerp
 * @param  {p5.Vector} v  <a href="#/p5.Vector">p5.Vector</a> to lerp toward.
 * @param  {Number}    amt
 * @chainable
 */
  lerp(x, y, z, amt) {
    if (x instanceof p5.Vector) {
      return this.lerp(x.x, x.y, x.z, y);
    }
    this.x += (x - this.x) * amt || 0;
    this.y += (y - this.y) * amt || 0;
    this.z += (z - this.z) * amt || 0;
    return this;
  }

  /**
 * Calculates a new heading and magnitude that are between two vectors.
 *
 * The `amt` parameter is the amount to interpolate between the old vector and
 * the new vector. 0.0 keeps the heading and magnitude equal to the old
 * vector's, 0.5 sets them halfway between, and 1.0 sets the heading and
 * magnitude equal to the new vector's.
 *
 * `slerp()` differs from <a href="#/p5.Vector/lerp">lerp()</a> because
 * it interpolates magnitude. Calling `v0.slerp(v1, 0.5)` sets `v0`'s
 * magnitude to a value halfway between its original magnitude and `v1`'s.
 * Calling `v0.lerp(v1, 0.5)` makes no such guarantee.
 *
 * The static version of `slerp()`, as in `p5.Vector.slerp(v0, v1, 0.5)`,
 * returns a new <a href="#/p5.Vector">p5.Vector</a> object and doesn't change
 * the original.
 *
 * @method slerp
 * @param {p5.Vector} v <a href="#/p5.Vector">p5.Vector</a> to slerp toward.
 * @param {Number} amt  amount of interpolation between 0.0 (old vector)
 *                      and 1.0 (new vector). 0.5 is halfway between.
 * @return {p5.Vector}
 *
 * @example
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create a p5.Vector object.
 *   let v0 = createVector(3, 0);
 *
 *   // Prints "3" to the console.
 *   print(v0.mag());
 *
 *   // Prints "0" to the console.
 *   print(v0.heading());
 *
 *   // Create a p5.Vector object.
 *   let v1 = createVector(0, 1);
 *
 *   // Prints "1" to the console.
 *   print(v1.mag());
 *
 *   // Prints "1.570..." to the console.
 *   print(v1.heading());
 *
 *   // Interpolate halfway between v0 and v1.
 *   v0.slerp(v1, 0.5);
 *
 *   // Prints "2" to the console.
 *   print(v0.mag());
 *
 *   // Prints "0.785..." to the console.
 *   print(v0.heading());
 * }
 * </code>
 * </div>
 *
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create a p5.Vector object.
 *   let v0 = createVector(3, 0);
 *
 *   // Prints "3" to the console.
 *   print(v0.mag());
 *
 *   // Prints "0" to the console.
 *   print(v0.heading());
 *
 *   // Create a p5.Vector object.
 *   let v1 = createVector(0, 1);
 *
 *   // Prints "1" to the console.
 *   print(v1.mag());
 *
 *   // Prints "1.570..." to the console.
 *   print(v1.heading());
 *
 *   // Create a p5.Vector that's halfway between v0 and v1.
 *   let v3 = p5.Vector.slerp(v0, v1, 0.5);
 *
 *   // Prints "2" to the console.
 *   print(v3.mag());
 *
 *   // Prints "0.785..." to the console.
 *   print(v3.heading());
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   describe('Three arrows extend from the center of a gray square. A red arrow points to the right, a blue arrow points to the left, and a purple arrow points down.');
 * }
 *
 * function draw() {
 *   background(200);
 *
 *   // Create p5.Vector objects.
 *   let v0 = createVector(50, 50);
 *   let v1 = createVector(20, 0);
 *   let v2 = createVector(-40, 0);
 *
 *   // Create a p5.Vector that's halfway between v1 and v2.
 *   let v3 = p5.Vector.slerp(v1, v2, 0.5);
 *
 *   // Draw the red arrow.
 *   drawArrow(v0, v1, 'red');
 *
 *   // Draw the blue arrow.
 *   drawArrow(v0, v2, 'blue');
 *
 *   // Draw the purple arrow.
 *   drawArrow(v0, v3, 'purple');
 * }
 *
 * // Draws an arrow between two vectors.
 * function drawArrow(base, vec, myColor) {
 *   push();
 *   stroke(myColor);
 *   strokeWeight(3);
 *   fill(myColor);
 *   translate(base.x, base.y);
 *   line(0, 0, vec.x, vec.y);
 *   rotate(vec.heading());
 *   let arrowSize = 7;
 *   translate(vec.mag() - arrowSize, 0);
 *   triangle(0, arrowSize / 2, 0, -arrowSize / 2, arrowSize, 0);
 *   pop();
 * }
 * </code>
 * </div>
 */
  slerp(v, amt) {
    // edge cases.
    if (amt === 0) { return this; }
    if (amt === 1) { return this.set(v); }

    // calculate magnitudes
    const selfMag = this.mag();
    const vMag = v.mag();
    const magmag = selfMag * vMag;
    // if either is a zero vector, linearly interpolate by these vectors
    if (magmag === 0) {
      this.mult(1 - amt).add(v.x * amt, v.y * amt, v.z * amt);
      return this;
    }
    // the cross product of 'this' and 'v' is the axis of rotation
    const axis = this.cross(v);
    const axisMag = axis.mag();
    // Calculates the angle between 'this' and 'v'
    const theta = Math.atan2(axisMag, this.dot(v));

    // However, if the norm of axis is 0, normalization cannot be performed,
    // so we will divide the cases
    if (axisMag > 0) {
      axis.x /= axisMag;
      axis.y /= axisMag;
      axis.z /= axisMag;
    } else if (theta < Math.PI * 0.5) {
      // if the norm is 0 and the angle is less than PI/2,
      // the angle is very close to 0, so do linear interpolation.
      this.mult(1 - amt).add(v.x * amt, v.y * amt, v.z * amt);
      return this;
    } else {
      // If the norm is 0 and the angle is more than PI/2, the angle is
      // very close to PI.
      // In this case v can be regarded as '-this', so take any vector
      // that is orthogonal to 'this' and use that as the axis.
      if (this.z === 0 && v.z === 0) {
        // if both this and v are 2D vectors, use (0,0,1)
        // this makes the result also a 2D vector.
        axis.set(0, 0, 1);
      } else if (this.x !== 0) {
        // if the x components is not 0, use (y, -x, 0)
        axis.set(this.y, -this.x, 0).normalize();
      } else {
        // if the x components is 0, use (1,0,0)
        axis.set(1, 0, 0);
      }
    }

    // Since 'axis' is a unit vector, ey is a vector of the same length as 'this'.
    const ey = axis.cross(this);
    // interpolate the length with 'this' and 'v'.
    const lerpedMagFactor = (1 - amt) + amt * vMag / selfMag;
    // imagine a situation where 'axis', 'this', and 'ey' are pointing
    // along the z, x, and y axes, respectively.
    // rotates 'this' around 'axis' by amt * theta towards 'ey'.
    const cosMultiplier = lerpedMagFactor * Math.cos(amt * theta);
    const sinMultiplier = lerpedMagFactor * Math.sin(amt * theta);
    // then, calculate 'result'.
    this.x = this.x * cosMultiplier + ey.x * sinMultiplier;
    this.y = this.y * cosMultiplier + ey.y * sinMultiplier;
    this.z = this.z * cosMultiplier + ey.z * sinMultiplier;

    return this;
  }

  /**
 * Reflects a vector about a line in 2D or a plane in 3D.
 *
 * The orientation of the line or plane is described by a normal vector that
 * points away from the shape.
 *
 * The static version of `reflect()`, as in `p5.Vector.reflect(v, n)`,
 * returns a new <a href="#/p5.Vector">p5.Vector</a> object and doesn't change
 * the original.
 *
 * @method reflect
 * @param  {p5.Vector} surfaceNormal  <a href="#/p5.Vector">p5.Vector</a>
 *                                    to reflect about.
 * @chainable
 * @example
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create a normal vector.
 *   let n = createVector(0, 1);
 *   // Create a vector to reflect.
 *   let v = createVector(4, 6);
 *
 *   // Reflect v about n.
 *   v.reflect(n);
 *
 *   // Prints "p5.Vector Object : [4, -6, 0]" to the console.
 *   print(v.toString());
 * }
 * </code>
 * </div>
 *
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create a normal vector.
 *   let n = createVector(0, 1);
 *
 *   // Create a vector to reflect.
 *   let v0 = createVector(4, 6);
 *
 *   // Create a reflected vector.
 *   let v1 = p5.Vector.reflect(v0, n);
 *
 *   // Prints "p5.Vector Object : [4, -6, 0]" to the console.
 *   print(v1.toString());
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   describe('Three arrows extend from the center of a gray square with a vertical line down its middle. A black arrow points to the right, a blue arrow points to the bottom left, and a red arrow points to the bottom right.');
 * }
 * function draw() {
 *   background(200);
 *
 *   // Draw a vertical line.
 *   line(50, 0, 50, 100);
 *
 *   // Create a normal vector.
 *   let n = createVector(1, 0);
 *
 *   // Center.
 *   let v0 = createVector(50, 50);
 *
 *   // Create a vector to reflect.
 *   let v1 = createVector(30, 40);
 *
 *   // Create a reflected vector.
 *   let v2 = p5.Vector.reflect(v1, n);
 *
 *   // Scale the normal vector for drawing.
 *   n.setMag(30);
 *
 *   // Draw the black arrow.
 *   drawArrow(v0, n, 'black');
 *
 *   // Draw the red arrow.
 *   drawArrow(v0, v1, 'red');
 *
 *   // Draw the blue arrow.
 *   drawArrow(v0, v2, 'blue');
 * }
 *
 * // Draws an arrow between two vectors.
 * function drawArrow(base, vec, myColor) {
 *   push();
 *   stroke(myColor);
 *   strokeWeight(3);
 *   fill(myColor);
 *   translate(base.x, base.y);
 *   line(0, 0, vec.x, vec.y);
 *   rotate(vec.heading());
 *   let arrowSize = 7;
 *   translate(vec.mag() - arrowSize, 0);
 *   triangle(0, arrowSize / 2, 0, -arrowSize / 2, arrowSize, 0);
 *   pop();
 * }
 * </code>
 * </div>
 */
  reflect(surfaceNormal) {
    const surfaceNormalCopy = p5.Vector.normalize(surfaceNormal);
    return this.sub(surfaceNormalCopy.mult(2 * this.dot(surfaceNormalCopy)));
  }

  /**
 * Returns the vector's components as an array of numbers.
 *
 * @method array
 * @return {Number[]} array with the vector's components.
 * @example
 * <div class = "norender">
 * <code>
 * function setup() {
 *   // Create a p5.Vector object.
 *   let v = createVector(20, 30);
 *
 *   // Prints "[20, 30, 0]" to the console.
 *   print(v.array());
 * }
 * </code>
 * </div>
 */
  array() {
    return [this.x || 0, this.y || 0, this.z || 0];
  }

  /**
 * Checks whether all the vector's components are equal to another vector's.
 *
 * `equals()` returns `true` if the vector's components are all the same as another
 * vector's and `false` if not.
 *
 * The version of `equals()` with one parameter interprets it as another
 * <a href="#/p5.Vector">p5.Vector</a> object.
 *
 * The version of `equals()` with multiple parameters interprets them as the
 * components of another vector. Any missing parameters are assigned the value
 * 0.
 *
 * The static version of `equals()`, as in `p5.Vector.equals(v0, v1)`,
 * interprets both parameters as <a href="#/p5.Vector">p5.Vector</a> objects.
 *
 * @method equals
 * @param {Number} [x] x component of the vector.
 * @param {Number} [y] y component of the vector.
 * @param {Number} [z] z component of the vector.
 * @return {Boolean} whether the vectors are equal.
 * @example
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create p5.Vector objects.
 *   let v0 = createVector(10, 20, 30);
 *   let v1 = createVector(10, 20, 30);
 *   let v2 = createVector(0, 0, 0);
 *
 *   // Prints "true" to the console.
 *   print(v0.equals(v1));
 *
 *   // Prints "false" to the console.
 *   print(v0.equals(v2));
 * }
 * </code>
 * </div>
 *
 * <div class = "norender">
 * <code>
 * function setup() {
 *   // Create p5.Vector objects.
 *   let v0 = createVector(5, 10, 20);
 *   let v1 = createVector(5, 10, 20);
 *   let v2 = createVector(13, 10, 19);
 *
 *   // Prints "true" to the console.
 *   print(v0.equals(v1.x, v1.y, v1.z));
 *
 *   // Prints "false" to the console.
 *   print(v0.equals(v2.x, v2.y, v2.z));
 * }
 * </code>
 * </div>
 *
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create p5.Vector objects.
 *   let v0 = createVector(10, 20, 30);
 *   let v1 = createVector(10, 20, 30);
 *   let v2 = createVector(0, 0, 0);
 *
 *   // Prints "true" to the console.
 *   print(p5.Vector.equals(v0, v1));
 *
 *   // Prints "false" to the console.
 *   print(p5.Vector.equals(v0, v2));
 * }
 * </code>
 * </div>
 */
  /**
 * @method equals
 * @param {p5.Vector|Array} value vector to compare.
 * @return {Boolean}
 */
  equals(x, y, z) {
    let a, b, c;
    if (x instanceof p5.Vector) {
      a = x.x || 0;
      b = x.y || 0;
      c = x.z || 0;
    } else if (Array.isArray(x)) {
      a = x[0] || 0;
      b = x[1] || 0;
      c = x[2] || 0;
    } else {
      a = x || 0;
      b = y || 0;
      c = z || 0;
    }
    return this.x === a && this.y === b && this.z === c;
  }

  // Static Methods

  /**
 * Creates a new 2D vector from an angle.
 *
 * @method fromAngle
 * @static
 * @param {Number}     angle desired angle, in radians. Unaffected by <a href="#/p5/angleMode">angleMode()</a>.
 * @param {Number}     [length] length of the new vector (defaults to 1).
 * @return {p5.Vector}       new <a href="#/p5.Vector">p5.Vector</a> object.
 *
 * @example
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create a p5.Vector object.
 *   let v = p5.Vector.fromAngle(0);
 *
 *   // Prints "p5.Vector Object : [1, 0, 0]" to the console.
 *   print(v.toString());
 * }
 * </code>
 * </div>
 *
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create a p5.Vector object.
 *   let v = p5.Vector.fromAngle(0, 30);
 *
 *   // Prints "p5.Vector Object : [30, 0, 0]" to the console.
 *   print(v.toString());
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   describe('A black arrow extends from the center of a gray square. It points to the right.');
 * }
 * function draw() {
 *   background(200);
 *
 *   // Create a p5.Vector to the center.
 *   let v0 = createVector(50, 50);
 *
 *   // Create a p5.Vector with an angle 0 and magnitude 30.
 *   let v1 = p5.Vector.fromAngle(0, 30);
 *
 *   // Draw the black arrow.
 *   drawArrow(v0, v1, 'black');
 * }
 *
 * // Draws an arrow between two vectors.
 * function drawArrow(base, vec, myColor) {
 *   push();
 *   stroke(myColor);
 *   strokeWeight(3);
 *   fill(myColor);
 *   translate(base.x, base.y);
 *   line(0, 0, vec.x, vec.y);
 *   rotate(vec.heading());
 *   let arrowSize = 7;
 *   translate(vec.mag() - arrowSize, 0);
 *   triangle(0, arrowSize / 2, 0, -arrowSize / 2, arrowSize, 0);
 *   pop();
 * }
 * </code>
 * </div>
 */
  static fromAngle(angle, length = 1) {
    return new p5.Vector(length * Math.cos(angle), length * Math.sin(angle), 0);
  }

  /**
 * Creates a new 3D vector from a pair of ISO spherical angles.
 *
 * @method fromAngles
 * @static
 * @param {Number}     theta    polar angle in radians (zero is up).
 * @param {Number}     phi      azimuthal angle in radians
 *                               (zero is out of the screen).
 * @param {Number}     [length] length of the new vector (defaults to 1).
 * @return {p5.Vector}          new <a href="#/p5.Vector">p5.Vector</a> object.
 *
 * @example
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create a p5.Vector object.
 *   let v = p5.Vector.fromAngles(0, 0);
 *
 *   // Prints "p5.Vector Object : [0, -1, 0]" to the console.
 *   print(v.toString());
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100, WEBGL);
 *
 *   describe('A light shines on a pink sphere as it orbits.');
 * }
 *
 * function draw() {
 *   background(0);
 *
 *   // Calculate the ISO angles.
 *   let theta = frameCount *  0.05;
 *   let phi = 0;
 *
 *   // Create a p5.Vector object.
 *   let v = p5.Vector.fromAngles(theta, phi, 100);
 *
 *   // Create a point light using the p5.Vector.
 *   let c = color('deeppink');
 *   pointLight(c, v);
 *
 *   // Style the sphere.
 *   fill(255);
 *   noStroke();
 *
 *   // Draw the sphere.
 *   sphere(35);
 * }
 * </code>
 * </div>
 */
  static fromAngles(theta, phi, length = 1) {
    const cosPhi = Math.cos(phi);
    const sinPhi = Math.sin(phi);
    const cosTheta = Math.cos(theta);
    const sinTheta = Math.sin(theta);

    return new p5.Vector(
      length * sinTheta * sinPhi,
      -length * cosTheta,
      length * sinTheta * cosPhi
    );
  }

  /**
 * Creates a new 2D unit vector with a random heading.
 *
 * @method random2D
 * @static
 * @return {p5.Vector} new <a href="#/p5.Vector">p5.Vector</a> object.
 * @example
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create a p5.Vector object.
 *   let v = p5.Vector.random2D();
 *
 *   // Prints "p5.Vector Object : [x, y, 0]" to the console
 *   // where x and y are small random numbers.
 *   print(v.toString());
 * }
 * </code>
 * </div>
 *
 * <div>
 * <code>
 * function setup() {
 *   createCanvas(100, 100);
 *
 *   // Slow the frame rate.
 *   frameRate(1);
 *
 *   describe('A black arrow in extends from the center of a gray square. It changes direction once per second.');
 * }
 *
 * function draw() {
 *   background(200);
 *
 *   // Create a p5.Vector to the center.
 *   let v0 = createVector(50, 50);
 *
 *   // Create a random p5.Vector.
 *   let v1 = p5.Vector.random2D();
 *
 *   // Scale v1 for drawing.
 *   v1.mult(30);
 *
 *   // Draw the black arrow.
 *   drawArrow(v0, v1, 'black');
 * }
 *
 * // Draws an arrow between two vectors.
 * function drawArrow(base, vec, myColor) {
 *   push();
 *   stroke(myColor);
 *   strokeWeight(3);
 *   fill(myColor);
 *   translate(base.x, base.y);
 *   line(0, 0, vec.x, vec.y);
 *   rotate(vec.heading());
 *   let arrowSize = 7;
 *   translate(vec.mag() - arrowSize, 0);
 *   triangle(0, arrowSize / 2, 0, -arrowSize / 2, arrowSize, 0);
 *   pop();
 * }
 * </code>
 * </div>
 */
  static random2D() {
    return this.fromAngle(Math.random() * constants.TWO_PI);
  }

  /**
 * Creates a new 3D unit vector with a random heading.
 *
 * @method random3D
 * @static
 * @return {p5.Vector} new <a href="#/p5.Vector">p5.Vector</a> object.
 * @example
 * <div class="norender">
 * <code>
 * function setup() {
 *   // Create a p5.Vector object.
 *   let v = p5.Vector.random3D();
 *
 *   // Prints "p5.Vector Object : [x, y, z]" to the console
 *   // where x, y, and z are small random numbers.
 *   print(v.toString());
 * }
 * </code>
 * </div>
 */
  static random3D() {
    const angle = Math.random() * constants.TWO_PI;
    const vz = Math.random() * 2 - 1;
    const vzBase = Math.sqrt(1 - vz * vz);
    const vx = vzBase * Math.cos(angle);
    const vy = vzBase * Math.sin(angle);
    return new p5.Vector(vx, vy, vz);
  }

  // Returns a copy of a vector.
  /**
 * @method copy
 * @static
 * @param  {p5.Vector} v the <a href="#/p5.Vector">p5.Vector</a> to create a copy of
 * @return {p5.Vector} the copy of the <a href="#/p5.Vector">p5.Vector</a> object
 */

  static copy(v) {
    return v.copy(v);
  }

  // Adds two vectors together and returns a new one.
  /**
 * @method add
 * @static
 * @param  {p5.Vector} v1 A <a href="#/p5.Vector">p5.Vector</a> to add
 * @param  {p5.Vector} v2 A <a href="#/p5.Vector">p5.Vector</a> to add
 * @param  {p5.Vector} [target] vector to receive the result.
 * @return {p5.Vector} resulting <a href="#/p5.Vector">p5.Vector</a>.
 */

  static add(...args) {
    let [v1, v2, target] = args;
    if (!target) {
      target = v1.copy();
      if (args.length === 3) {
        p5._friendlyError(
          'The target parameter is undefined, it should be of type p5.Vector',
          'p5.Vector.add'
        );
      }
    } else {
      target.set(v1);
    }
    target.add(v2);
    return target;
  }

  // Returns a vector remainder when it is divided by another vector
  /**
 * @method rem
 * @static
 * @param  {p5.Vector} v1 The dividend <a href="#/p5.Vector">p5.Vector</a>
 * @param  {p5.Vector} v2 The divisor <a href="#/p5.Vector">p5.Vector</a>
 */
  /**
 * @method rem
 * @static
 * @param  {p5.Vector} v1
 * @param  {p5.Vector} v2
 * @return {p5.Vector} The resulting <a href="#/p5.Vector">p5.Vector</a>
 */
  static rem(v1, v2) {
    if (v1 instanceof p5.Vector && v2 instanceof p5.Vector) {
      let target = v1.copy();
      target.rem(v2);
      return target;
    }
  }

  /*
 * Subtracts one <a href="#/p5.Vector">p5.Vector</a> from another and returns a new one.  The second
 * vector (`v2`) is subtracted from the first (`v1`), resulting in `v1-v2`.
 */
  /**
 * @method sub
 * @static
 * @param  {p5.Vector} v1 A <a href="#/p5.Vector">p5.Vector</a> to subtract from
 * @param  {p5.Vector} v2 A <a href="#/p5.Vector">p5.Vector</a> to subtract
 * @param  {p5.Vector} [target] vector to receive the result.
 * @return {p5.Vector} The resulting <a href="#/p5.Vector">p5.Vector</a>
 */

  static sub(...args) {
    let [v1, v2, target] = args;
    if (!target) {
      target = v1.copy();
      if (args.length === 3) {
        p5._friendlyError(
          'The target parameter is undefined, it should be of type p5.Vector',
          'p5.Vector.sub'
        );
      }
    } else {
      target.set(v1);
    }
    target.sub(v2);
    return target;
  }

  /**
 * Multiplies a vector by a scalar and returns a new vector.
 */

  /**
 * @method mult
 * @static
 * @param  {Number} x
 * @param  {Number} y
 * @param  {Number} [z]
 * @return {p5.Vector} resulting new <a href="#/p5.Vector">p5.Vector</a>.
 */

  /**
 * @method mult
 * @static
 * @param  {p5.Vector} v
 * @param  {Number}  n
 * @param  {p5.Vector} [target] vector to receive the result.
 * @return {p5.Vector} The resulting new <a href="#/p5.Vector">p5.Vector</a>
 */

  /**
 * @method mult
 * @static
 * @param  {p5.Vector} v0
 * @param  {p5.Vector} v1
 * @param  {p5.Vector} [target]
 * @return {p5.Vector} The resulting new <a href="#/p5.Vector">p5.Vector</a>
 */

  /**
 * @method mult
 * @static
 * @param  {p5.Vector} v0
 * @param  {Number[]} arr
 * @param  {p5.Vector} [target]
 * @return {p5.Vector} The resulting new <a href="#/p5.Vector">p5.Vector</a>
 */
  static mult(...args) {
    let [v, n, target] = args;
    if (!target) {
      target = v.copy();
      if (args.length === 3) {
        p5._friendlyError(
          'The target parameter is undefined, it should be of type p5.Vector',
          'p5.Vector.mult'
        );
      }
    } else {
      target.set(v);
    }
    target.mult(n);
    return target;
  }

  /**
 * Rotates the vector (only 2D vectors) by the given angle; magnitude remains the same. Returns a new vector.
 */

  /**
 * @method rotate
 * @static
 * @param  {p5.Vector} v
 * @param  {Number} angle
 * @param  {p5.Vector} [target] The vector to receive the result
 * @return {p5.Vector} The resulting new <a href="#/p5.Vector">p5.Vector</a>
 */
  static rotate(...args) {
    let [v, a, target] = args;
    if (args.length === 2) {
      target = v.copy();
    } else {
      if (!(target instanceof p5.Vector)) {
        p5._friendlyError(
          'The target parameter should be of type p5.Vector',
          'p5.Vector.rotate'
        );
      }
      target.set(v);
    }
    target.rotate(a);
    return target;
  }

  /**
 * Divides a vector by a scalar and returns a new vector.
 */

  /**
 * @method div
 * @static
 * @param  {Number} x
 * @param  {Number} y
 * @param  {Number} [z]
 * @return {p5.Vector} The resulting new <a href="#/p5.Vector">p5.Vector</a>
 */

  /**
 * @method div
 * @static
 * @param  {p5.Vector} v
 * @param  {Number}  n
 * @param  {p5.Vector} [target] The vector to receive the result
 * @return {p5.Vector} The resulting new <a href="#/p5.Vector">p5.Vector</a>
 */

  /**
 * @method div
 * @static
 * @param  {p5.Vector} v0
 * @param  {p5.Vector} v1
 * @param  {p5.Vector} [target]
 * @return {p5.Vector} The resulting new <a href="#/p5.Vector">p5.Vector</a>
 */

  /**
 * @method div
 * @static
 * @param  {p5.Vector} v0
 * @param  {Number[]} arr
 * @param  {p5.Vector} [target]
 * @return {p5.Vector} The resulting new <a href="#/p5.Vector">p5.Vector</a>
 */
  static div(...args) {
    let [v, n, target] = args;
    if (!target) {
      target = v.copy();

      if (args.length === 3) {
        p5._friendlyError(
          'The target parameter is undefined, it should be of type p5.Vector',
          'p5.Vector.div'
        );
      }
    } else {
      target.set(v);
    }
    target.div(n);
    return target;
  }

  /**
 * Calculates the dot product of two vectors.
 */
  /**
 * @method dot
 * @static
 * @param  {p5.Vector} v1 first <a href="#/p5.Vector">p5.Vector</a>.
 * @param  {p5.Vector} v2 second <a href="#/p5.Vector">p5.Vector</a>.
 * @return {Number}     dot product.
 */
  static dot(v1, v2) {
    return v1.dot(v2);
  }

  /**
 * Calculates the cross product of two vectors.
 */
  /**
 * @method cross
 * @static
 * @param  {p5.Vector} v1 first <a href="#/p5.Vector">p5.Vector</a>.
 * @param  {p5.Vector} v2 second <a href="#/p5.Vector">p5.Vector</a>.
 * @return {Number}     cross product.
 */
  static cross(v1, v2) {
    return v1.cross(v2);
  }

  /**
 * Calculates the Euclidean distance between two points (considering a
 * point as a vector object).
 */
  /**
 * @method dist
 * @static
 * @param  {p5.Vector} v1 The first <a href="#/p5.Vector">p5.Vector</a>
 * @param  {p5.Vector} v2 The second <a href="#/p5.Vector">p5.Vector</a>
 * @return {Number}     The distance
 */
  static dist(v1, v2) {
    return v1.dist(v2);
  }

  /**
 * Linear interpolate a vector to another vector and return the result as a
 * new vector.
 */
  /**
 * @method lerp
 * @static
 * @param {p5.Vector} v1
 * @param {p5.Vector} v2
 * @param {Number} amt
 * @param {p5.Vector} [target] The vector to receive the result
 * @return {p5.Vector}      The lerped value
 */
  static lerp(...args) {
    let [v1, v2, amt, target] = args;
    if (!target) {
      target = v1.copy();
      if (args.length === 4) {
        p5._friendlyError(
          'The target parameter is undefined, it should be of type p5.Vector',
          'p5.Vector.lerp'
        );
      }
    } else {
      target.set(v1);
    }
    target.lerp(v2, amt);
    return target;
  }

  /**
 * Performs spherical linear interpolation with the other vector
 * and returns the resulting vector.
 * This works in both 3D and 2D. As for 2D, the result of slerping
 * between 2D vectors is always a 2D vector.
 */
  /**
 * @method slerp
 * @static
 * @param {p5.Vector} v1 old vector.
 * @param {p5.Vector} v2 new vector.
 * @param {Number} amt
 * @param {p5.Vector} [target] vector to receive the result.
 * @return {p5.Vector} slerped vector between v1 and v2
 */
  static slerp(...args) {
    let [v1, v2, amt, target] = args;
    if (!target) {
      target = v1.copy();
      if (args.length === 4) {
        p5._friendlyError(
          'The target parameter is undefined, it should be of type p5.Vector',
          'p5.Vector.slerp'
        );
      }
    } else {
      target.set(v1);
    }
    target.slerp(v2, amt);
    return target;
  }

  /**
 * Calculates the magnitude (length) of the vector and returns the result as
 * a float (this is simply the equation `sqrt(x*x + y*y + z*z)`.)
 */
  /**
 * @method mag
 * @static
 * @param {p5.Vector} vecT The vector to return the magnitude of
 * @return {Number}        The magnitude of vecT
 */
  static mag(vecT) {
    return vecT.mag();
  }

  /**
 * Calculates the squared magnitude of the vector and returns the result
 * as a float (this is simply the equation <em>(x\*x + y\*y + z\*z)</em>.)
 * Faster if the real length is not required in the
 * case of comparing vectors, etc.
 */
  /**
 * @method magSq
 * @static
 * @param {p5.Vector} vecT the vector to return the squared magnitude of
 * @return {Number}        the squared magnitude of vecT
 */
  static magSq(vecT) {
    return vecT.magSq();
  }

  /**
 * Normalize the vector to length 1 (make it a unit vector).
 */
  /**
 * @method normalize
 * @static
 * @param {p5.Vector} v  The vector to normalize
 * @param {p5.Vector} [target] The vector to receive the result
 * @return {p5.Vector}   The vector v, normalized to a length of 1
 */
  static normalize(...args) {
    let [v, target] = args;
    if (args.length < 2) {
      target = v.copy();
    } else {
      if (!(target instanceof p5.Vector)) {
        p5._friendlyError(
          'The target parameter should be of type p5.Vector',
          'p5.Vector.normalize'
        );
      }
      target.set(v);
    }
    return target.normalize();
  }

  /**
 * Limit the magnitude of the vector to the value used for the <b>max</b>
 * parameter.
 */
  /**
 * @method limit
 * @static
 * @param {p5.Vector} v  the vector to limit
 * @param {Number}    max
 * @param {p5.Vector} [target] the vector to receive the result (Optional)
 * @return {p5.Vector} v with a magnitude limited to max
 */
  static limit(...args) {
    let [v, max, target] = args;
    if (args.length < 3) {
      target = v.copy();
    } else {
      if (!(target instanceof p5.Vector)) {
        p5._friendlyError(
          'The target parameter should be of type p5.Vector',
          'p5.Vector.limit'
        );
      }
      target.set(v);
    }
    return target.limit(max);
  }

  /**
 * Set the magnitude of the vector to the value used for the <b>len</b>
 * parameter.
 */
  /**
 * @method setMag
 * @static
 * @param {p5.Vector} v  the vector to set the magnitude of
 * @param {number}    len
 * @param {p5.Vector} [target] the vector to receive the result (Optional)
 * @return {p5.Vector} v with a magnitude set to len
 */
  static setMag(...args) {
    let [v, len, target] = args;
    if (args.length < 3) {
      target = v.copy();
    } else {
      if (!(target instanceof p5.Vector)) {
        p5._friendlyError(
          'The target parameter should be of type p5.Vector',
          'p5.Vector.setMag'
        );
      }
      target.set(v);
    }
    return target.setMag(len);
  }

  /**
 * Calculate the angle of rotation for this vector (only 2D vectors).
 * p5.Vectors created using <a href="#/p5/createVector">createVector()</a>
 * will take the current <a href="#/p5/angleMode">angleMode</a> into
 * consideration, and give the angle in radians or degrees accordingly.
 */
  /**
 * @method heading
 * @static
 * @param {p5.Vector} v the vector to find the angle of
 * @return {Number} the angle of rotation
 */
  static heading(v) {
    return v.heading();
  }

  /**
 * Calculates and returns the angle between two vectors. This function will take
 * the <a href="#/p5/angleMode">angleMode</a> on v1 into consideration, and
 * give the angle in radians or degrees accordingly.
 */
  /**
 * @method angleBetween
 * @static
 * @param  {p5.Vector}    v1 the first vector.
 * @param  {p5.Vector}    v2 the second vector.
 * @return {Number}       angle between the two vectors.
 */
  static angleBetween(v1, v2) {
    return v1.angleBetween(v2);
  }

  /**
 * Reflect a vector about a normal to a line in 2D, or about a normal to a
 * plane in 3D.
 */
  /**
 * @method reflect
 * @static
 * @param  {p5.Vector} incidentVector vector to be reflected.
 * @param  {p5.Vector} surfaceNormal
 * @param  {p5.Vector} [target] vector to receive the result.
 * @return {p5.Vector} the reflected vector
 */
  static reflect(...args) {
    let [incidentVector, surfaceNormal, target] = args;
    if (args.length < 3) {
      target = incidentVector.copy();
    } else {
      if (!(target instanceof p5.Vector)) {
        p5._friendlyError(
          'The target parameter should be of type p5.Vector',
          'p5.Vector.reflect'
        );
      }
      target.set(incidentVector);
    }
    return target.reflect(surfaceNormal);
  }

  /**
 * Return a representation of this vector as a float array. This is only
 * for temporary use. If used in any other fashion, the contents should be
 * copied by using the <b>p5.Vector.<a href="#/p5.Vector/copy">copy()</a></b>
 * method to copy into your own vector.
 */
  /**
 * @method array
 * @static
 * @param  {p5.Vector} v the vector to convert to an array
 * @return {Number[]} an Array with the 3 values
 */
  static array(v) {
    return v.array();
  }

  /**
 * Equality check against a <a href="#/p5.Vector">p5.Vector</a>
 */
  /**
 * @method equals
 * @static
 * @param {p5.Vector|Array} v1 the first vector to compare
 * @param {p5.Vector|Array} v2 the second vector to compare
 * @return {Boolean}
 */
  static equals(v1, v2) {
    let v;
    if (v1 instanceof p5.Vector) {
      v = v1;
    } else if (Array.isArray(v1)) {
      v = new p5.Vector().set(v1);
    } else {
      p5._friendlyError(
        'The v1 parameter should be of type Array or p5.Vector',
        'p5.Vector.equals'
      );
    }
    return v.equals(v2);
  }


  /**
 * Replaces the components of a <a href="#/p5.Vector">p5.Vector</a> that are very close to zero with zero.
 *
 * In computers, handling numbers with decimals can give slightly imprecise answers due to the way those numbers are represented.
 * This can make it hard to check if a number is zero, as it may be close but not exactly zero.
 * This method rounds very close numbers to zero to make those checks easier
 *
 * https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number/EPSILON
 *
 * @method clampToZero
 * @return {p5.Vector} with components very close to zero replaced with zero.
 * @chainable
 */
  clampToZero() {
    this.x = this._clampToZero(this.x);
    this.y = this._clampToZero(this.y);
    this.z = this._clampToZero(this.z);
    return this;
  }

  /**
     * Helper function for clampToZero
   * @private
   */
  _clampToZero(val) {
    return Math.abs((val||0) - 0) <= Number.EPSILON ? 0 : val;
  }
};export default p5.Vector;