phaser/src/math/Vector3.js

/**
 * @author       Richard Davey <rich@photonstorm.com>
 * @copyright    2020 Photon Storm Ltd.
 * @license      {@link https://opensource.org/licenses/MIT|MIT License}
 */

//  Adapted from [gl-matrix](https://github.com/toji/gl-matrix) by toji
//  and [vecmath](https://github.com/mattdesl/vecmath) by mattdesl

var Class = require('../utils/Class');

/**
 * @classdesc
 * A representation of a vector in 3D space.
 *
 * A three-component vector.
 *
 * @class Vector3
 * @memberof Phaser.Math
 * @constructor
 * @since 3.0.0
 *
 * @param {number} [x] - The x component.
 * @param {number} [y] - The y component.
 * @param {number} [z] - The z component.
 */
var Vector3 = new Class({

    initialize:

    function Vector3 (x, y, z)
    {
        /**
         * The x component of this Vector.
         *
         * @name Phaser.Math.Vector3#x
         * @type {number}
         * @default 0
         * @since 3.0.0
         */
        this.x = 0;

        /**
         * The y component of this Vector.
         *
         * @name Phaser.Math.Vector3#y
         * @type {number}
         * @default 0
         * @since 3.0.0
         */
        this.y = 0;

        /**
         * The z component of this Vector.
         *
         * @name Phaser.Math.Vector3#z
         * @type {number}
         * @default 0
         * @since 3.0.0
         */
        this.z = 0;

        if (typeof x === 'object')
        {
            this.x = x.x || 0;
            this.y = x.y || 0;
            this.z = x.z || 0;
        }
        else
        {
            this.x = x || 0;
            this.y = y || 0;
            this.z = z || 0;
        }
    },

    /**
     * Set this Vector to point up.
     *
     * Sets the y component of the vector to 1, and the others to 0.
     *
     * @method Phaser.Math.Vector3#up
     * @since 3.0.0
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    up: function ()
    {
        this.x = 0;
        this.y = 1;
        this.z = 0;

        return this;
    },

    /**
     * Make a clone of this Vector3.
     *
     * @method Phaser.Math.Vector3#clone
     * @since 3.0.0
     *
     * @return {Phaser.Math.Vector3} A new Vector3 object containing this Vectors values.
     */
    clone: function ()
    {
        return new Vector3(this.x, this.y, this.z);
    },

    /**
     * Calculate the cross (vector) product of two given Vectors.
     *
     * @method Phaser.Math.Vector3#crossVectors
     * @since 3.0.0
     *
     * @param {Phaser.Math.Vector3} a - The first Vector to multiply.
     * @param {Phaser.Math.Vector3} b - The second Vector to multiply.
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    crossVectors: function (a, b)
    {
        var ax = a.x;
        var ay = a.y;
        var az = a.z;
        var bx = b.x;
        var by = b.y;
        var bz = b.z;

        this.x = ay * bz - az * by;
        this.y = az * bx - ax * bz;
        this.z = ax * by - ay * bx;

        return this;
    },

    /**
     * Check whether this Vector is equal to a given Vector.
     *
     * Performs a strict equality check against each Vector's components.
     *
     * @method Phaser.Math.Vector3#equals
     * @since 3.0.0
     *
     * @param {Phaser.Math.Vector3} v - The Vector3 to compare against.
     *
     * @return {boolean} True if the two vectors strictly match, otherwise false.
     */
    equals: function (v)
    {
        return ((this.x === v.x) && (this.y === v.y) && (this.z === v.z));
    },

    /**
     * Copy the components of a given Vector into this Vector.
     *
     * @method Phaser.Math.Vector3#copy
     * @since 3.0.0
     *
     * @param {(Phaser.Math.Vector2|Phaser.Math.Vector3)} src - The Vector to copy the components from.
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    copy: function (src)
    {
        this.x = src.x;
        this.y = src.y;
        this.z = src.z || 0;

        return this;
    },

    /**
     * Set the `x`, `y`, and `z` components of this Vector to the given `x`, `y`, and `z` values.
     *
     * @method Phaser.Math.Vector3#set
     * @since 3.0.0
     *
     * @param {(number|object)} x - The x value to set for this Vector, or an object containing x, y and z components.
     * @param {number} [y] - The y value to set for this Vector.
     * @param {number} [z] - The z value to set for this Vector.
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    set: function (x, y, z)
    {
        if (typeof x === 'object')
        {
            this.x = x.x || 0;
            this.y = x.y || 0;
            this.z = x.z || 0;
        }
        else
        {
            this.x = x || 0;
            this.y = y || 0;
            this.z = z || 0;
        }

        return this;
    },

    /**
     * Add a given Vector to this Vector. Addition is component-wise.
     *
     * @method Phaser.Math.Vector3#add
     * @since 3.0.0
     *
     * @param {(Phaser.Math.Vector2|Phaser.Math.Vector3)} v - The Vector to add to this Vector.
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    add: function (v)
    {
        this.x += v.x;
        this.y += v.y;
        this.z += v.z || 0;

        return this;
    },

    /**
     * Add and scale a given Vector to this Vector. Addition is component-wise.
     *
     * @method Phaser.Math.Vector3#addScale
     * @since 3.50.0
     *
     * @param {(Phaser.Math.Vector2|Phaser.Math.Vector3)} v - The Vector to add to this Vector.
     * @param {number} scale - The amount to scale `v` by.
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    addScale: function (v, scale)
    {
        this.x += v.x * scale;
        this.y += v.y * scale;
        this.z += v.z * scale || 0;

        return this;
    },

    /**
     * Subtract the given Vector from this Vector. Subtraction is component-wise.
     *
     * @method Phaser.Math.Vector3#subtract
     * @since 3.0.0
     *
     * @param {(Phaser.Math.Vector2|Phaser.Math.Vector3)} v - The Vector to subtract from this Vector.
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    subtract: function (v)
    {
        this.x -= v.x;
        this.y -= v.y;
        this.z -= v.z || 0;

        return this;
    },

    /**
     * Perform a component-wise multiplication between this Vector and the given Vector.
     *
     * Multiplies this Vector by the given Vector.
     *
     * @method Phaser.Math.Vector3#multiply
     * @since 3.0.0
     *
     * @param {(Phaser.Math.Vector2|Phaser.Math.Vector3)} v - The Vector to multiply this Vector by.
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    multiply: function (v)
    {
        this.x *= v.x;
        this.y *= v.y;
        this.z *= v.z || 1;

        return this;
    },

    /**
     * Scale this Vector by the given value.
     *
     * @method Phaser.Math.Vector3#scale
     * @since 3.0.0
     *
     * @param {number} scale - The value to scale this Vector by.
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    scale: function (scale)
    {
        if (isFinite(scale))
        {
            this.x *= scale;
            this.y *= scale;
            this.z *= scale;
        }
        else
        {
            this.x = 0;
            this.y = 0;
            this.z = 0;
        }

        return this;
    },

    /**
     * Perform a component-wise division between this Vector and the given Vector.
     *
     * Divides this Vector by the given Vector.
     *
     * @method Phaser.Math.Vector3#divide
     * @since 3.0.0
     *
     * @param {(Phaser.Math.Vector2|Phaser.Math.Vector3)} v - The Vector to divide this Vector by.
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    divide: function (v)
    {
        this.x /= v.x;
        this.y /= v.y;
        this.z /= v.z || 1;

        return this;
    },

    /**
     * Negate the `x`, `y` and `z` components of this Vector.
     *
     * @method Phaser.Math.Vector3#negate
     * @since 3.0.0
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    negate: function ()
    {
        this.x = -this.x;
        this.y = -this.y;
        this.z = -this.z;

        return this;
    },

    /**
     * Calculate the distance between this Vector and the given Vector.
     *
     * @method Phaser.Math.Vector3#distance
     * @since 3.0.0
     *
     * @param {(Phaser.Math.Vector2|Phaser.Math.Vector3)} v - The Vector to calculate the distance to.
     *
     * @return {number} The distance from this Vector to the given Vector.
     */
    distance: function (v)
    {
        var dx = v.x - this.x;
        var dy = v.y - this.y;
        var dz = v.z - this.z || 0;

        return Math.sqrt(dx * dx + dy * dy + dz * dz);
    },

    /**
     * Calculate the distance between this Vector and the given Vector, squared.
     *
     * @method Phaser.Math.Vector3#distanceSq
     * @since 3.0.0
     *
     * @param {(Phaser.Math.Vector2|Phaser.Math.Vector3)} v - The Vector to calculate the distance to.
     *
     * @return {number} The distance from this Vector to the given Vector, squared.
     */
    distanceSq: function (v)
    {
        var dx = v.x - this.x;
        var dy = v.y - this.y;
        var dz = v.z - this.z || 0;

        return dx * dx + dy * dy + dz * dz;
    },

    /**
     * Calculate the length (or magnitude) of this Vector.
     *
     * @method Phaser.Math.Vector3#length
     * @since 3.0.0
     *
     * @return {number} The length of this Vector.
     */
    length: function ()
    {
        var x = this.x;
        var y = this.y;
        var z = this.z;

        return Math.sqrt(x * x + y * y + z * z);
    },

    /**
     * Calculate the length of this Vector squared.
     *
     * @method Phaser.Math.Vector3#lengthSq
     * @since 3.0.0
     *
     * @return {number} The length of this Vector, squared.
     */
    lengthSq: function ()
    {
        var x = this.x;
        var y = this.y;
        var z = this.z;

        return x * x + y * y + z * z;
    },

    /**
     * Normalize this Vector.
     *
     * Makes the vector a unit length vector (magnitude of 1) in the same direction.
     *
     * @method Phaser.Math.Vector3#normalize
     * @since 3.0.0
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    normalize: function ()
    {
        var x = this.x;
        var y = this.y;
        var z = this.z;
        var len = x * x + y * y + z * z;

        if (len > 0)
        {
            len = 1 / Math.sqrt(len);

            this.x = x * len;
            this.y = y * len;
            this.z = z * len;
        }

        return this;
    },

    /**
     * Calculate the dot product of this Vector and the given Vector.
     *
     * @method Phaser.Math.Vector3#dot
     * @since 3.0.0
     *
     * @param {Phaser.Math.Vector3} v - The Vector3 to dot product with this Vector3.
     *
     * @return {number} The dot product of this Vector and `v`.
     */
    dot: function (v)
    {
        return this.x * v.x + this.y * v.y + this.z * v.z;
    },

    /**
     * Calculate the cross (vector) product of this Vector (which will be modified) and the given Vector.
     *
     * @method Phaser.Math.Vector3#cross
     * @since 3.0.0
     *
     * @param {Phaser.Math.Vector3} v - The Vector to cross product with.
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    cross: function (v)
    {
        var ax = this.x;
        var ay = this.y;
        var az = this.z;
        var bx = v.x;
        var by = v.y;
        var bz = v.z;

        this.x = ay * bz - az * by;
        this.y = az * bx - ax * bz;
        this.z = ax * by - ay * bx;

        return this;
    },

    /**
     * Linearly interpolate between this Vector and the given Vector.
     *
     * Interpolates this Vector towards the given Vector.
     *
     * @method Phaser.Math.Vector3#lerp
     * @since 3.0.0
     *
     * @param {Phaser.Math.Vector3} v - The Vector3 to interpolate towards.
     * @param {number} [t=0] - The interpolation percentage, between 0 and 1.
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    lerp: function (v, t)
    {
        if (t === undefined) { t = 0; }

        var ax = this.x;
        var ay = this.y;
        var az = this.z;

        this.x = ax + t * (v.x - ax);
        this.y = ay + t * (v.y - ay);
        this.z = az + t * (v.z - az);

        return this;
    },

    /**
     * Transform this Vector with the given Matrix.
     *
     * @method Phaser.Math.Vector3#transformMat3
     * @since 3.0.0
     *
     * @param {Phaser.Math.Matrix3} mat - The Matrix3 to transform this Vector3 with.
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    transformMat3: function (mat)
    {
        var x = this.x;
        var y = this.y;
        var z = this.z;
        var m = mat.val;

        this.x = x * m[0] + y * m[3] + z * m[6];
        this.y = x * m[1] + y * m[4] + z * m[7];
        this.z = x * m[2] + y * m[5] + z * m[8];

        return this;
    },

    /**
     * Transform this Vector with the given Matrix.
     *
     * @method Phaser.Math.Vector3#transformMat4
     * @since 3.0.0
     *
     * @param {Phaser.Math.Matrix4} mat - The Matrix4 to transform this Vector3 with.
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    transformMat4: function (mat)
    {
        var x = this.x;
        var y = this.y;
        var z = this.z;
        var m = mat.val;

        this.x = m[0] * x + m[4] * y + m[8] * z + m[12];
        this.y = m[1] * x + m[5] * y + m[9] * z + m[13];
        this.z = m[2] * x + m[6] * y + m[10] * z + m[14];

        return this;
    },

    /**
     * Transforms the coordinates of this Vector3 with the given Matrix4.
     *
     * @method Phaser.Math.Vector3#transformCoordinates
     * @since 3.0.0
     *
     * @param {Phaser.Math.Matrix4} mat - The Matrix4 to transform this Vector3 with.
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    transformCoordinates: function (mat)
    {
        var x = this.x;
        var y = this.y;
        var z = this.z;
        var m = mat.val;

        var tx = (x * m[0]) + (y * m[4]) + (z * m[8]) + m[12];
        var ty = (x * m[1]) + (y * m[5]) + (z * m[9]) + m[13];
        var tz = (x * m[2]) + (y * m[6]) + (z * m[10]) + m[14];
        var tw = (x * m[3]) + (y * m[7]) + (z * m[11]) + m[15];

        this.x = tx / tw;
        this.y = ty / tw;
        this.z = tz / tw;

        return this;
    },

    /**
     * Transform this Vector with the given Quaternion.
     *
     * @method Phaser.Math.Vector3#transformQuat
     * @since 3.0.0
     *
     * @param {Phaser.Math.Quaternion} q - The Quaternion to transform this Vector with.
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    transformQuat: function (q)
    {
        // benchmarks: http://jsperf.com/quaternion-transform-vec3-implementations
        var x = this.x;
        var y = this.y;
        var z = this.z;
        var qx = q.x;
        var qy = q.y;
        var qz = q.z;
        var qw = q.w;

        // calculate quat * vec
        var ix = qw * x + qy * z - qz * y;
        var iy = qw * y + qz * x - qx * z;
        var iz = qw * z + qx * y - qy * x;
        var iw = -qx * x - qy * y - qz * z;

        // calculate result * inverse quat
        this.x = ix * qw + iw * -qx + iy * -qz - iz * -qy;
        this.y = iy * qw + iw * -qy + iz * -qx - ix * -qz;
        this.z = iz * qw + iw * -qz + ix * -qy - iy * -qx;

        return this;
    },

    /**
     * Multiplies this Vector3 by the specified matrix, applying a W divide. This is useful for projection,
     * e.g. unprojecting a 2D point into 3D space.
     *
     * @method Phaser.Math.Vector3#project
     * @since 3.0.0
     *
     * @param {Phaser.Math.Matrix4} mat - The Matrix4 to multiply this Vector3 with.
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    project: function (mat)
    {
        var x = this.x;
        var y = this.y;
        var z = this.z;
        var m = mat.val;

        var a00 = m[0];
        var a01 = m[1];
        var a02 = m[2];
        var a03 = m[3];
        var a10 = m[4];
        var a11 = m[5];
        var a12 = m[6];
        var a13 = m[7];
        var a20 = m[8];
        var a21 = m[9];
        var a22 = m[10];
        var a23 = m[11];
        var a30 = m[12];
        var a31 = m[13];
        var a32 = m[14];
        var a33 = m[15];

        var lw = 1 / (x * a03 + y * a13 + z * a23 + a33);

        this.x = (x * a00 + y * a10 + z * a20 + a30) * lw;
        this.y = (x * a01 + y * a11 + z * a21 + a31) * lw;
        this.z = (x * a02 + y * a12 + z * a22 + a32) * lw;

        return this;
    },

    /**
     * Unproject this point from 2D space to 3D space.
     * The point should have its x and y properties set to
     * 2D screen space, and the z either at 0 (near plane)
     * or 1 (far plane). The provided matrix is assumed to already
     * be combined, i.e. projection * view * model.
     *
     * After this operation, this vector's (x, y, z) components will
     * represent the unprojected 3D coordinate.
     *
     * @method Phaser.Math.Vector3#unproject
     * @since 3.0.0
     *
     * @param {Phaser.Math.Vector4} viewport - Screen x, y, width and height in pixels.
     * @param {Phaser.Math.Matrix4} invProjectionView - Combined projection and view matrix.
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    unproject: function (viewport, invProjectionView)
    {
        var viewX = viewport.x;
        var viewY = viewport.y;
        var viewWidth = viewport.z;
        var viewHeight = viewport.w;

        var x = this.x - viewX;
        var y = (viewHeight - this.y - 1) - viewY;
        var z = this.z;

        this.x = (2 * x) / viewWidth - 1;
        this.y = (2 * y) / viewHeight - 1;
        this.z = 2 * z - 1;

        return this.project(invProjectionView);
    },

    /**
     * Make this Vector the zero vector (0, 0, 0).
     *
     * @method Phaser.Math.Vector3#reset
     * @since 3.0.0
     *
     * @return {Phaser.Math.Vector3} This Vector3.
     */
    reset: function ()
    {
        this.x = 0;
        this.y = 0;
        this.z = 0;

        return this;
    }

});

/**
 * A static zero Vector3 for use by reference.
 *
 * This constant is meant for comparison operations and should not be modified directly.
 *
 * @constant
 * @name Phaser.Math.Vector3.ZERO
 * @type {Phaser.Math.Vector3}
 * @since 3.16.0
 */
Vector3.ZERO = new Vector3();

/**
 * A static right Vector3 for use by reference.
 *
 * This constant is meant for comparison operations and should not be modified directly.
 *
 * @constant
 * @name Phaser.Math.Vector3.RIGHT
 * @type {Phaser.Math.Vector3}
 * @since 3.16.0
 */
Vector3.RIGHT = new Vector3(1, 0, 0);

/**
 * A static left Vector3 for use by reference.
 *
 * This constant is meant for comparison operations and should not be modified directly.
 *
 * @constant
 * @name Phaser.Math.Vector3.LEFT
 * @type {Phaser.Math.Vector3}
 * @since 3.16.0
 */
Vector3.LEFT = new Vector3(-1, 0, 0);

/**
 * A static up Vector3 for use by reference.
 *
 * This constant is meant for comparison operations and should not be modified directly.
 *
 * @constant
 * @name Phaser.Math.Vector3.UP
 * @type {Phaser.Math.Vector3}
 * @since 3.16.0
 */
Vector3.UP = new Vector3(0, -1, 0);

/**
 * A static down Vector3 for use by reference.
 *
 * This constant is meant for comparison operations and should not be modified directly.
 *
 * @constant
 * @name Phaser.Math.Vector3.DOWN
 * @type {Phaser.Math.Vector3}
 * @since 3.16.0
 */
Vector3.DOWN = new Vector3(0, 1, 0);

/**
 * A static forward Vector3 for use by reference.
 *
 * This constant is meant for comparison operations and should not be modified directly.
 *
 * @constant
 * @name Phaser.Math.Vector3.FORWARD
 * @type {Phaser.Math.Vector3}
 * @since 3.16.0
 */
Vector3.FORWARD = new Vector3(0, 0, 1);

/**
 * A static back Vector3 for use by reference.
 *
 * This constant is meant for comparison operations and should not be modified directly.
 *
 * @constant
 * @name Phaser.Math.Vector3.BACK
 * @type {Phaser.Math.Vector3}
 * @since 3.16.0
 */
Vector3.BACK = new Vector3(0, 0, -1);

/**
 * A static one Vector3 for use by reference.
 *
 * This constant is meant for comparison operations and should not be modified directly.
 *
 * @constant
 * @name Phaser.Math.Vector3.ONE
 * @type {Phaser.Math.Vector3}
 * @since 3.16.0
 */
Vector3.ONE = new Vector3(1, 1, 1);

module.exports = Vector3;