import {Quat} from "./Quat";
import {Vec4, NumberArray4} from "./Vec4";
import {NumberArray2} from "./Vec2";
export type NumberArray3 = [number, number, number];
/**
* Class represents a 3d vector.
* @class
* @param {number} [x] - First value.
* @param {number} [y] - Second value.
* @param {number} [z] - Third value.
*/
export class Vec3 {
/**
* @public
* @type {number}
*/
public x: number;
/**
* @public
* @type {number}
*/
public y: number;
/**
* @public
* @type {number}
*/
public z: number;
constructor(x: number = 0.0, y: number = 0.0, z: number = 0.0) {
this.x = x;
this.y = y;
this.z = z;
}
/** @const */
static get UP(): Vec3 {
return new Vec3(0, 1, 0);
}
/** @const */
static get DOWN(): Vec3 {
return new Vec3(0, -1, 0);
}
/** @const */
static get RIGHT(): Vec3 {
return new Vec3(1, 0, 0);
}
/** @const */
static get LEFT(): Vec3 {
return new Vec3(-1, 0, 0);
}
/** @const */
static get FORWARD(): Vec3 {
return new Vec3(0, 0, -1);
}
/** @const */
static get BACKWARD(): Vec3 {
return new Vec3(0, 0, 1);
}
/** @const */
static get ZERO(): Vec3 {
return new Vec3();
}
/** @const */
static get UNIT_X(): Vec3 {
return new Vec3(1, 0, 0);
}
/** @const */
static get UNIT_Y(): Vec3 {
return new Vec3(0, 1, 0);
}
/** @const */
static get UNIT_Z(): Vec3 {
return new Vec3(0, 0, 1);
}
/** @const */
static get NORTH(): Vec3 {
return Vec3.UNIT_Z;
}
/**
* Separate 63 bit Vec3 to two Vec3 32-bit float values.
* @function
* @param {Vec3} v - Double type value.
* @param {Vec3} high - Out vector high values.
* @param {Vec3} low - Out vector low values.
*/
static doubleToTwoFloats(v: Vec3, high: Vec3, low: Vec3) {
let x = v.x,
y = v.y,
z = v.z;
if (x >= 0.0) {
let doubleHigh = Math.floor(x / 65536.0) * 65536.0;
high.x = Math.fround(doubleHigh);
low.x = Math.fround(x - doubleHigh);
} else {
let doubleHigh = Math.floor(-x / 65536.0) * 65536.0;
high.x = Math.fround(-doubleHigh);
low.x = Math.fround(x + doubleHigh);
}
if (y >= 0.0) {
let doubleHigh = Math.floor(y / 65536.0) * 65536.0;
high.y = Math.fround(doubleHigh);
low.y = Math.fround(y - doubleHigh);
} else {
let doubleHigh = Math.floor(-y / 65536.0) * 65536.0;
high.y = Math.fround(-doubleHigh);
low.y = Math.fround(y + doubleHigh);
}
if (z >= 0.0) {
let doubleHigh = Math.floor(z / 65536.0) * 65536.0;
high.z = Math.fround(doubleHigh);
low.z = Math.fround(z - doubleHigh);
} else {
let doubleHigh = Math.floor(-z / 65536.0) * 65536.0;
high.z = Math.fround(-doubleHigh);
low.z = Math.fround(z + doubleHigh);
}
}
/**
* Separate 63 bit Vec3 to two Vec3 32-bit float values.
* @function
* @param {Vec3} v - Double type value.
* @param {Float32Array} high - Out vector high values.
* @param {Float32Array} low - Out vector low values.
* @returns {Array.<number>} Encoded array. (exactly 2 entries)
*/
static doubleToTwoFloat32Array(v: Vec3, high: Float32Array | NumberArray3, low: Float32Array | NumberArray3) {
let x = v.x,
y = v.y,
z = v.z;
if (x >= 0.0) {
let doubleHigh = Math.floor(x / 65536.0) * 65536.0;
high[0] = Math.fround(doubleHigh);
low[0] = Math.fround(x - doubleHigh);
} else {
let doubleHigh = Math.floor(-x / 65536.0) * 65536.0;
high[0] = Math.fround(-doubleHigh);
low[0] = Math.fround(x + doubleHigh);
}
if (y >= 0.0) {
let doubleHigh = Math.floor(y / 65536.0) * 65536.0;
high[1] = Math.fround(doubleHigh);
low[1] = Math.fround(y - doubleHigh);
} else {
let doubleHigh = Math.floor(-y / 65536.0) * 65536.0;
high[1] = Math.fround(-doubleHigh);
low[1] = Math.fround(y + doubleHigh);
}
if (z >= 0.0) {
let doubleHigh = Math.floor(z / 65536.0) * 65536.0;
high[2] = Math.fround(doubleHigh);
low[2] = Math.fround(z - doubleHigh);
} else {
let doubleHigh = Math.floor(-z / 65536.0) * 65536.0;
high[2] = Math.fround(-doubleHigh);
low[2] = Math.fround(z + doubleHigh);
}
}
/**
* Creates 3d vector from array.
* @function
* @param {NumberArray2 | NumberArray3 | NumberArray4} arr - Input array (exactly 3 entries)
* @returns {Vec3} -
*/
static fromVec(arr: NumberArray2 | NumberArray3 | NumberArray4): Vec3 {
return new Vec3(arr[0], arr[1], arr[2]);
}
/**
* Gets angle between two vectors.
* @static
* @param {Vec3} a - First vector.
* @param {Vec3} b - Second vector.
* @returns {number} -
*/
static angle(a: Vec3, b: Vec3): number {
return Math.acos(a.dot(b) / Math.sqrt(a.length2() * b.length2()));
}
/**
* Returns two vectors linear interpolation.
* @static
* @param {Vec3} v1 - Start vector.
* @param {Vec3} v2 - End vector.
* @param {number} l - Interpolate value.
* @returns {Vec3} -
*/
static lerp(v1: Vec3, v2: Vec3, l: number) {
return new Vec3(v1.x + (v2.x - v1.x) * l, v1.y + (v2.y - v1.y) * l, v1.z + (v2.z - v1.z) * l);
}
/**
* Returns summary vector.
* @static
* @param {Vec3} a - First vector.
* @param {Vec3} b - Second vector.
* @returns {Vec3} - Summary vector.
*/
static add(a: Vec3, b: Vec3): Vec3 {
let res = new Vec3(a.x, a.y, a.z);
res.addA(b);
return res;
}
/**
* Returns two vectors subtraction.
* @static
* @param {Vec3} a - First vector.
* @param {Vec3} b - Second vector.
* @returns {Vec3} - Vectors subtraction.
*/
static sub(a: Vec3, b: Vec3): Vec3 {
let res = new Vec3(a.x, a.y, a.z);
res.subA(b);
return res;
}
/**
* Returns scaled vector.
* @static
* @param {Vec3} a - Input vector.
* @param {number} scale - Scale value.
* @returns {Vec3} -
*/
static scale(a: Vec3, scale: number): Vec3 {
return a.scaleTo(scale);
}
/**
* Returns two vectors production.
* @static
* @param {Vec3} a - First vector.
* @param {Vec3} b - Second vector.
* @returns {Vec3} -
*/
static mul(a: Vec3, b: Vec3): Vec3 {
let res = new Vec3(a.x, a.y, a.z);
res.mulA(b);
return res;
}
/**
* Returns true if two vectors are non-collinear.
* @public
* @param {Vec3} a - First vector.
* @param {Vec3} b - Second vector.
* @returns {Vec3} -
*/
static noncollinear(a: Vec3, b: Vec3): boolean {
return Boolean(a.y * b.z - a.z * b.y || a.z * b.x - a.x * b.z || a.x * b.y - a.y * b.z);
}
/**
* Get projection of the vector to plane where n - normal to the plane.
* @static
* @param {Vec3} b - Vector to project.
* @param {Vec3} n - Plane normal.
* @param {Vec3} [def] - Default value for non existed result.
* @returns {Vec3} -
*/
static proj_b_to_plane(b: Vec3, n: Vec3, def?: Vec3): Vec3 {
let res = b.sub(n.scaleTo(n.dot(b) / n.dot(n)));
if (def && res.isZero()) {
return new Vec3(def.x, def.y, def.z);
}
return res;
}
/**
* Get projection of the first vector to the second.
* @static
* @param {Vec3} b - First vector.
* @param {Vec3} a - Second vector.
* @returns {Vec3} -
*/
static proj_b_to_a(b: Vec3, a: Vec3): Vec3 {
return a.scaleTo(a.dot(b) / a.dot(a));
}
/**
* Makes vectors normalized and orthogonal to each other.
* Normalizes normal. Normalizes tangent and makes sure it is orthogonal to normal (that is, angle between them is 90 degrees).
* @static
* @param {Vec3} normal - Normal vector.
* @param {Vec3} tangent - Tangent vector.
* @returns {Vec3} -
*/
static orthoNormalize(normal: Vec3, tangent: Vec3): Vec3 {
normal = normal.getNormal();
normal.scale(tangent.dot(normal));
return tangent.subA(normal).normalize();
}
/**
* Returns vector components division product one to another.
* @static
* @param {Vec3} a - First vector.
* @param {Vec3} b - Second vector.
* @returns {Vec3} -
*/
static div(a: Vec3, b: Vec3): Vec3 {
let res = new Vec3(a.x, a.y, a.z);
res.divA(b);
return res;
}
static length2(a: Vec3): number {
return a.length2();
}
// static length(a: Vec3): number {
// return a.length();
// }
static dot(a: Vec3, b: Vec3): number {
return a.dot(b);
}
/**
* Converts to 4d vector, Fourth value is 1.0.
* @public
* @returns {Vec4} -
*/
public toVec4(): Vec4 {
return new Vec4(this.x, this.y, this.z, 1.0);
}
/**
* Returns clone vector.
* @public
* @returns {Vec3} -
*/
public clone(): Vec3 {
return new Vec3(this.x, this.y, this.z);
}
/**
* Converts vector to text string.
* @public
* @returns {string} -
*/
public toString(): string {
return `(${this.x},${this.y},${this.z})`;
}
/**
* Returns true if vector's values are zero.
* @public
* @returns {boolean} -
*/
public isZero(): boolean {
return !(this.x || this.y || this.z);
}
/**
* Get projection of the first vector to the second.
* @static
* @param {Vec3} a - Project vector.
* @returns {Vec3} -
*/
public projToVec(a: Vec3): Vec3 {
return a.scaleTo(a.dot(this) / a.dot(a));
}
/**
* Compares with vector. Returns true if it equals another.
* @public
* @param {Vec3} p - Vector to compare.
* @returns {boolean} -
*/
public equal(p: Vec3): boolean {
return this.x === p.x && this.y === p.y && this.z === p.z;
}
/**
* Copy input vector's values.
* @param {Vec3} p - Vector to copy.
* @returns {Vec3} -
*/
public copy(p: Vec3): Vec3 {
this.x = p.x;
this.y = p.y;
this.z = p.z;
return this;
}
/**
* Gets vector's length.
* @public
* @returns {number} -
*/
public length(): number {
return Math.sqrt(this.x * this.x + this.y * this.y + this.z * this.z);
}
/**
* Returns squared vector's length.
* @public
* @returns {number} -
*/
public length2(): number {
return this.x * this.x + this.y * this.y + this.z * this.z;
}
/**
* Converts vector's values to a quaternion object.
* @public
* @returns {Quat} -
*/
public getQuat(): Quat {
return new Quat(this.x, this.y, this.z);
}
/**
* Adds vector to the current.
* @public
* @param {Vec3} p - Point to add.
* @returns {Vec3} -
*/
public addA(p: Vec3): Vec3 {
this.x += p.x;
this.y += p.y;
this.z += p.z;
return this;
}
/**
* Gets two vectors summarization.
* @public
* @param {Vec3} p - Vector to add.
* @returns {Vec3} Returns a sum vector.
*/
public add(p: Vec3): Vec3 {
return new Vec3(this.x + p.x, this.y + p.y, this.z + p.z);
}
/**
* Subtract vector from the current.
* @public
* @param {Vec3} p - Subtract vector.
* @returns {Vec3} -
*/
public subA(p: Vec3): Vec3 {
this.x -= p.x;
this.y -= p.y;
this.z -= p.z;
return this;
}
/**
* Gets vector subtraction.
* @public
* @param {Vec3} p - Subtract vector.
* @return {Vec3} Returns new instance of a subtraction
*/
public sub(p: Vec3): Vec3 {
return new Vec3(this.x - p.x, this.y - p.y, this.z - p.z);
}
/**
* Scale current vector.
* @public
* @param {number} scale - Scale value.
* @returns {Vec3} -
*/
public scale(scale: number): Vec3 {
this.x *= scale;
this.y *= scale;
this.z *= scale;
return this;
}
/**
* Scale current vector to another instance.
* @public
* @param {number} scale - Scale value.
* @returns {Vec3} -
*/
public scaleTo(scale: number): Vec3 {
return new Vec3(this.x * scale, this.y * scale, this.z * scale);
}
/**
* Multiply current vector object to another and store result in the current instance.
* @public
* @param {Vec3} vec - Multiply vector.
* @returns {Vec3} -
*/
public mulA(vec: Vec3): Vec3 {
this.x *= vec.x;
this.y *= vec.y;
this.z *= vec.z;
return this;
}
/**
* Multiply current vector object to another and returns new vector instance.
* @public
* @param {Vec3} vec - Multiply vector.
* @returns {Vec3} -
*/
public mul(vec: Vec3): Vec3 {
return new Vec3(this.x * vec.x, this.y * vec.y, this.z * vec.z);
}
/**
* Divide current vector's components to another. Results stores in the current vector object.
* @public
* @param {Vec3} vec - Div vector.
* @returns {Vec3} -
*/
public divA(vec: Vec3): Vec3 {
this.x /= vec.x;
this.y /= vec.y;
this.z /= vec.z;
return this;
}
/**
* Divide current vector's components to another and returns new vector instance.
* @public
* @param {Vec3} vec - Div vector.
* @returns {Vec3} -
*/
public div(vec: Vec3): Vec3 {
return new Vec3(this.x / vec.x, this.y / vec.y, this.z / vec.z);
}
/**
* Gets vectors dot production.
* @public
* @param {Vec3} a - Another vector.
* @returns {number} -
*/
public dot(a: Vec3): number {
return a.x * this.x + a.y * this.y + a.z * this.z;
}
/**
* Gets vectors dot production.
* @public
* @param {Array.<number>} arr - Array vector. (exactly 3 entries)
* @returns {number} -
*/
public dotArr(arr: NumberArray3 | NumberArray4): number {
return arr[0] * this.x + arr[1] * this.y + arr[2] * this.z;
}
/**
* Gets vectors cross production.
* @public
* @param {Vec3} point3 - Another vector.
* @returns {Vec3} -
*/
public cross(point3: Vec3): Vec3 {
return new Vec3(
this.y * point3.z - this.z * point3.y,
this.z * point3.x - this.x * point3.z,
this.x * point3.y - this.y * point3.x
);
}
/**
* Sets vector to zero.
* @public
* @returns {Vec3} -
*/
public clear(): Vec3 {
this.x = this.y = this.z = 0;
return this;
}
/**
* Returns normalized vector.
* @public
* @returns {Vec3} -
*/
public getNormal(): Vec3 {
let res = new Vec3();
res.copy(this);
let length = 1.0 / res.length();
res.x *= length;
res.y *= length;
res.z *= length;
return res;
}
/**
* Returns normalized vector.
* @deprecated
* @public
* @returns {Vec3} -
*/
public normal(): Vec3 {
let res = new Vec3();
res.copy(this);
let length = 1.0 / res.length();
res.x *= length;
res.y *= length;
res.z *= length;
return res;
}
/**
* Returns normalized negate vector.
* @public
* @returns {Vec3} -
*/
public normalNegate(): Vec3 {
let res = new Vec3();
res.copy(this);
let length = -1.0 / res.length();
res.x *= length;
res.y *= length;
res.z *= length;
return res;
}
/**
* Returns normalized negate scale vector.
* @public
* @returns {Vec3} -
*/
public normalNegateScale(scale: number): Vec3 {
let res = new Vec3();
res.copy(this);
let length = -scale / res.length();
res.x *= length;
res.y *= length;
res.z *= length;
return res;
}
/**
* Returns normalized scale vector.
* @public
* @returns {Vec3} -
*/
public normalScale(scale: number): Vec3 {
let res = new Vec3();
res.copy(this);
let length = scale / res.length();
res.x *= length;
res.y *= length;
res.z *= length;
return res;
}
/**
* Normalize current vector.
* @public
* @returns {Vec3} -
*/
public normalize(): Vec3 {
let length = 1.0 / this.length();
this.x *= length;
this.y *= length;
this.z *= length;
return this;
}
/**
* Converts vector to a number array.
* @public
* @returns {Array.<number>} - (exactly 3 entries)
* @deprecated
*/
public toVec(): NumberArray3 {
return [this.x, this.y, this.z];
}
/**
* Converts vector to a number array.
* @public
* @returns {Array.<number>} - (exactly 3 entries)
*/
public toArray(): NumberArray3 {
return [this.x, this.y, this.z];
}
/**
* Gets distance to point.
* @public
* @param {Vec3} p - Distant point.
* @returns {number} -
*/
public distance(p: Vec3): number {
let dx = this.x - p.x,
dy = this.y - p.y,
dz = this.z - p.z;
return Math.sqrt(dx * dx + dy * dy + dz * dz);
}
/**
* Gets square distance to point.
* @public
* @param {Vec3} p - Distant point.
* @returns {number} -
*/
public distance2(p: Vec3): number {
let dx = this.x - p.x,
dy = this.y - p.y,
dz = this.z - p.z;
return dx * dx + dy * dy + dz * dz;
}
/**
* Sets vector's values.
* @public
* @param {number} x - Value X.
* @param {number} y - Value Y.
* @param {number} z - Value Z.
* @returns {Vec3} -
*/
public set(x: number, y: number, z: number): Vec3 {
this.x = x;
this.y = y;
this.z = z;
return this;
}
/**
* Negate current vector.
* @public
* @returns {Vec3} -
*/
public negate(): Vec3 {
this.x = -this.x;
this.y = -this.y;
this.z = -this.z;
return this;
}
/**
* Negate current vector to another instance.
* @public
* @returns {Vec3} -
*/
public negateTo(): Vec3 {
return new Vec3(-this.x, -this.y, -this.z);
}
/**
* Gets projected point coordinates of the current vector on the ray.
* @public
* @param {Vec3} pos - Ray position.
* @param {Vec3} direction - Ray direction.
* @returns {Vec3} -
*/
public projToRay(pos: Vec3, direction: Vec3): Vec3 {
let v = Vec3.proj_b_to_a(Vec3.sub(this, pos), direction);
v.addA(pos);
return v;
}
/**
* Gets angle between two vectors.
* @public
* @param {Vec3} a - Another vector.
* @returns {number} -
*/
public angle(a: Vec3): number {
return Vec3.angle(this, a);
}
/**
* Returns two vectors linear interpolation.
* @public
* @param {Vec3} v2 - End vector.
* @param {number} l - Interpolate value.
* @returns {Vec3} -
*/
public lerp(v2: Vec3, l: number) {
return new Vec3(
this.x + (v2.x - this.x) * l,
this.y + (v2.y - this.y) * l,
this.z + (v2.z - this.z) * l
);
}
/**
* Returns vector interpolation by v(t) = v1 * t + v2 * (1 - t)
* @public
* @param {Vec3} v2 - End vector.
* @param {number} t - Interpolate value.
* @returns {Vec3} -
*/
public smerp(v2: Vec3, t: number): Vec3 {
let one_d = 1 - t;
return new Vec3(
this.x * t + v2.x * one_d,
this.y * t + v2.y * one_d,
this.z * t + v2.z * one_d
);
}
static get LERP_DELTA(): number {
return 1e-6;
}
/**
* Spherically interpolates between two vectors.
* Interpolates between current and v2 vector by amount t. The difference between this and linear interpolation (aka, "lerp") is that
* the vectors are treated as directions rather than points in space. The direction of the returned vector is interpolated
* by the angle and its magnitude is interpolated between the magnitudes of from and to.
* @public
* @param {Vec3} v2 -
* @param {number} t - The parameter t is clamped to the range [0, 1].
* @returns {Vec3} -
*/
public slerp(v2: Vec3, t: number): Vec3 {
let res = new Vec3();
if (t <= 0.0) {
res.copy(this);
return res;
} else if (t >= 1.0) {
res.copy(v2);
return res;
}
let omega, sinom, scale0, scale1;
let cosom = this.dot(v2);
if (1.0 - cosom > Vec3.LERP_DELTA) {
omega = Math.acos(cosom);
sinom = Math.sin(omega);
scale0 = Math.sin((1.0 - t) * omega) / sinom;
scale1 = Math.sin(t * omega) / sinom;
} else {
scale0 = 1.0 - t;
scale1 = t;
}
return Vec3.add(this.scaleTo(scale0), v2.scale(scale1));
}
/**
* Gets the shortest arc quaternion to rotate this vector to the destination vector.
* @param {Vec3} dest -
* @param {Vec3} fallbackAxis -
* @returns {Quat} -
* @todo: TEST IT!
*/
public getRotationTo(dest: Vec3, fallbackAxis: Vec3): Quat {
// Based on Stan Melax's article in Game Programming Gems
// Copy, since cannot modify local
let v0 = this.clone();
let v1 = dest.clone();
v0.normalize();
v1.normalize();
let d = v0.dot(v1);
// If dot == 1, vectors are the same
if (d >= 1.0) {
return Quat.IDENTITY.clone();
}
if (d < 1e-6 - 1.0) {
if (!fallbackAxis.equal(Vec3.ZERO)) {
// rotate 180 degrees about the fallback axis
return Quat.axisAngleToQuat(fallbackAxis, Math.PI);
} else {
// Generate an axis
let axis = Vec3.UNIT_X.cross(v0);
if (axis.isZero()) {
// pick another if colinear
axis = Vec3.UNIT_Y.cross(v0);
}
axis.normalize();
return Quat.axisAngleToQuat(axis, Math.PI);
}
} else {
let s = Math.sqrt((1 + d) * 2);
let invs = 1.0 / s;
let c = v0.cross(v1);
let q = new Quat(c.x * invs, c.y * invs, c.z * invs, s * 0.5);
q.normalize();
return q;
}
}
}
/**
* Vector 3d object creator.
* @function
* @param {number} [x] - value X.
* @param {number} [y] - value Y.
* @param {number} [z] - value Z.
* @returns {Vec3} -
*/
export function vec3(x: number = 0, y: number = 0, z: number = 0): Vec3 {
return new Vec3(x, y, z);
}