src/Vector4.js
/**
* A vector with four components.
*/
export class Vector4 {
/**
* Constructs a new vector.
*
* @param {Number} [x=0] - The X component.
* @param {Number} [y=0] - The Y component.
* @param {Number} [z=0] - The Z component.
* @param {Number} [w=0] - The W component.
*/
constructor(x = 0, y = 0, z = 0, w = 0) {
/**
* The X component.
*
* @type {Number}
*/
this.x = x;
/**
* The Y component.
*
* @type {Number}
*/
this.y = y;
/**
* The Z component.
*
* @type {Number}
*/
this.z = z;
/**
* The W component.
*
* @type {Number}
*/
this.w = w;
}
/**
* Sets the values of this vector
*
* @param {Number} x - The X component.
* @param {Number} y - The Y component.
* @param {Number} z - The Z component.
* @param {Number} w - The W component.
* @return {Vector4} This vector.
*/
set(x, y, z, w) {
this.x = x;
this.y = y;
this.z = z;
this.w = w;
return this;
}
/**
* Randomizes the values of this vector
*
* @return {Vector4} This vector.
*/
random() {
this.x = Math.random();
this.y = Math.random();
this.z = Math.random();
this.w = Math.random();
return this;
}
/**
* Copies the values of another vector.
*
* @param {Vector4} v - A vector.
* @return {Vector4} This vector.
*/
copy(v) {
this.x = v.x;
this.y = v.y;
this.z = v.z;
this.w = v.w;
return this;
}
/**
* Clones this vector.
*
* @return {Vector4} A clone of this vector.
*/
clone() {
return new this.constructor(this.x, this.y, this.z, this.w);
}
/**
* Copies values from an array.
*
* @param {Number[]} array - An array.
* @param {Number} offset - An offset.
* @return {Vector4} This vector.
*/
fromArray(array, offset = 0) {
this.x = array[offset];
this.y = array[offset + 1];
this.z = array[offset + 2];
this.w = array[offset + 3];
return this;
}
/**
* Stores this vector in an array.
*
* @param {Array} [array] - A target array.
* @param {Number} offset - An offset.
* @return {Number[]} The array.
*/
toArray(array = [], offset = 0) {
array[offset] = this.x;
array[offset + 1] = this.y;
array[offset + 2] = this.z;
array[offset + 3] = this.w;
return array;
}
/**
* Stores the axis angle from the given quaternion in this vector.
*
* For more details see:
* http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToAngle/index.htm
*
* @param {Quaternion} q - A quaternion. Assumed to be normalized
* @return {Vector4} This vector.
*/
setAxisAngleFromQuaternion(q) {
this.w = 2 * Math.acos(q.w);
const s = Math.sqrt(1 - q.w * q.w);
if(s < 1e-4) {
this.x = 1;
this.y = 0;
this.z = 0;
} else {
this.x = q.x / s;
this.y = q.y / s;
this.z = q.z / s;
}
return this;
}
/**
* Stores the axis angle from the given rotation matrix in this vector.
*
* For more details see:
* http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToAngle/index.htm
*
* @param {Matrix4} m - A matrix. The upper 3x3 must be a pure rotation matrix (i.e. unscaled).
* @return {Vector4} This vector.
*/
setAxisAngleFromRotationMatrix(m) {
// Margin to allow for rounding errors.
const E = 0.01;
// Margin to distinguish between 0 and 180 degrees.
const H = 0.1;
const me = m.elements;
const m00 = me[0], m01 = me[4], m02 = me[8];
const m10 = me[1], m11 = me[5], m12 = me[9];
const m20 = me[2], m21 = me[6], m22 = me[10];
let angle;
let x, y, z;
let xx, yy, zz;
let xy, xz, yz;
let s;
if((Math.abs(m01 - m10) < E) && (Math.abs(m02 - m20) < E) && (Math.abs(m12 - m21) < E)) {
/* Singularity found. First, check for identity matrix which must have +1
for all terms in the leading diagonal and zero in other terms. */
if((Math.abs(m01 + m10) < H) && (Math.abs(m02 + m20) < H) && (Math.abs(m12 + m21) < H) && (Math.abs(m00 + m11 + m22 - 3) < H)) {
// This singularity is the identity matrix. The angle is zero.
this.set(1, 0, 0, 0);
} else {
// The angle is 180.
angle = Math.PI;
xx = (m00 + 1) / 2;
yy = (m11 + 1) / 2;
zz = (m22 + 1) / 2;
xy = (m01 + m10) / 4;
xz = (m02 + m20) / 4;
yz = (m12 + m21) / 4;
if((xx > yy) && (xx > zz)) {
// m00 is the largest diagonal term.
if(xx < E) {
x = 0;
y = 0.707106781;
z = 0.707106781;
} else {
x = Math.sqrt(xx);
y = xy / x;
z = xz / x;
}
} else if(yy > zz) {
// m11 is the largest diagonal term.
if(yy < E) {
x = 0.707106781;
y = 0;
z = 0.707106781;
} else {
y = Math.sqrt(yy);
x = xy / y;
z = yz / y;
}
} else {
// m22 is the largest diagonal term.
if(zz < E) {
x = 0.707106781;
y = 0.707106781;
z = 0;
} else {
z = Math.sqrt(zz);
x = xz / z;
y = yz / z;
}
}
this.set(x, y, z, angle);
}
} else {
// There are no singularities.
s = Math.sqrt(
(m21 - m12) * (m21 - m12) +
(m02 - m20) * (m02 - m20) +
(m10 - m01) * (m10 - m01)
);
// Prevent division by zero.
if(Math.abs(s) < 0.001) {
s = 1;
}
this.x = (m21 - m12) / s;
this.y = (m02 - m20) / s;
this.z = (m10 - m01) / s;
this.w = Math.acos((m00 + m11 + m22 - 1) / 2);
}
return this;
}
/**
* Adds a vector to this one.
*
* @param {Vector4} v - The vector to add.
* @return {Vector4} This vector.
*/
add(v) {
this.x += v.x;
this.y += v.y;
this.z += v.z;
this.w += v.w;
return this;
}
/**
* Adds a scalar to this vector.
*
* @param {Number} s - The scalar to add.
* @return {Vector4} This vector.
*/
addScalar(s) {
this.x += s;
this.y += s;
this.z += s;
this.w += s;
return this;
}
/**
* Sets this vector to the sum of two given vectors.
*
* @param {Vector4} a - A vector.
* @param {Vector4} b - Another vector.
* @return {Vector4} This vector.
*/
addVectors(a, b) {
this.x = a.x + b.x;
this.y = a.y + b.y;
this.z = a.z + b.z;
this.w = a.w + b.w;
return this;
}
/**
* Adds a scaled vector to this one.
*
* @param {Vector4} v - The vector to scale and add.
* @param {Number} s - A scalar.
* @return {Vector4} This vector.
*/
addScaledVector(v, s) {
this.x += v.x * s;
this.y += v.y * s;
this.z += v.z * s;
this.w += v.w * s;
return this;
}
/**
* Subtracts a vector from this vector.
*
* @param {Vector4} v - The vector to subtract.
* @return {Vector4} This vector.
*/
sub(v) {
this.x -= v.x;
this.y -= v.y;
this.z -= v.z;
this.w -= v.w;
return this;
}
/**
* Subtracts a scalar from this vector.
*
* @param {Number} s - The scalar to subtract.
* @return {Vector4} This vector.
*/
subScalar(s) {
this.x -= s;
this.y -= s;
this.z -= s;
this.w -= s;
return this;
}
/**
* Sets this vector to the difference between two given vectors.
*
* @param {Vector4} a - A vector.
* @param {Vector4} b - A second vector.
* @return {Vector4} This vector.
*/
subVectors(a, b) {
this.x = a.x - b.x;
this.y = a.y - b.y;
this.z = a.z - b.z;
this.w = a.w - b.w;
return this;
}
/**
* Multiplies this vector with another vector.
*
* @param {Vector4} v - A vector.
* @return {Vector4} This vector.
*/
multiply(v) {
this.x *= v.x;
this.y *= v.y;
this.z *= v.z;
this.w *= v.w;
return this;
}
/**
* Multiplies this vector with a given scalar.
*
* @param {Number} s - A scalar.
* @return {Vector4} This vector.
*/
multiplyScalar(s) {
this.x *= s;
this.y *= s;
this.z *= s;
this.w *= s;
return this;
}
/**
* Sets this vector to the product of two given vectors.
*
* @param {Vector4} a - A vector.
* @param {Vector4} b - Another vector.
* @return {Vector4} This vector.
*/
multiplyVectors(a, b) {
this.x = a.x * b.x;
this.y = a.y * b.y;
this.z = a.z * b.z;
this.w = a.w * b.w;
return this;
}
/**
* Divides this vector by another vector.
*
* @param {Vector4} v - A vector.
* @return {Vector4} This vector.
*/
divide(v) {
this.x /= v.x;
this.y /= v.y;
this.z /= v.z;
this.w /= v.w;
return this;
}
/**
* Divides this vector by a given scalar.
*
* @param {Number} s - A scalar.
* @return {Vector4} This vector.
*/
divideScalar(s) {
this.x /= s;
this.y /= s;
this.z /= s;
this.w /= s;
return this;
}
/**
* Applies a matrix to this vector.
*
* @param {Matrix4} m - A matrix.
* @return {Vector4} This vector.
*/
applyMatrix4(m) {
const x = this.x, y = this.y, z = this.z, w = this.w;
const e = m.elements;
this.x = e[0] * x + e[4] * y + e[8] * z + e[12] * w;
this.y = e[1] * x + e[5] * y + e[9] * z + e[13] * w;
this.z = e[2] * x + e[6] * y + e[10] * z + e[14] * w;
this.w = e[3] * x + e[7] * y + e[11] * z + e[15] * w;
return this;
}
/**
* Negates this vector.
*
* @return {Vector4} This vector.
*/
negate() {
this.x = -this.x;
this.y = -this.y;
this.z = -this.z;
this.w = -this.w;
return this;
}
/**
* Calculates the dot product with another vector.
*
* @param {Vector4} v - A vector.
* @return {Number} The dot product.
*/
dot(v) {
return this.x * v.x + this.y * v.y + this.z * v.z + this.w * v.w;
}
/**
* Calculates the Manhattan length of this vector.
*
* @return {Number} The length.
*/
manhattanLength() {
return Math.abs(this.x) + Math.abs(this.y) + Math.abs(this.z) + Math.abs(this.w);
}
/**
* Calculates the squared length of this vector.
*
* @return {Number} The squared length.
*/
lengthSquared() {
return (
this.x * this.x +
this.y * this.y +
this.z * this.z +
this.w * this.w
);
}
/**
* Calculates the length of this vector.
*
* @return {Number} The length.
*/
length() {
return Math.sqrt(
this.x * this.x +
this.y * this.y +
this.z * this.z +
this.w * this.w
);
}
/**
* Calculates the Manhattan distance to a given vector.
*
* @param {Vector4} v - A vector.
* @return {Number} The distance.
*/
manhattanDistanceTo(v) {
return (
Math.abs(this.x - v.x) +
Math.abs(this.y - v.y) +
Math.abs(this.z - v.z) +
Math.abs(this.w - v.w)
);
}
/**
* Calculates the squared distance to a given vector.
*
* @param {Vector4} v - A vector.
* @return {Number} The squared distance.
*/
distanceToSquared(v) {
const dx = this.x - v.x;
const dy = this.y - v.y;
const dz = this.z - v.z;
const dw = this.w - v.w;
return dx * dx + dy * dy + dz * dz + dw * dw;
}
/**
* Calculates the distance to a given vector.
*
* @param {Vector4} v - A vector.
* @return {Number} The distance.
*/
distanceTo(v) {
return Math.sqrt(this.distanceToSquared(v));
}
/**
* Normalizes this vector.
*
* @return {Vector4} This vector.
*/
normalize() {
return this.divideScalar(this.length());
}
/**
* Sets the length of this vector.
*
* @param {Number} length - The new length.
* @return {Vector4} This vector.
*/
setLength(length) {
return this.normalize().multiplyScalar(length);
}
/**
* Adopts the min value for each component of this vector and the given one.
*
* @param {Vector4} v - A vector.
* @return {Vector4} This vector.
*/
min(v) {
this.x = Math.min(this.x, v.x);
this.y = Math.min(this.y, v.y);
this.z = Math.min(this.z, v.z);
this.w = Math.min(this.w, v.w);
return this;
}
/**
* Adopts the max value for each component of this vector and the given one.
*
* @param {Vector4} v - A vector.
* @return {Vector4} This vector.
*/
max(v) {
this.x = Math.max(this.x, v.x);
this.y = Math.max(this.y, v.y);
this.z = Math.max(this.z, v.z);
this.w = Math.max(this.w, v.w);
return this;
}
/**
* Clamps this vector.
*
* @param {Vector4} min - The lower bounds. Assumed to be smaller than max.
* @param {Vector4} max - The upper bounds. Assumed to be greater than min.
* @return {Vector4} This vector.
*/
clamp(min, max) {
this.x = Math.max(min.x, Math.min(max.x, this.x));
this.y = Math.max(min.y, Math.min(max.y, this.y));
this.z = Math.max(min.z, Math.min(max.z, this.z));
this.w = Math.max(min.w, Math.min(max.w, this.w));
return this;
}
/**
* Floors this vector.
*
* @return {Vector4} This vector.
*/
floor() {
this.x = Math.floor(this.x);
this.y = Math.floor(this.y);
this.z = Math.floor(this.z);
this.w = Math.floor(this.w);
return this;
}
/**
* Ceils this vector.
*
* @return {Vector4} This vector.
*/
ceil() {
this.x = Math.ceil(this.x);
this.y = Math.ceil(this.y);
this.z = Math.ceil(this.z);
this.w = Math.ceil(this.w);
return this;
}
/**
* Rounds this vector.
*
* @return {Vector4} This vector.
*/
round() {
this.x = Math.round(this.x);
this.y = Math.round(this.y);
this.z = Math.round(this.z);
this.w = Math.round(this.w);
return this;
}
/**
* Lerps towards the given vector.
*
* @param {Vector4} v - The target vector.
* @param {Number} alpha - The lerp factor.
* @return {Vector4} This vector.
*/
lerp(v, alpha) {
this.x += (v.x - this.x) * alpha;
this.y += (v.y - this.y) * alpha;
this.z += (v.z - this.z) * alpha;
this.w += (v.w - this.w) * alpha;
return this;
}
/**
* Sets this vector to the lerp result of the given vectors.
*
* @param {Vector4} v1 - A base vector.
* @param {Vector4} v2 - The target vector.
* @param {Number} alpha - The lerp factor.
* @return {Vector4} This vector.
*/
lerpVectors(v1, v2, alpha) {
return this.subVectors(v2, v1).multiplyScalar(alpha).add(v1);
}
/**
* Checks if this vector equals the given one.
*
* @param {Vector4} v - A vector.
* @return {Boolean} Whether this vector equals the given one.
*/
equals(v) {
return (v.x === this.x && v.y === this.y && v.z === this.z && v.w === this.w);
}
}
