three
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JavaScript 3D library
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JavaScript
import { clamp } from './MathUtils.js';
/**
* Class representing a 4D vector. A 4D vector is an ordered quadruplet of numbers
* (labeled x, y, z and w), which can be used to represent a number of things, such as:
*
* - A point in 4D space.
* - A direction and length in 4D space. In three.js the length will
* always be the Euclidean distance(straight-line distance) from `(0, 0, 0, 0)` to `(x, y, z, w)`
* and the direction is also measured from `(0, 0, 0, 0)` towards `(x, y, z, w)`.
* - Any arbitrary ordered quadruplet of numbers.
*
* There are other things a 4D vector can be used to represent, however these
* are the most common uses in *three.js*.
*
* Iterating through a vector instance will yield its components `(x, y, z, w)` in
* the corresponding order.
* ```js
* const a = new THREE.Vector4( 0, 1, 0, 0 );
*
* //no arguments; will be initialised to (0, 0, 0, 1)
* const b = new THREE.Vector4( );
*
* const d = a.dot( b );
* ```
*/
class Vector4 {
/**
* Constructs a new 4D vector.
*
* @param {number} [x=0] - The x value of this vector.
* @param {number} [y=0] - The y value of this vector.
* @param {number} [z=0] - The z value of this vector.
* @param {number} [w=1] - The w value of this vector.
*/
constructor( x = 0, y = 0, z = 0, w = 1 ) {
/**
* This flag can be used for type testing.
*
* @type {boolean}
* @readonly
* @default true
*/
Vector4.prototype.isVector4 = true;
/**
* The x value of this vector.
*
* @type {number}
*/
this.x = x;
/**
* The y value of this vector.
*
* @type {number}
*/
this.y = y;
/**
* The z value of this vector.
*
* @type {number}
*/
this.z = z;
/**
* The w value of this vector.
*
* @type {number}
*/
this.w = w;
}
/**
* Alias for {@link Vector4#z}.
*
* @type {number}
*/
get width() {
return this.z;
}
set width( value ) {
this.z = value;
}
/**
* Alias for {@link Vector4#w}.
*
* @type {number}
*/
get height() {
return this.w;
}
set height( value ) {
this.w = value;
}
/**
* Sets the vector components.
*
* @param {number} x - The value of the x component.
* @param {number} y - The value of the y component.
* @param {number} z - The value of the z component.
* @param {number} w - The value of the w component.
* @return {Vector4} A reference to this vector.
*/
set( x, y, z, w ) {
this.x = x;
this.y = y;
this.z = z;
this.w = w;
return this;
}
/**
* Sets the vector components to the same value.
*
* @param {number} scalar - The value to set for all vector components.
* @return {Vector4} A reference to this vector.
*/
setScalar( scalar ) {
this.x = scalar;
this.y = scalar;
this.z = scalar;
this.w = scalar;
return this;
}
/**
* Sets the vector's x component to the given value
*
* @param {number} x - The value to set.
* @return {Vector4} A reference to this vector.
*/
setX( x ) {
this.x = x;
return this;
}
/**
* Sets the vector's y component to the given value
*
* @param {number} y - The value to set.
* @return {Vector4} A reference to this vector.
*/
setY( y ) {
this.y = y;
return this;
}
/**
* Sets the vector's z component to the given value
*
* @param {number} z - The value to set.
* @return {Vector4} A reference to this vector.
*/
setZ( z ) {
this.z = z;
return this;
}
/**
* Sets the vector's w component to the given value
*
* @param {number} w - The value to set.
* @return {Vector4} A reference to this vector.
*/
setW( w ) {
this.w = w;
return this;
}
/**
* Allows to set a vector component with an index.
*
* @param {number} index - The component index. `0` equals to x, `1` equals to y,
* `2` equals to z, `3` equals to w.
* @param {number} value - The value to set.
* @return {Vector4} A reference to this vector.
*/
setComponent( index, value ) {
switch ( index ) {
case 0: this.x = value; break;
case 1: this.y = value; break;
case 2: this.z = value; break;
case 3: this.w = value; break;
default: throw new Error( 'index is out of range: ' + index );
}
return this;
}
/**
* Returns the value of the vector component which matches the given index.
*
* @param {number} index - The component index. `0` equals to x, `1` equals to y,
* `2` equals to z, `3` equals to w.
* @return {number} A vector component value.
*/
getComponent( index ) {
switch ( index ) {
case 0: return this.x;
case 1: return this.y;
case 2: return this.z;
case 3: return this.w;
default: throw new Error( 'index is out of range: ' + index );
}
}
/**
* Returns a new vector with copied values from this instance.
*
* @return {Vector4} A clone of this instance.
*/
clone() {
return new this.constructor( this.x, this.y, this.z, this.w );
}
/**
* Copies the values of the given vector to this instance.
*
* @param {Vector3|Vector4} v - The vector to copy.
* @return {Vector4} A reference to this vector.
*/
copy( v ) {
this.x = v.x;
this.y = v.y;
this.z = v.z;
this.w = ( v.w !== undefined ) ? v.w : 1;
return this;
}
/**
* Adds the given vector to this instance.
*
* @param {Vector4} v - The vector to add.
* @return {Vector4} A reference to this vector.
*/
add( v ) {
this.x += v.x;
this.y += v.y;
this.z += v.z;
this.w += v.w;
return this;
}
/**
* Adds the given scalar value to all components of this instance.
*
* @param {number} s - The scalar to add.
* @return {Vector4} A reference to this vector.
*/
addScalar( s ) {
this.x += s;
this.y += s;
this.z += s;
this.w += s;
return this;
}
/**
* Adds the given vectors and stores the result in this instance.
*
* @param {Vector4} a - The first vector.
* @param {Vector4} b - The second vector.
* @return {Vector4} A reference to 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 the given vector scaled by the given factor to this instance.
*
* @param {Vector4} v - The vector.
* @param {number} s - The factor that scales `v`.
* @return {Vector4} A reference to 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 the given vector from this instance.
*
* @param {Vector4} v - The vector to subtract.
* @return {Vector4} A reference to this vector.
*/
sub( v ) {
this.x -= v.x;
this.y -= v.y;
this.z -= v.z;
this.w -= v.w;
return this;
}
/**
* Subtracts the given scalar value from all components of this instance.
*
* @param {number} s - The scalar to subtract.
* @return {Vector4} A reference to this vector.
*/
subScalar( s ) {
this.x -= s;
this.y -= s;
this.z -= s;
this.w -= s;
return this;
}
/**
* Subtracts the given vectors and stores the result in this instance.
*
* @param {Vector4} a - The first vector.
* @param {Vector4} b - The second vector.
* @return {Vector4} A reference to 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 the given vector with this instance.
*
* @param {Vector4} v - The vector to multiply.
* @return {Vector4} A reference to this vector.
*/
multiply( v ) {
this.x *= v.x;
this.y *= v.y;
this.z *= v.z;
this.w *= v.w;
return this;
}
/**
* Multiplies the given scalar value with all components of this instance.
*
* @param {number} scalar - The scalar to multiply.
* @return {Vector4} A reference to this vector.
*/
multiplyScalar( scalar ) {
this.x *= scalar;
this.y *= scalar;
this.z *= scalar;
this.w *= scalar;
return this;
}
/**
* Multiplies this vector with the given 4x4 matrix.
*
* @param {Matrix4} m - The 4x4 matrix.
* @return {Vector4} A reference to 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;
}
/**
* Divides this instance by the given vector.
*
* @param {Vector4} v - The vector to divide.
* @return {Vector4} A reference to 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 the given scalar.
*
* @param {number} scalar - The scalar to divide.
* @return {Vector4} A reference to this vector.
*/
divideScalar( scalar ) {
return this.multiplyScalar( 1 / scalar );
}
/**
* Sets the x, y and z components of this
* vector to the quaternion's axis and w to the angle.
*
* @param {Quaternion} q - The Quaternion to set.
* @return {Vector4} A reference to this vector.
*/
setAxisAngleFromQuaternion( q ) {
// http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToAngle/index.htm
// q is assumed to be normalized
this.w = 2 * Math.acos( q.w );
const s = Math.sqrt( 1 - q.w * q.w );
if ( s < 0.0001 ) {
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;
}
/**
* Sets the x, y and z components of this
* vector to the axis of rotation and w to the angle.
*
* @param {Matrix4} m - A 4x4 matrix of which the upper left 3x3 matrix is a pure rotation matrix.
* @return {Vector4} A reference to this vector.
*/
setAxisAngleFromRotationMatrix( m ) {
// http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToAngle/index.htm
// assumes the upper 3x3 of m is a pure rotation matrix (i.e, unscaled)
let angle, x, y, z; // variables for result
const epsilon = 0.01, // margin to allow for rounding errors
epsilon2 = 0.1, // margin to distinguish between 0 and 180 degrees
te = m.elements,
m11 = te[ 0 ], m12 = te[ 4 ], m13 = te[ 8 ],
m21 = te[ 1 ], m22 = te[ 5 ], m23 = te[ 9 ],
m31 = te[ 2 ], m32 = te[ 6 ], m33 = te[ 10 ];
if ( ( Math.abs( m12 - m21 ) < epsilon ) &&
( Math.abs( m13 - m31 ) < epsilon ) &&
( Math.abs( m23 - m32 ) < epsilon ) ) {
// singularity found
// first check for identity matrix which must have +1 for all terms
// in leading diagonal and zero in other terms
if ( ( Math.abs( m12 + m21 ) < epsilon2 ) &&
( Math.abs( m13 + m31 ) < epsilon2 ) &&
( Math.abs( m23 + m32 ) < epsilon2 ) &&
( Math.abs( m11 + m22 + m33 - 3 ) < epsilon2 ) ) {
// this singularity is identity matrix so angle = 0
this.set( 1, 0, 0, 0 );
return this; // zero angle, arbitrary axis
}
// otherwise this singularity is angle = 180
angle = Math.PI;
const xx = ( m11 + 1 ) / 2;
const yy = ( m22 + 1 ) / 2;
const zz = ( m33 + 1 ) / 2;
const xy = ( m12 + m21 ) / 4;
const xz = ( m13 + m31 ) / 4;
const yz = ( m23 + m32 ) / 4;
if ( ( xx > yy ) && ( xx > zz ) ) {
// m11 is the largest diagonal term
if ( xx < epsilon ) {
x = 0;
y = 0.707106781;
z = 0.707106781;
} else {
x = Math.sqrt( xx );
y = xy / x;
z = xz / x;
}
} else if ( yy > zz ) {
// m22 is the largest diagonal term
if ( yy < epsilon ) {
x = 0.707106781;
y = 0;
z = 0.707106781;
} else {
y = Math.sqrt( yy );
x = xy / y;
z = yz / y;
}
} else {
// m33 is the largest diagonal term so base result on this
if ( zz < epsilon ) {
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 );
return this; // return 180 deg rotation
}
// as we have reached here there are no singularities so we can handle normally
let s = Math.sqrt( ( m32 - m23 ) * ( m32 - m23 ) +
( m13 - m31 ) * ( m13 - m31 ) +
( m21 - m12 ) * ( m21 - m12 ) ); // used to normalize
if ( Math.abs( s ) < 0.001 ) s = 1;
// prevent divide by zero, should not happen if matrix is orthogonal and should be
// caught by singularity test above, but I've left it in just in case
this.x = ( m32 - m23 ) / s;
this.y = ( m13 - m31 ) / s;
this.z = ( m21 - m12 ) / s;
this.w = Math.acos( ( m11 + m22 + m33 - 1 ) / 2 );
return this;
}
/**
* Sets the vector components to the position elements of the
* given transformation matrix.
*
* @param {Matrix4} m - The 4x4 matrix.
* @return {Vector4} A reference to this vector.
*/
setFromMatrixPosition( m ) {
const e = m.elements;
this.x = e[ 12 ];
this.y = e[ 13 ];
this.z = e[ 14 ];
this.w = e[ 15 ];
return this;
}
/**
* If this vector's x, y, z or w value is greater than the given vector's x, y, z or w
* value, replace that value with the corresponding min value.
*
* @param {Vector4} v - The vector.
* @return {Vector4} A reference to 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;
}
/**
* If this vector's x, y, z or w value is less than the given vector's x, y, z or w
* value, replace that value with the corresponding max value.
*
* @param {Vector4} v - The vector.
* @return {Vector4} A reference to 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;
}
/**
* If this vector's x, y, z or w value is greater than the max vector's x, y, z or w
* value, it is replaced by the corresponding value.
* If this vector's x, y, z or w value is less than the min vector's x, y, z or w value,
* it is replaced by the corresponding value.
*
* @param {Vector4} min - The minimum x, y and z values.
* @param {Vector4} max - The maximum x, y and z values in the desired range.
* @return {Vector4} A reference to this vector.
*/
clamp( min, max ) {
// assumes min < max, componentwise
this.x = clamp( this.x, min.x, max.x );
this.y = clamp( this.y, min.y, max.y );
this.z = clamp( this.z, min.z, max.z );
this.w = clamp( this.w, min.w, max.w );
return this;
}
/**
* If this vector's x, y, z or w values are greater than the max value, they are
* replaced by the max value.
* If this vector's x, y, z or w values are less than the min value, they are
* replaced by the min value.
*
* @param {number} minVal - The minimum value the components will be clamped to.
* @param {number} maxVal - The maximum value the components will be clamped to.
* @return {Vector4} A reference to this vector.
*/
clampScalar( minVal, maxVal ) {
this.x = clamp( this.x, minVal, maxVal );
this.y = clamp( this.y, minVal, maxVal );
this.z = clamp( this.z, minVal, maxVal );
this.w = clamp( this.w, minVal, maxVal );
return this;
}
/**
* If this vector's length is greater than the max value, it is replaced by
* the max value.
* If this vector's length is less than the min value, it is replaced by the
* min value.
*
* @param {number} min - The minimum value the vector length will be clamped to.
* @param {number} max - The maximum value the vector length will be clamped to.
* @return {Vector4} A reference to this vector.
*/
clampLength( min, max ) {
const length = this.length();
return this.divideScalar( length || 1 ).multiplyScalar( clamp( length, min, max ) );
}
/**
* The components of this vector are rounded down to the nearest integer value.
*
* @return {Vector4} A reference to 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;
}
/**
* The components of this vector are rounded up to the nearest integer value.
*
* @return {Vector4} A reference to 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;
}
/**
* The components of this vector are rounded to the nearest integer value
*
* @return {Vector4} A reference to 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;
}
/**
* The components of this vector are rounded towards zero (up if negative,
* down if positive) to an integer value.
*
* @return {Vector4} A reference to this vector.
*/
roundToZero() {
this.x = Math.trunc( this.x );
this.y = Math.trunc( this.y );
this.z = Math.trunc( this.z );
this.w = Math.trunc( this.w );
return this;
}
/**
* Inverts this vector - i.e. sets x = -x, y = -y, z = -z, w = -w.
*
* @return {Vector4} A reference to 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 of the given vector with this instance.
*
* @param {Vector4} v - The vector to compute the dot product with.
* @return {number} The result of the dot product.
*/
dot( v ) {
return this.x * v.x + this.y * v.y + this.z * v.z + this.w * v.w;
}
/**
* Computes the square of the Euclidean length (straight-line length) from
* (0, 0, 0, 0) to (x, y, z, w). If you are comparing the lengths of vectors, you should
* compare the length squared instead as it is slightly more efficient to calculate.
*
* @return {number} The square length of this vector.
*/
lengthSq() {
return this.x * this.x + this.y * this.y + this.z * this.z + this.w * this.w;
}
/**
* Computes the Euclidean length (straight-line length) from (0, 0, 0, 0) to (x, y, z, w).
*
* @return {number} The length of this vector.
*/
length() {
return Math.sqrt( this.x * this.x + this.y * this.y + this.z * this.z + this.w * this.w );
}
/**
* Computes the Manhattan length of this vector.
*
* @return {number} The length of this vector.
*/
manhattanLength() {
return Math.abs( this.x ) + Math.abs( this.y ) + Math.abs( this.z ) + Math.abs( this.w );
}
/**
* Converts this vector to a unit vector - that is, sets it equal to a vector
* with the same direction as this one, but with a vector length of `1`.
*
* @return {Vector4} A reference to this vector.
*/
normalize() {
return this.divideScalar( this.length() || 1 );
}
/**
* Sets this vector to a vector with the same direction as this one, but
* with the specified length.
*
* @param {number} length - The new length of this vector.
* @return {Vector4} A reference to this vector.
*/
setLength( length ) {
return this.normalize().multiplyScalar( length );
}
/**
* Linearly interpolates between the given vector and this instance, where
* alpha is the percent distance along the line - alpha = 0 will be this
* vector, and alpha = 1 will be the given one.
*
* @param {Vector4} v - The vector to interpolate towards.
* @param {number} alpha - The interpolation factor, typically in the closed interval `[0, 1]`.
* @return {Vector4} A reference to 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;
}
/**
* Linearly interpolates between the given vectors, where alpha is the percent
* distance along the line - alpha = 0 will be first vector, and alpha = 1 will
* be the second one. The result is stored in this instance.
*
* @param {Vector4} v1 - The first vector.
* @param {Vector4} v2 - The second vector.
* @param {number} alpha - The interpolation factor, typically in the closed interval `[0, 1]`.
* @return {Vector4} A reference to this vector.
*/
lerpVectors( v1, v2, alpha ) {
this.x = v1.x + ( v2.x - v1.x ) * alpha;
this.y = v1.y + ( v2.y - v1.y ) * alpha;
this.z = v1.z + ( v2.z - v1.z ) * alpha;
this.w = v1.w + ( v2.w - v1.w ) * alpha;
return this;
}
/**
* Returns `true` if this vector is equal with the given one.
*
* @param {Vector4} v - The vector to test for equality.
* @return {boolean} Whether this vector is equal with the given one.
*/
equals( v ) {
return ( ( v.x === this.x ) && ( v.y === this.y ) && ( v.z === this.z ) && ( v.w === this.w ) );
}
/**
* Sets this vector's x value to be `array[ offset ]`, y value to be `array[ offset + 1 ]`,
* z value to be `array[ offset + 2 ]`, w value to be `array[ offset + 3 ]`.
*
* @param {Array<number>} array - An array holding the vector component values.
* @param {number} [offset=0] - The offset into the array.
* @return {Vector4} A reference to 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;
}
/**
* Writes the components of this vector to the given array. If no array is provided,
* the method returns a new instance.
*
* @param {Array<number>} [array=[]] - The target array holding the vector components.
* @param {number} [offset=0] - Index of the first element in the array.
* @return {Array<number>} The vector components.
*/
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;
}
/**
* Sets the components of this vector from the given buffer attribute.
*
* @param {BufferAttribute} attribute - The buffer attribute holding vector data.
* @param {number} index - The index into the attribute.
* @return {Vector4} A reference to this vector.
*/
fromBufferAttribute( attribute, index ) {
this.x = attribute.getX( index );
this.y = attribute.getY( index );
this.z = attribute.getZ( index );
this.w = attribute.getW( index );
return this;
}
/**
* Sets each component of this vector to a pseudo-random value between `0` and
* `1`, excluding `1`.
*
* @return {Vector4} A reference to this vector.
*/
random() {
this.x = Math.random();
this.y = Math.random();
this.z = Math.random();
this.w = Math.random();
return this;
}
*[ Symbol.iterator ]() {
yield this.x;
yield this.y;
yield this.z;
yield this.w;
}
}
export { Vector4 };