# Vector3

Class representing a 3D vector. A 3D vector is an ordered triplet of numbers (labeled x, y, and z), which can be used to represent a number of things, such as:

• A point in 3D space.
• A direction and length in 3D space. In Verge3D the length will always be the Euclidean distance (straight-line distance) from `(0, 0, 0)` to `(x, y, z)` and the direction is also measured from `(0, 0, 0)` towards `(x, y, z)`.
• Any arbitrary ordered triplet of numbers.

There are other things a 3D vector can be used to represent, such as momentum vectors and so on, however these are the most common uses in Verge3D.

Iterating through a Vector3 instance will yield its components `(x, y, z)` in the corresponding order.

## Code Example

``` const a = new v3d.Vector3(0, 1, 0); // no arguments; will be initialised to (0, 0, 0) const b = new v3d.Vector3(); const d = a.distanceTo(b); ```

## Constructor

### Vector3(x : Float, y : Float, z : Float)

x — the x value of this vector. Default is `0`.
y — the y value of this vector. Default is `0`.
z — the z value of this vector. Default is `0`.

Creates a new Vector3.

## Properties

### # .isVector3 : Boolean

Read-only flag to check if a given object is of type Vector3.

## Methods

### # .addScalar(s : Float) → this

Adds the scalar value s to this vector's x, y and z values.

### # .addScaledVector(v : Vector3, s : Float) → this

Adds the multiple of v and s to this vector.

### # .addVectors(a : Vector3, b : Vector3) → this

Sets this vector to a + b.

### # .applyAxisAngle(axis : Vector3, angle : Float) → this

axis — A normalized Vector3.
angle — An angle in radians.

Applies a rotation specified by an axis and an angle to this vector.

### # .applyEuler(euler : Euler) → this

Applies euler transform to this vector by converting the Euler object to a Quaternion and applying.

### # .applyMatrix3(m : Matrix3) → this

Multiplies this vector by m

### # .applyMatrix4(m : Matrix4) → this

Multiplies this vector (with an implicit 1 in the 4th dimension) and m, and divides by perspective.

### # .applyNormalMatrix(m : Matrix3) → this

Multiplies this vector by normal matrix m and normalizes the result.

### # .applyQuaternion(quaternion : Quaternion) → this

Applies a Quaternion transform to this vector.

### # .angleTo(v : Vector3) → Float

Returns the angle between this vector and vector v in radians.

### # .ceil() → this

The x, y and z components of this vector are rounded up to the nearest integer value.

### # .clamp(min : Vector3, max : Vector3) → this

min — the minimum x, y and z values.
max — the maximum x, y and z values in the desired range.

If this vector's x, y or z value is greater than the max vector's x, y or z value, it is replaced by the corresponding value. If this vector's x, y or z value is less than the min vector's x, y or z value, it is replaced by the corresponding value.

### # .clampLength(min : Float, max : Float) → this

min — the minimum value the length will be clamped to.
max — the maximum value the length will be clamped to.

If this vector's length is greater than the max value, the vector will be scaled down so its length is the max value. If this vector's length is less than the min value, the vector will be scaled up so its length is the min value.

### # .clampScalar(min : Float, max : Float) → this

min — the minimum value the components will be clamped to.
max — the maximum value the components will be clamped to.

If this vector's x, y or z values are greater than the max value, they are replaced by the max value. If this vector's x, y or z values are less than the min value, they are replaced by the min value.

### # .clone() → Vector3

Returns a new vector3 with the same x, y and z values as this one.

### # .copy(v : Vector3) → this

Copies the values of the passed vector3's x, y and z properties to this vector3.

### # .cross(v : Vector3) → this

Sets this vector to cross product of itself and v.

### # .crossVectors(a : Vector3, b : Vector3) → this

Sets this vector to cross product of a and b.

### # .distanceTo(v : Vector3) → Float

Computes the distance from this vector to v.

### # .manhattanDistanceTo(v : Vector3) → Float

Computes the Manhattan distance from this vector to v.

### # .distanceToSquared(v : Vector3) → Float

Computes the squared distance from this vector to v. If you are just comparing the distance with another distance, you should compare the distance squared instead as it is slightly more efficient to calculate.

### # .divide(v : Vector3) → this

Divides this vector by v.

### # .divideScalar(s : Float) → this

Divides this vector by scalar s.

### # .dot(v : Vector3) → Float

Calculate the dot product of this vector and v.

### # .equals(v : Vector3) → Boolean

Returns `true` if the components of this vector and v are strictly equal; `false` otherwise.

### # .floor() → this

The components of this vector are rounded down to the nearest integer value.

### # .fromArray(array : Array, offset : Integer) → this

array — the source array.
offset — (optional) offset into the array. Default is `0`.

Sets this vector's x value to be `array[offset + 0]`, y value to be `array[offset + 1]` and z value to be `array[offset + 2]`.

### # .fromBufferAttribute(attribute : BufferAttribute, index : Integer) → this

attribute — the source attribute.
index — index in the attribute.

Sets this vector's x, y and z values from the attribute.

### # .getComponent(index : Integer) → Float

index`0`, `1`, or `2`.

If index equals 0 returns the x value.
If index equals 1 returns the y value.
If index equals 2 returns the z value.

### # .length() → Float

Computes the Euclidean length (straight-line length) from (0, 0, 0) to (x, y, z).

### # .manhattanLength() → Float

Computes the Manhattan length of this vector.

### # .lengthSq() → Float

Computes the square of the Euclidean length (straight-line length) from (0, 0, 0) to (x, y, z). If you are comparing the lengths of vectors, you should compare the length squared instead as it is slightly more efficient to calculate.

### # .lerp(v : Vector3, alpha : Float) → this

vVector3 to interpolate towards.
alpha — interpolation factor, typically in the closed interval `[0, 1]`.

Linearly interpolate between this vector and v, where alpha is the percent distance along the line - alpha = 0 will be this vector, and alpha = 1 will be v.

### # .lerpVectors(v1 : Vector3, v2 : Vector3, alpha : Float) → this

v1 — the starting Vector3.
v2 - Vector3 to interpolate towards.
alpha — interpolation factor, typically in the closed interval `[0, 1]`.

Sets this vector to be the vector linearly interpolated between v1 and v2 where alpha is the percent distance along the line connecting the two vectors. If `alpha = 0` it will be v1, and if `alpha = 1` it will be v2.

### # .max(v : Vector3) → this

If this vector's x, y or z value is less than v's x, y or z value, replace that value with the corresponding max value.

### # .min(v : Vector3) → this

If this vector's x, y or z value is greater than v's x, y or z value, replace that value with the corresponding min value.

### # .multiply(v : Vector3) → this

Multiplies this vector by v.

### # .multiplyScalar(s : Float) → this

Multiplies this vector by scalar s.

### # .multiplyVectors(a : Vector3, b : Vector3) → this

Sets this vector equal to a * b, component-wise.

### # .negate() → this

Inverts this vector — i.e. sets `x = -x`, `y = -y`, and `z = -z`.

### # .normalize() → this

Convert this vector to a unit vector — that is, sets it equal to a vector with the same direction as this one, but length 1.

### # .project(camera : Camera) → this

camera — camera to use in the projection.

Projects this vector from world space into the camera's normalized device coordinate (NDC) space.

### # .projectOnPlane(planeNormal : Vector3) → this

planeNormal — A vector representing a plane normal.

Projects this vector onto a plane by subtracting this vector projected onto the plane's normal from this vector.

### # .projectOnVector(v : Vector3) → this

Projects this vector onto v.

### # .reflect(normal : Vector3) → this

normal — the normal to the reflecting plane.

Reflect this vector off of plane orthogonal to normal. Normal is assumed to have unit length.

### # .round() → this

The components of this vector are rounded to the nearest integer value.

### # .roundToZero() → this

The components of this vector are rounded towards zero (up if negative, down if positive) to an integer value.

### # .set(x : Float, y : Float, z : Float) → this

Sets the x, y and z components of this vector.

### # .setComponent(index : Integer, value : Float) → this

index`0`, `1`, or `2`.
valueFloat.

If index equals 0 set x to value.
If index equals 1 set y to value.
If index equals 2 set z to value

### # .setFromCylindrical(c : Cylindrical) → this

Sets this vector from the cylindrical coordinates c.

### # .setFromCylindricalCoords(radius : Float, theta : Float, y : Float) → this

Sets this vector from the cylindrical coordinates radius, theta and y.

### # .setFromEuler(euler : Euler) → this

Sets this vector's x, y and z components from the x, y, and z components of the specified Euler Angle.

### # .setFromMatrixColumn(matrix : Matrix4, index : Integer) → this

Sets this vector's x, y and z components from index column of matrix.

### # .setFromMatrix3Column(matrix : Matrix3, index : Integer) → this

Sets this vector's x, y and z components from index column of matrix.

### # .setFromMatrixPosition(m : Matrix4) → this

Sets this vector to the position elements of the transformation matrix m.

### # .setFromMatrixScale(m : Matrix4) → this

Sets this vector to the scale elements of the transformation matrix m.

### # .setFromSpherical(s : Spherical) → this

Sets this vector from the spherical coordinates s.

### # .setFromSphericalCoords(radius : Float, phi : Float, theta : Float) → this

Sets this vector from the spherical coordinates radius, phi and theta.

### # .setLength(l : Float) → this

Set this vector to a vector with the same direction as this one, but length l.

### # .setScalar(scalar : Float) → this

Set the x, y and z values of this vector both equal to scalar.

### # .setX(x : Float) → this

Replace this vector's x value with x.

### # .setY(y : Float) → this

Replace this vector's y value with y.

### # .setZ(z : Float) → this

Replace this vector's z value with z.

### # .sub(v : Vector3) → this

Subtracts v from this vector.

### # .subScalar(s : Float) → this

Subtracts s from this vector's x, y and z components.

### # .subVectors(a : Vector3, b : Vector3) → this

Sets this vector to a - b.

### # .toArray(array : Array, offset : Integer) → Array

array — (optional) array to store this vector to. If this is not provided a new array will be created.
offset — (optional) optional offset into the array.

Returns an array [x, y, z], or copies x, y and z into the provided array.

### # .transformDirection(m : Matrix4) → this

Transforms the direction of this vector by a matrix (the upper left 3 x 3 subset of a m) and then normalizes the result.

### # .unproject(camera : Camera) → this

camera — camera to use in the projection.

Projects this vector from the camera's normalized device coordinate (NDC) space into world space.

### # .random() → this

Sets each component of this vector to a pseudo-random value between 0 and 1, excluding 1.

### # .randomDirection() → this

Sets this vector to a uniformly random point on a unit sphere.

## Puzzles

The following puzzles can be used to create and perform math operations on vectors in a visual manner: