A nodejs library for 3D transformations similar to Unity3D containing necessary classes and functions for matrices, vectors, quaternions and transforms.
npm install math3d#math3d
> Vectors, Matrices and Quaternions for Node.js
Table Of Contents:
* Features
* Installation
* API
- About Classes
- Coordinate System
- Vector3
- Static variables
- Variables
- Constructors
- Public functions
- Vector4
- Static variables
- Variables
- Constructors
- Public functions
- Quaternion
- Static variables
- Variables
- Constructors
- Public functions
- Matrix4x4
- Static variables
- Variables
- Constructors
- Public functions
- Transform
- Static variables
- Variables
- Constructors
- Public functions
* Only the necessary classes and functions for 3D graphics.
* Easily adaptable to Unity3D.
- Same coordinate system
- Same rotation order
- Similar syntax
With npm:
``bash`
npm install math3d
All classes except Transform provide immutable objects.
As I used this project later on with Unity3D, I tried to keep everything as similar as possible.
The coordinate system is the same as in Unity: y-Axis up, x-Axis right, z-Axis forward.
The rotation order for Euler angles (used in Quaternion) is z then x then y.
A three-dimensional vector with x, y, z values; used for positions, directions or scales in 3D space.
`javascript
var Vector3 = math3d.Vector3;
var v1 = new Vector3(42, 42, 42);
v1.add(Vector3.up); // Vector3(42, 43, 42);
`
#### Static variables
* back: Shorthand for writing Vector3(0, 0, -1).
* down: Shorthand for writing Vector3(0, -1, 0).
* forward: Shorthand for writing Vector3(0, 0, 1).
* left: Shorthand for writing Vector3(-1, 0, 0).
* one: Shorthand for writing Vector3(1, 1, -1).
* right: Shorthand for writing Vector3(1, 0, 0).
* up: Shorthand for writing Vector3(0, 1, 0).
* zero: Shorthand for writing Vector3(0, 0, 0).
* dimension: Always 3 for Vector3
#### Variables
* homogeneous: Returns the homogeneous Vector4 with w value 1 (readonly)
* magnitude: Magnitude (length) of the vector (readonly)
* values: An array containing the x, y, z values (readonly)
* vector4: Returns the responding Vector4 with w value 0 (readonly)
* x: x component of the vector (readonly)
* y: y component of the vector (readonly)
* z: z component of the vector (readonly)
#### Constructors
* Vector3([x: Number], [y: Number], [z: Number])
- Creates a Vector3 from the given x, y, z components
- All parameters are optional with default value 0
* Vector3.FromVector4(vector4)
- Creates a Vector3 from a Vector4 by clipping the w value
#### Public functions
* add(vector3: Vector3) -> Vector3
- Returns the sum of two vectors
* average(vector3: Vector3) -> Vector3
- Returns the average of two vectors
* cross(vector3: Vector3) -> Vector3
- Cross product of two vectors
* distanceTo(vector3: Vector3) -> Number
- Distance from one vector to another
* dot(vector3: Vector3) -> Number
- Dot product of two vectors
* equals(vector3: Vector3) -> Boolean
- Returns true if two vectors are equal
* mulScalar(scalar: Number) -> Vector3
- Multiplies the vector with a scalar
* negate() -> Vector3
- Returns a vector with the opposite direction (multiplied by -1)
* normalize() -> Vector3
- Returns a normalized vector
* scale(vector3: Vector3) -> Vector3
- Scales the vector component by component with the given vector
* sub(vector3: Vector3) -> Vector3
- Subtracts one vector from another (this - vector3)
* toString() -> String
- A string responding to the vector in form (x,y,z)
A four-dimensional vector with x, y, z, w values.
Used mostly for homogeneous coordinates.
`javascript
var Vector3 = math3d.Vector3;
var Vector4 = math3d.Vector4;
var v1 = new Vector4(42, 42); // v1 = Vector4(42, 42, 0, 1)
var v2 = Vector3.fromVector4(v1); // v2 = Vector3(42, 42, 0)
var v3 = v2.vector4; // v3 = Vector4(42, 42, 0, 0)
var v4 = v2.homogeneous; // v4 = Vector4(42, 42, 0, 1)
v4.sub(v3).equals(new Vector4()) // false
`
#### Static variables
* one: Shorthand for writing Vector4(1, 1, 1, 1).
* zero: Shorthand for writing Vector4(0, 0, 0, 0).
* dimension: Always 4 for Vector4
#### Variables
* magnitude: Magnitude (length) of the vector (readonly)
* values: An array containing the x, y, z, w values (readonly)
* x: x component of the vector (readonly)
* y: y component of the vector (readonly)
* z: z component of the vector (readonly)
* w: w component of the vector (readonly)
#### Constructors
* Vector4([x: Number], [y: Number], [z: Number], [w: Number])
- Creates a Vector4 from the given x, y, z, w components
- All parameters are optional with default value 0
#### Public functions
* add(vector4: Vector4) -> Vector4
- Returns the sum of two vectors
* distanceTo(vector4: Vector4) -> Number
- Distance from one vector to another
* dot(vector4: Vector4) -> Number
- Dot product of two vectors
* equals(vector4: Vector4) -> Boolean
- Returns true if two vectors are equal
* mulScalar(scalar: Number) -> Vector4
- Multiplies the vector with a scalar
* negate() -> Vector4
- Returns a vector with the opposite direction (multiplied by -1)
* normalize() -> Vector3
- Returns a normalized vector
* sub(vector4: Vector4) -> Vector3
- Subtracts one vector from another (this - vector4)
* toString() -> String
- A string responding to the vector in form (x,y,z,w)
Each quaternion is composed of a vector (xyz) and a scalar rotation (w).
Although their values are not very intuitive, they are used instead of the Euler angles to:
- avoid Gimbal lock
- avoid different rotation orders for Euler angles
- avoid multiple representation of the same rotation
It is advised not to use the x, y, z, w values directly, unless you really know what you are doing.
`javascript
var Vector3 = math3d.Vector3;
var v1 = Vector3.forward; // v1 = Vector3(0, 0, 1)
var q1 = Quaternion.Euler(0, 90, 0);
q1.mulVector3(v1); // (0, 0, -1) <- v1 rotated 90 degrees in y-Axis
q1.angleAxis; // {axis: Vector3(0, 1, 0), angle: 90}
`
#### Static variables
* identity: Shorthand for writing Quaternion(0, 0, 0, 1).
* zero: Shorthand for writing Quaternion(0, 0, 0, 0).
#### Variables
* angleAxis: Angle Axis representation of the quaternion in form {axis: (Vector3), angle: Number} (readonly)
* eulerAngles: Euler angles responding to the quaternion in form {x: Number, y: Number, z: Number} (readonly)
* x: x component of the quaternion (readonly)
* y: y component of the quaternion (readonly)
* z: z component of the quaternion (readonly)
* w: w component of the quaternion (readonly)
#### Constructors
* Quaternion([x: Number], [y: Number], [z: Number], [w: Number])
- Creates a quaternion from the given x, y, z, w values
- All values are optional with default value 0 for x, y, z and 1 for w
* Quaternion.Euler(x: Number, y: Number, z: Number)
- Creates a quaternion that is rotated /z/ degrees around z-axis, /x/ degrees around x-axis and /y/ degrees around y-axis, in that exact order
* Quaternion.AngleAxis(axis: Vector3, angle: Number)
- Creates a quaternion that responds to a rotation of /angle/ degrees around /axis/
#### Public functions
* angleTo(quaternion: Quaternion) -> Number
- Angle between two quaternions in degrees (0 - 180)
* conjugate() -> Quaternion
- Returns the conjugate of the quaternion (defined as (-x, -y, -z, w))
* distanceTo(quaternion: Quaternion) -> Number
- A notion to measure the similarity between two quaternions (quick)
- The return value varies between 0 and 1. Same quaternions return 0.
* dot(quaternion: Quaternion) -> Number
- Dot (inner) product of two quaternions
* equals(quaternion: Quaternion) -> Boolean
- Returns true if two quaternions are equal
* inverse() -> Quaternion
- Returns the inverse of the quaternion (inverse = conjugate)
* mul(quaternion: Quaternion) -> Quaternion
- Right multiplies the quaternion in the argument (this * quaternion)
* mulVector3(vector3: Vector3) -> Vector3
- Multiplies the quaternion with the vector (applies rotation)
* toString() -> String
- A string responding to the quaternion in form (x,y,z,w)
A 4x4 matrix with some required functions for translation, rotation and scaling.
`javascript
var Vector3 = math3d.Vector3;
var Matrix4x4 = math3d.Matrix4x4;
var v1 = new Vector3(3, 4, 5);
var m1 = Matrix4x4.scaleMatrix(v1); // m1 = |3 0 0 0|
// |0 4 0 0|
// |0 0 5 0|
// |0 0 0 1|
m1.mulVector3(Vector3.up); // Vector3(0, 4, 0)
`
#### Static variables
* identity: 4x4 identity matrix.
* zero: Shorthand for writing Matrix4x4([]]).
#### Variables
* columns: An two-dimensional array containing the columns of a matrix (readonly)
* m11: first element of first row
* m12: second element of first row
* m13: third element of first row
* m14: fourth element of first row
* m21: first element of second row
* m22: second element of second row
* m23: third element of second row
* m24: fourth element of second row
* m31: first element of third row
* m32: second element of third row
* m33: third element of third row
* m34: fourth element of third row
* m41: first element of fourth row
* m42: second element of fourth row
* m43: third element of fourth row
* m44: fourth element of fourth row
* rows: An two-dimensional array containing the rows of a matrix (readonly)
* size: Size (number of rows and columns) of a matrix in form {rows: Number, columns: Number} (readonly)
* values: A one-dimensional array containing the elements of the matrix (rows first) (readonly)
#### Constructors
* Matrix4x4(data: Array)
- Creates a 4x4 matrix with the given number array
- If the length of the array is smaller, the rest is filled with zeros
* Matrix4x4.FlipMatrix(flipX: Boolean, flipY: Boolean, flipZ: Boolean)
- Creates a matrix that changes the direction of the axii that are chosen to be flipped
* Matrix4x4.ScaleMatrix(scale: Number|Vector3)
- Creates a scaling matrix with the given scale factor
- Scale factor can also be given as a number, a uniform vector of it will be created automatically
* Matrix4x4.RotationMatrix(quaternion: Quaternion)
- Creates a rotation matrix for the given quaternion
* Matrix4x4.TranslationMatrix(translation: Vector3)
- Creates a translation matrix from the given vector
* Matrix4x4.TRS(translation: Vector3, rotation: Quaternion, scale: Number|Vector3)
- Creates translation-rotation-scale matrix
* Matrix4x4.LocalToWorldMatrix(position: Vector3, rotation: Quaternion, scale: Number|Vector3)
- Creates a matrix that transforms from a local space to the world space
- The local coordinate system is at /position/ with /rotation/ according to the world space
- /scale/ is defined by (local space scale) / (world space scale)
* Matrix4x4.WorldToLocalMatrix(position: Vector3, rotation: Quaternion, scale: Number|Vector3)
- Creates a matrix that transforms from world space to a local space
- The local coordinate system is at /position/ with /rotation/ according to the world space
- /scale/ is defined by (local space scale) / (world space scale)
#### Public functions
* determinant() -> Number
- Determinant of the matrix
* inverse() -> Matrix4x4|undefined
- Inverse of the matrix, undefined if it is not unique
* negate() -> Matrix4x4
- The negative matrix computed by multiplying the matrix by -1
* transpose() -> Matrix4x4
- Transpose of the matrix
* add(matrix4x4: Matrix4x4) -> Matrix4x4
- Returns the sum of two matrices
* sub(matrix4x4: Matrix4x4) -> Matrix4x4
- Subtracts one matrix from another (this - matrix4x4)
* mul(matrix4x4: Matrix4x4) -> Matrix4x4
- Right multiplies with the given matrix (this * matrix4x4)
* mulScalar(scalar: Number) -> Matrix4x4
- Multiplies the matrix with a scalar
* mulVector3(vector3: Vector3) -> Vector3
- Multiplies the matrix with the given vector
- Uses the homogeneous vector representation for the multiplication
A class to contain the position and the rotation of an object and create an object hierarchy.
`javascript
var Vector3 = math3d.Vector3;
var Quaternion = math3d.Quaternion;
var Transform = math3d.Transform;
var t1 = new Transform(Vector3.zero, Quaternion.Euler(90, 0, 0));
var t2 = new Transform();
t2.parent = t1;
t2.translate(new Vector3(3,4,5));
t2.rotate(15, 20, 90, Transform.Space.World);
``
#### Static variables
* Space: An enumeration to decide in which coordinate system to operate
- Self: Applies transformation relative to the local coordinate system
- World: Applies transformation relative to the world coordinate system
#### Variables
* forward: Forward vector in world coordinate system (readonly)
* localPosition: Position in local coordinate system
* localRotation: Rotation in local coordinate system
* localToWorldMatrix: A matrix to transform points from local space to world space (readonly)
* name: Name of the object (default: "object")
* parent: Parent transform of the object (undefined if none)
* position: Position in world coordinate system
* right: Right vector in world coordinate system (readonly)
* root The topmost transform in the hierarchy (readonly)
* rotation: Rotation in world coordinate system
* up: Up vector in world coordinate system (readonly)
* worldToLocalMatrix: A matrix to transform points from world space to local space (readonly)
#### Constructors
* Transform([position: Vector3], [rotation: Quaternion])
- Creates a transform object at the given position and rotation
- Parameters are optional with default values Vector3.zero and Quaternion.identity respectively
#### Public functions
* addChild(child: Transform)
- Adds a child transform
* inverseTransformPosition(position: Vector3) -> Vector3
- Transforms position from world space to local space
* removeChild(child: Transform)
- Removes a child transform
* transformPosition(position: Vector3) -> Vector3
- Transforms position from local space to world space
* translate(translation: Vector3, [relativeTo: Transform.Space]) -> Transform
- Translates by /translation/ relative to /relativeTo/
- /relativeTo/ is optional with default value Transform.Space.Self
* rotate(x: Number, y: Number, z: Number, [relativeTo: Transform.Space]) -> Transform
- Rotates /z/ degrees around z-axis, /x/ degrees around x axis and /y/ degrees around y-axis relative to /relativeTo/ in that exact order
- /relativeTo/ is optional with default value Transform.Space.Self