Math.Matrix4

A high performance linear algebra library using native JS arrays. Geared towards 3D graphics and use with Graphics.WebGL. All matrices are immutable.

This library uses the convention that the prefix make is creating a new array,as without the prefix, you are applying some transform to an existing matrix.

Create

type Mat4

4x4 matrix type

identity : Mat4

A matrix with all 0s, except 1s on the diagonal.

Operations

inverse : Mat4 -> Maybe Mat4

Computes the inverse of any matrix. This is somewhat computationally intensive. If the matrix is not invertible, Nothing is returned.

inverseOrthonormal : Mat4 -> Mat4

Computes the inverse of the given matrix, assuming that the matrix is orthonormal. This algorithm is more efficient than general matrix inversion, and has no possibility of failing.

mul : Mat4 -> Mat4 -> Mat4

Matrix multiplcation: a * b

mulAffine : Mat4 -> Mat4 -> Mat4

Matrix multiplication, assuming a and b are affine: a * b

transpose : Mat4 -> Mat4

"Flip" the matrix across the diagonal by swapping row index and column index.

makeBasis : Vec3 -> Vec3 -> Vec3 -> Mat4

Creates a transform from a basis consisting of 3 linearly independent vectors.

transform : Mat4 -> Vec3 -> Vec3

Multiply a vector by a 4x4 matrix: m * v

Projections

makeFrustum : Float -> Float -> Float -> Float -> Float -> Float -> Mat4

Creates a matrix for a projection frustum with the given parameters.

Parameters:

left - the left coordinate of the frustum
right- the right coordinate of the frustum
bottom - the bottom coordinate of the frustum
top - the top coordinate of the frustum
znear - the near z distance of the frustum
zfar - the far z distance of the frustum

makePerspective : Float -> Float -> Float -> Float -> Mat4

Creates a matrix for a perspective projection with the given parameters.

Parameters:

fovy - field of view in the y axis, in degrees
aspect - aspect ratio
znear - the near z distance of the projection
zfar - the far z distance of the projection

makeOrtho : Float -> Float -> Float -> Float -> Float -> Float -> Mat4

Creates a matrix for an orthogonal frustum projection with the given parameters.

Parameters:

left - the left coordinate of the frustum
right- the right coordinate of the frustum
bottom - the bottom coordinate of the frustum
top - the top coordinate of the frustum
znear - the near z distance of the frustum
zfar - the far z distance of the frustum

makeOrtho2D : Float -> Float -> Float -> Float -> Mat4

Creates a matrix for a 2D orthogonal frustum projection with the given parameters. znear and zfar are assumed to be -1 and 1, respectively.

Parameters:

left - the left coordinate of the frustum
right- the right coordinate of the frustum
bottom - the bottom coordinate of the frustum
top - the top coordinate of the frustum

makeLookAt : Vec3 -> Vec3 -> Vec3 -> Mat4

Creates a transformation matrix for a camera.

Parameters:

eye - The location of the camera
center - The location of the focused object
up - The "up" direction according to the camera

Apply Transformations

rotate : Float -> Vec3 -> Mat4 -> Mat4

Concatenates a rotation in radians about an axis to the given matrix.

scale : Vec3 -> Mat4 -> Mat4

Concatenates a scaling to the given matrix.

scale3 : Float -> Float -> Float -> Mat4 -> Mat4

Concatenates a scaling to the given matrix.

translate : Vec3 -> Mat4 -> Mat4

Concatenates a translation to the given matrix.

translate3 : Float -> Float -> Float -> Mat4 -> Mat4

Concatenates a translation to the given matrix.

Create Transformations

makeRotate : Float -> Vec3 -> Mat4

Creates a transformation matrix for rotation in radians about the 3-element vector axis.

makeScale : Vec3 -> Mat4

Creates a transformation matrix for scaling each of the x, y, and z axes by the amount given in the corresponding element of the 3-element vector.

makeScale3 : Float -> Float -> Float -> Mat4

Creates a transformation matrix for scaling by 3 scalar values, one for each of the x, y, and z directions.

makeTranslate : Vec3 -> Mat4

Creates a transformation matrix for translating each of the x, y, and z axes by the amount given in the corresponding element of the 3-element vector.

makeTranslate3 : Float -> Float -> Float -> Mat4

Creates a transformation matrix for translating by 3 scalar values, one for each of the x, y, and z directions.

Conversions

toRecord :

Mat4

-> { m11 : Float

, m21 : Float

, m31 : Float

, m41 : Float

, m12 : Float

, m22 : Float

, m32 : Float

, m42 : Float

, m13 : Float

, m23 : Float

, m33 : Float

, m43 : Float

, m14 : Float

, m24 : Float

, m34 : Float

, m44 : Float

}

Convert a matrix to a record. Elements are given by their row and column indices, starting at 1, so m23 means the element in the second row, third column.

fromRecord :

{ m11 : Float

, m21 : Float

, m31 : Float

, m41 : Float

, m12 : Float

, m22 : Float

, m32 : Float

, m42 : Float

, m13 : Float

, m23 : Float

, m33 : Float

, m43 : Float

, m14 : Float

, m24 : Float

, m34 : Float

, m44 : Float

}

-> Mat4

Convert a record to a matrix.

elm-explorations/linear-algebra/1.0.2

Math.Matrix4

Create

Operations

Projections

Apply Transformations

Create Transformations

Conversions

Modules