Scenic

v0.9.0

Scenic v0.9.0 Scenic.Math.Matrix View Source

A collection of functions to work with matrices.

All the matrix fucntions in this module work exclusively with the binary form of a matrix, which is a compact binary of 16 4-byte floats.

If you would like to convert back and forth from the more human friendly list version, then please use the functions in Scenic.Math.Matrix.Utils

Link to this section Summary

Functions

add(matrix_a, matrix_b)

Add two matrices together

adjugate(matrix)

Calculate the adjugate of a matrix

build_rotate_around(angle, pin)

Build a matrix that represents a 2D rotation around a point

build_rotation(angle)

Build a matrix that represents a 2D rotation around the origin

build_scale(scale)

Build a matrix that represents a scaling operation

build_translation(vector_2)

Build a matrix that represents a simple translation

close?(matrix_a, matrix_b, tolerance \\ 1.0e-6)

Test if two matrices are close in value to each other

determinant(matrix)

Calculate the determinant of a matrix

div(matrix, scalar)

Divide a matrix by a scalar

get(matrix, x, y)

Get a single value out of a binary matrix

get_xy(matrix)

Extract the 2D vector represented by the matrix

identity()

The identity matrix

invert(matrix)

Inverte a matrix

mul(matrix_list)

Multiply a list of matrices together

mul(matrix, multiplier)

Multiply a matrix by another matrix or a scalar

project_vector(matrix, arg)

Project a vector by a matrix

project_vectors(a, vector_bin)

Project a list of vectors by a matrix

put(matrix, x, y, v)

Put a single value into a binary matrix

rotate(matrix, angle)

Multiply a matrix by a rotation

scale(matrix, scale)

Multiply a matrix by a scale factor

sub(matrix_a, matrix_b)

Subtract one matrix from another

translate(matrix, vector_2)

Multiply a matrix by a translation

transpose(matrix)

Transpose a matrix

zero()

A matrix where all the values are 0

Link to this section Functions

Link to this function add(matrix_a, matrix_b) View Source 
add(matrix_a :: Scenic.Math.matrix(), matrix_b :: Scenic.Math.matrix()) ::
  Scenic.Math.matrix()

Add two matrices together.

This operation is implemented as a NIF for performance.

Parameters:

  • matrix_a: The first matrix
  • matrix_b: The second matrix

Returns: The resulting matrix

Link to this function adjugate(matrix) View Source 
adjugate(matrix :: Scenic.Math.matrix()) :: Scenic.Math.matrix()

Calculate the adjugate of a matrix

This operation is implemented as a NIF for performance.

Parameters:

  • matrix: A matrix

Returns: The resulting matrix

Link to this function build_rotate_around(angle, pin) View Source 
build_rotate_around(angle :: number(), pin :: Scenic.Math.point()) ::
  Scenic.Math.matrix()

Build a matrix that represents a 2D rotation around a point.

Parameters:

  • angle: the amount to rotate, in radians
  • pin: position to pin the rotation around

Returns: A binary matrix

Link to this function build_rotation(angle) View Source 
build_rotation(angle :: number()) :: Scenic.Math.matrix()

Build a matrix that represents a 2D rotation around the origin.

Parameters:

  • angle: the amount to rotate, in radians

Returns: A binary matrix

Link to this function build_scale(scale) View Source 
build_scale(scale :: number() | Scenic.Math.vector_2()) :: Scenic.Math.matrix()

Build a matrix that represents a scaling operation.

Parameters:

  • scale: the amount to scale by. Can be either a number or a vector_2

Returns: A binary matrix

Link to this function build_translation(vector_2) View Source 
build_translation(vector_2 :: Scenic.Math.vector_2()) :: Scenic.Math.matrix()

Build a matrix that represents a simple translation.

Parameters:

  • vector_2: the vector defining how much to translate

Returns: A binary matrix

Link to this function close?(matrix_a, matrix_b, tolerance \\ 1.0e-6) View Source 
close?(
  matrix_a :: Scenic.Math.matrix(),
  matrix_a :: Scenic.Math.matrix(),
  tolerance :: number()
) :: boolean()

Test if two matrices are close in value to each other.

Parameters:

  • matrix_a: The first matrix
  • matrix_b: The second matrix
  • tolerance: Defines what close means. Defaults to: 0.000001

Returns: A boolean

Link to this function determinant(matrix) View Source 
determinant(matrix :: Scenic.Math.matrix()) :: Scenic.Math.matrix()

Calculate the determinant of a matrix

This operation is implemented as a NIF for performance.

Parameters:

  • matrix: A matrix

Returns: The resulting matrix

Link to this function div(matrix, scalar) View Source 
div(matrix :: Scenic.Math.matrix(), divisor :: number()) :: Scenic.Math.matrix()

Divide a matrix by a scalar.

This operation is implemented as a NIF for performance.

Parameters:

  • matrix: A matrix
  • divisor: A number (scalar) to divide by

Returns: The resulting matrix

Link to this function get(matrix, x, y) View Source 
get(matrix :: Scenic.Math.matrix(), x :: number(), y :: number()) :: number()

Get a single value out of a binary matrix.

Parameters:

  • matrix: The source matrix
  • x: the column to pull the data from
  • y: the row to pull the data from

Returns: A number

Link to this function get_xy(matrix) View Source 
get_xy(matrix :: Scenic.Math.matrix()) :: Scenic.Math.vector_2()

Extract the 2D vector represented by the matrix.

Parameters:

  • matrix: The source matrix

Returns: A vector_2

Link to this function identity() View Source 
identity() :: Scenic.Math.matrix()

The identity matrix

Link to this function invert(matrix) View Source 
invert(matrix :: Scenic.Math.matrix()) :: Scenic.Math.matrix()

Inverte a matrix.

This operation is implemented as a NIF for performance.

Parameters:

  • matrix: A matrix

Returns: The resulting matrix

Link to this function mul(matrix_list) View Source 
mul(matrix_list :: [Scenic.Math.matrix()]) :: Scenic.Math.matrix()

Multiply a list of matrices together.

This operation is implemented as a NIF for performance.

Parameters:

  • matrix_list: A list of matrices

Returns: The resulting matrix

Link to this function mul(matrix, multiplier) View Source 
mul(
  matrix :: Scenic.Math.matrix(),
  multiplier :: number() | Scenic.Math.matrix()
) :: Scenic.Math.matrix()

Multiply a matrix by another matrix or a scalar.

This operation is implemented as a NIF for performance.

Parameters:

  • matrix: A matrix
  • multiplier: A number (scalar) or a matrix to multiply by

Returns: The resulting matrix

Link to this function project_vector(matrix, arg) View Source 
project_vector(
  matrix :: Scenic.Math.matrix(),
  vector_2 :: Scenic.Math.vector_2()
) :: Scenic.Math.vector_2()
project_vector(
  matrix :: Scenic.Math.matrix(),
  vector_list :: [Scenic.Math.vector_2()]
) :: [Scenic.Math.vector_2()]

Project a vector by a matrix.

This operation is implemented as a NIF for performance.

Parameters:

  • matrix: A matrix
  • vector: The vector to project

Returns: The projected vector

Link to this function project_vectors(a, vector_bin) View Source

Project a list of vectors by a matrix.

This operation is implemented as a NIF for performance.

Parameters:

  • matrix: A matrix
  • vectors: The list of vectors to project

Returns: A list of projected vectors

Link to this function put(matrix, x, y, v) View Source 
put(matrix :: Scenic.Math.matrix(), x :: number(), y :: number(), v :: number()) ::
  Scenic.Math.matrix()

Put a single value into a binary matrix.

Parameters:

  • matrix: The source matrix
  • x: the column to pull the data from
  • y: the row to pull the data from
  • v: the value to put into the matrix. Must be a number.

Returns: A number

Link to this function rotate(matrix, angle) View Source 
rotate(matrix :: Scenic.Math.matrix(), angle :: number() | nil) ::
  Scenic.Math.matrix()

Multiply a matrix by a rotation.

Parameters:

  • matrix: The incoming source matrix
  • angle: the amount to rotate, in radians or nil (which does nothing

Returns: A binary matrix

Link to this function scale(matrix, scale) View Source 
scale(
  matrix :: Scenic.Math.matrix(),
  scale :: number() | Scenic.Math.vector_2() | nil
) :: Scenic.Math.matrix()

Multiply a matrix by a scale factor.

Parameters:

  • matrix: The incoming source matrix
  • scale: the amount to scale by. Can be either a number, a vector, or nil (which does nothing)

Returns: A binary matrix

Link to this function sub(matrix_a, matrix_b) View Source 
sub(matrix_a :: Scenic.Math.matrix(), matrix_b :: Scenic.Math.matrix()) ::
  Scenic.Math.matrix()

Subtract one matrix from another.

This operation is implemented as a NIF for performance.

Parameters:

  • matrix_a: The first matrix
  • matrix_b: The second matrix, which is subtracted from the first

Returns: The resulting matrix

Link to this function translate(matrix, vector_2) View Source 
translate(
  matrix :: Scenic.Math.matrix(),
  vector_2 :: Scenic.Math.vector_2() | nil
) :: Scenic.Math.matrix()

Multiply a matrix by a translation.

Parameters:

  • matrix: The incoming source matrix
  • vector_2: the vector to translate by or nil (which does nothing)

Returns: A binary matrix

Link to this function transpose(matrix) View Source 
transpose(matrix :: Scenic.Math.matrix()) :: Scenic.Math.matrix()

Transpose a matrix

This operation is implemented as a NIF for performance.

Parameters:

  • matrix: A matrix

Returns: The resulting matrix

Link to this function zero() View Source 
zero() :: Scenic.Math.matrix()

A matrix where all the values are 0