Scenic

v0.10.2

Scenic v0.10.2 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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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identity() View Source 
identity() :: Scenic.Math.matrix()

The identity matrix

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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zero() View Source 
zero() :: Scenic.Math.matrix()

A matrix where all the values are 0