# module Geode::Matrix3x3Transforms3DConstructors(T)

## Overview

Transformation that can be performed in three-dimensions with 3x3 matrices.

Multiplying a 3D object by the matrices produced by these methods will apply the operation to the object. The matrix must be on the right-hand-side of the multiplication operation.

``object * matrix``

Matrix multiplication is not commutative, therefore the ordering matters. If it's desired to have the matrix on the left-hand-side, transpose it before multiplying.

``matrix.transpose * object``

To combine multiple operations, multiply the matrices from these methods together.

This module should be extended.

## Defined in:

geode/matrices/transforms3d.cr

## Instance Method Detail

def reflect_x : self #

Creates a 3D reflecting matrix.

Multiplying a 3D object by this matrix will reflect it along the x-axis.

``````vector = Vector3[1, 2, 3]
matrix = Matrix3(Int32).reflect_x
vector * matrix # => (-1, 2, 3)``````

def reflect_y : self #

Creates a 3D reflective matrix.

Multiplying a 3D object by this matrix will reflect it along the y-axis.

``````vector = Vector3[1, 2, 3]
matrix = Matrix3(Int32).reflect_y
vector * matrix # => (1, -2, 3)``````

def reflect_z : self #

Creates a 3D reflecting matrix.

Multiplying a 3D object by this matrix will reflect it along the z-axis.

``````vector = Vector3[1, 2, 3]
matrix = Matrix3(Int32).reflect_z
vector * matrix # => (1, 2, -3)``````

def rotate(angle : Number | Angle, axis : CommonVector(T, 3)) : self #

Creates a 3D rotation matrix.

Multiplying a 3D object by this matrix will rotate it the specified amount. The angle must be a `Number` in radians or an `Angle`. The object is rotated around the specified axis.

``````axis = Vector3[1, 1, 1].normalize
vector = Vector3[1, 2, 3]
matrix = Matrix3(Float64).rotate(45.degrees, axis)
vector * matrix # => (1.701141509, 1.183503419, 3.115355072)``````

def rotate_x(angle : Number | Angle) : self #

Creates a 3D rotation matrix.

Multiplying a 3D object by this matrix will rotate it around the x-axis. The angle must be a `Number` in radians or an `Angle`.

``````vector = Vector3[1, 1, 1]
matrix = Matrix3(Float64).rotate_x(45.degrees)
vector * matrix # => (1.0, 0.0, 1.414213562)``````

def rotate_y(angle : Number | Angle) : self #

Creates a 3D rotation matrix.

Multiplying a 3D object by this matrix will rotate it around the y-axis. The angle must be a `Number` in radians or an `Angle`.

``````vector = Vector3[1, 1, 1]
matrix = Matrix3(Float64).rotate_y(45.degrees)
vector * matrix # => (1.414213562, 1.0, 0.0)``````

def rotate_z(angle : Number | Angle) : self #

Creates a 3D rotation matrix.

Multiplying a 3D object by this matrix will rotate it around the z-axis. The angle must be a `Number` in radians or an `Angle`.

``````vector = Vector3[1, 1, 1]
matrix = Matrix3(Float64).rotate_z(45.degrees)
vector * matrix # => (0.0, 1.414213562, 1.0)``````

def scale(x : T, y : T, z : T) : self #

Creates a 3D scaling matrix.

Non-uniformly scales an object (squash and stretch). Multiplying a 3D object by this matrix will scale it by x amount along the x-axis and y amount along the y-axis. Values for x and y smaller than 1 will shrink it. Values larger than 1 will enlarge it. Negative values will flip it.

``````vector = Vector3[2, 3, 4]
matrix = Matrix3(Float64).scale(1.5, 2, 2.5)
vector * matrix # => (3.0, 6.0, 9.0)``````

def scale(amount : T) : self #

Creates a 3D scaling matrix.

Uniformly scales an object. Multiplying a 3D object by this matrix will scale it by amount. Values for amount smaller than 1 will shrink it. Values larger than 1 will enlarge it. Negative values will flip it.

``````vector = Vector3[2, 3, 4]
matrix = Matrix3(Int32).scale(2)
vector * matrix # => (4, 6, 8)``````

def shear_x(y : T, z : T) : self #

Creates a 3D shearing matrix.

Multiplying a 3D object by this matrix will shear it along the y and z-axis based on the x-axis. For each unit along the x-axis, the y value will be adjusted by y and the z value will be adjusted by z.

``````vector = Vector3[2, 3, 4]
matrix = Matrix3(Int32).shear_x(2, 3)
vector * matrix # => (2, 7, 10)``````

def shear_y(x : T, z : T) : self #

Creates a 3D shearing matrix.

Multiplying a 3D object by this matrix will shear it along the x and z-axis based on the y-axis. For each unit along the y-axis, the x value will be adjusted by x and the z value will be adjusted by z.

``````vector = Vector3[2, 3, 4]
matrix = Matrix3(Int32).shear_y(2, 3)
vector * matrix # => (8, 3, 13)``````

def shear_z(x : T, y : T) : self #

Creates a 3D shearing matrix.

Multiplying a 3D object by this matrix will shear it along the x and y-axis based on the z-axis. For each unit along the z-axis, the x value will be adjusted by x and the y value will be adjusted by y.

``````vector = Vector3[2, 3, 4]
matrix = Matrix3(Int32).shear_z(2, 3)
vector * matrix # => (10, 15, 4)``````