Libraries.Compute.Affine2

Affine2 is a specialized three-by-three matrix that represents a series of 2D transformations, such as translations, scales, flips, rotations, and shears. The last row of an affine is always 0, 0, 1.

Example Code

use Libraries.Compute.Affine2

Affine2 affine
affine:SetToTranslationRotationScale(3, 3, 45, 2, 2)

number row0column0 = affine:row0column0
number row0column1 = affine:row0column1
number row0column2 = affine:row0column2
number row1column0 = affine:row1column0
number row1column1 = affine:row1column1
number row1column2 = affine:row1column2

output "The affine is: "
output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
output "|0, 0, 1|"

This action applies the affine transformation(s) to the passed point. The passed vector representing the point is altered as a result of this action.

Example Code

use Libraries.Compute.Affine2
    use Libraries.Compute.Vector2

    Affine2 affine
    Vector2 point

    affine:SetToTranslationRotationScale(3, 3, 45, 2, 2)

    point:Set(3, 4)

    affine:ApplyAffineTransformation(point)

    number x = point:GetX()
    number y = point:GetY()

    output "The new point is [" + x + ", " + y + "]"

This action compares two object hash codes and returns an integer. The result is larger if this hash code is larger than the object passed as a parameter, smaller, or equal. In this case, -1 means smaller, 0 means equal, and 1 means larger. This action was changed in Quorum 7 to return an integer, instead of a CompareResult object, because the previous implementation was causing efficiency issues.

Example Code

Object o
        Object t
        integer result = o:Compare(t) //1 (larger), 0 (equal), or -1 (smaller)

This action calculates the determinant of the affine matrix.

Example Code

use Libraries.Compute.Affine2

    Affine2 affine

    affine:SetToTranslationRotationScale(3, 3, 45, 2, 2)

    number determinant = affine:Determinant()

    output "The determinant is " + determinant

This action determines if two objects are equal based on their hash code values.

Example Code

use Libraries.Language.Object
        use Libraries.Language.Types.Text
        Object o
        Text t
        boolean result = o:Equals(t)

This action gets the hash code for an object.

Example Code

Object o
        integer hash = o:GetHashCode()

This action gets the x and y translation component of the affine matrix.

Example Code

use Libraries.Compute.Affine2
    use Libraries.Compute.Vector2

    Affine2 affine
    Vector2 translation

    affine:SetToTranslationRotationScale(3, 3, 45, 2, 2)

    translation = affine:GetTranslation()

    number x = translation:GetX()
    number y = translation:GetY()

    output "The translation vector is [" + x + ", " + y + "]"

This action constructs an identity matrix. The resulting affine transformation is: 1.0 | 0.0 | 0.0 0.0 | 1.0 | 0.0 0.0 | 0.0 | 1.0

Example Code

use Libraries.Compute.Affine2

    Affine2 affine
    affine:Identity()

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action inverts the affine matrix.

Example Code

use Libraries.Compute.Affine2

    Affine2 affine

    affine:SetToTranslationRotationScale(3, 3, 45, 2, 2)

    affine:Invert()

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action determines whether this affine matrix is the identity matrix.

Example Code

use Libraries.Compute.Affine2

    Affine2 affine

    if affine:IsIdentityMatris()
        output "The affine is the identity matrix."
    else
        output "The affine is not the identity matrix."
    end

This action determines whether this affine matrix is a translation matrix.

Example Code

use Libraries.Compute.Affine2

    Affine2 affine

    affine:SetToTranslation(3, 2)

    if affine:IsTranslation()
        output "The affine is a translation affine"
    else
        output "The affine is not a translation affine"
    end

This action multiplies this affine matrix with the passed affine matrix.

Example Code

use Libraries.Compute.Affine2

    Affine2 affine
    Affine2 other

    affine:SetToTranslationRotationScale(2, 2, 45, 3, 3)
    other:SetToTranslationScale(1, 1, 3, 3)

    affine:Multiply(other)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action multiplies the affine matrix with the (counter-clockwise) rotation matrix.

Example Code

use Libraries.Compute.Affine2

    Affine2 affine

    affine:SetToTranslationRotationScale(3, 3, 45, 2, 2)

    affine:Rotate(90)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action multiplies the affine matrix with the (counter-clockwise) rotation matrix.

Example Code

use Libraries.Compute.Affine2
    use Libraries.Compute.Math

    Affine2 affine
    Math math

    affine:SetToTranslationRotationScale(3, 3, 45, 2, 2)

    affine:RotateRadians(math:pi / 2)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action multiplies the affine matrix with the scale matrix.

Example Code

use Libraries.Compute.Affine2
    use Libraries.Compute.Vector2
    
    Affine2 affine
    Vector2 vector

    affine:SetToTranslationRotationScale(3, 3, 45, 2, 2)
    vector:Set(4, 4)

    affine:Scale(vector)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action multiplies the affine matrix with the scale matrix.

Example Code

use Libraries.Compute.Affine2

    Affine2 affine

    affine:SetToTranslationRotationScale(3, 3, 45, 2, 2)

    affine:Scale(4, 4)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action sets the affine matrix to the 2D transformation components of the passed 4x4 matrix.

Example Code

use Libraries.Compute.Affine2
    use Libraries.Compute.Matrix4

    Affine2 affine
    Matrix4 matrix

    matrix:Set(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)

    affine:Set(matrix)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action sets the affine matrix to the passed 3x3 matrix.

Example Code

use Libraries.Compute.Affine2
    use Libraries.Compute.Matrix3

    Affine2 affine
    Matrix3 matrix

    matrix:Set(0, 1, 2, 3, 4, 5, 6, 7, 8)

    affine:Set(matrix)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action sets the affine transformation to the passed affine transformation.

Example Code

use Libraries.Compute.Affine2

    Affine2 affine
    Affine2 setAffine

    setAffine:SetToTranslation(3, 4)

    affine:Set(setAffine)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action sets the affine matrix to the product of the passed affine matrices.

Example Code

use Libraries.Compute.Affine2

    Affine2 affine
    Affine2 left
    Affine2 right

    left:SetToTranslationScale(3, 3, 2, 2)
    right:SetToTranslationRotationScale(2, 3, 45, 2, 2)

    affine:SetToProduct(left, right)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action sets the affine matrix to the rotation matrix that will rotate any vector in the counter-clockwise direction around the z-axis (the axis coming out of the screen).

Example Code

use Libraries.Compute.Affine2
    use Libraries.Compute.Math

    Math math

    Affine2 affine

    affine:SetToRotation(math:SquareRoot(2) / 2, math:SquareRoot(2) / 2)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action sets the affine matrix as the rotation matrix with the given rotation angle in degrees.

Example Code

use Libraries.Compute.Affine2

    Affine2 affine
    
    affine:SetToRotation(45)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action sets the affine matrix to the rotation matrix with the given rotation angle in radians.

Example Code

use Libraries.Compute.Affine2
    use Libraries.Compute.Math
    
    Math math

    Affine2 affine

    affine:SetToRotationRadians(math:pi / 4)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action sets the affine matrix to the scaling matrix with the given x and y scales.

Example Code

use Libraries.Compute.Affine2
    
    Affine2 affine

    affine:SetToScaling(2, 2)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action sets the affine matrix to the scaling matrix with the given scaling vector.

Example Code

use Libraries.Compute.Affine2
    use Libraries.Compute.Vector2

    Affine2 affine
    Vector2 vector

    vector:Set(2, 2)

    affine:SetToScaling(vector)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action sets the affine matrix to the shearing matrix with the passed shear in x and y.

Example Code

use Libraries.Compute.Affine2

    Affine2 affine

    affine:SetToShearing(3, 2)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action sets the affine matrix to the shearing matrix with the passed shear vector.

Example Code

use Libraries.Compute.Affine2
    use Libraries.Compute.Vector2

    Affine2 affine
    Vector2 vector

    vector:Set(3, 2)

    affine:SetToShearing(vector)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action sets the affine matrix to the translation matrix with the given vector.

Example Code

use Libraries.Compute.Affine2
    use Libraries.Compute.Vector2

    Affine2 affine
    Vector2 vector

    vector:Set(3, 4)

    affine:SetToTranslation(vector)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action sets the affine matrix to the translation matrix with the given x and y translations.

Example Code

use Libraries.Compute.Affine2

    Affine2 affine

    affine:SetToTranslation(3, 4)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action sets the affine matrix to the concatenation of translation, rotation, and scale. This is more efficient than doing all three transformations separately.

Example Code

use Libraries.Compute.Affine2
    use Libraries.Compute.Math

    Math math

    Affine2 affine

    affine:SetToTranslationRotationRadiansScale(3, 3, math:pi / 4, 2, 2)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action sets the affine matrix to the concatenation of translation, rotation, and scale. This is more efficient than doing all three transformations separately.

Example Code

use Libraries.Compute.Affine2
    use Libraries.Compute.Vector2
    use Libraries.Compute.Math

    Math math

    Affine2 affine
    Vector2 translation
    Vector2 scale

    translation:Set(3, 3)
    scale:Set(2, 2)

    affine:SetToTranslationRotationRadiansScale(translation, math:pi / 4, scale)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action sets the affine matrix to the concatenation of translation, rotation, and scale. This is more efficient than doing all three transformations separately.

Example Code

use Libraries.Compute.Affine2
    use Libraries.Compute.Vector2

    Affine2 affine
    Vector2 translation
    Vector2 scale

    translation:Set(3, 3)
    scale:Set(2, 2)

    affine:SetToTranslationRotationScale(translation, 45, scale)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action sets the affine matrix to the concatenation of translation, rotation, and scale. This is more efficient than doing all three transformations separately.

Example Code

use Libraries.Compute.Affine2

    Affine2 affine

    affine:SetToTranslationRotationScale(3, 3, 45, 2, 2)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action sets the affine matrix to the concatenation of translation and scale. This is more efficient than doing both separately.

Example Code

use Libraries.Compute.Affine2

    Affine2 affine

    affine:SetToTranslationScale(3, 3, 2, 2)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action sets the affine matrix to the concatenation of translation and scale. This is more efficient than doing both separately.

Example Code

use Libraries.Compute.Affine2
    use Libraries.Compute.Vector2

    Affine2 affine
    Vector2 translation
    Vector2 scale

    translation:Set(3, 3)
    scale:Set(2, 2)

    affine:SetToTranslationScale(translation, scale)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action multiplies the affine matrix by the shear matrix.

Example Code

use Libraries.Compute.Affine2

    Affine2 affine

    affine:SetToTranslationRotationScale(3, 3, 45, 2, 2)

    affine:Shear(2, 2)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action multiplies the affine matrix by the shear matrix.

Example Code

use Libraries.Compute.Affine2
    use Libraries.Compute.Vector2

    Affine2 affine
    Vector2 vector

    vector:Set(2, 2)
    affine:SetToTranslationRotationScale(3, 3, 45, 2, 2)

    affine:Shear(vector)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action multiplies the affine matrix with the translation matrix.

Example Code

use Libraries.Compute.Affine2
    
    Affine2 affine

    affine:SetToTranslationRotationScale(3, 3, 45, 2, 2)
    
    affine:Translate(4, 3)

    number row0column0 = affine:row0column0
    number row0column1 = affine:row0column1
    number row0column2 = affine:row0column2
    number row1column0 = affine:row1column0
    number row1column1 = affine:row1column1
    number row1column2 = affine:row1column2

    output "The affine is: "
    output "|" + row0column0 + ", " + row0column1 + ", " + row0column2 + "|"
    output "|" + row1column0 + ", " + row1column1 + ", " + row1column2 + "|"
    output "|0, 0, 1|"

This action multiplies this affine matrix with the translation matrix.

Example Code

use Libraries.Compute.Affine2
    use Libraries.Compute.Vector2

    Affine2 affine
    Vector2 vector

    affine:SetToTranslationRotationScale(3, 3, 45, 2, 2)

    vector:Set(4, 3)

    affine:Translate(vector)