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Vector Matrix Toolset v1.0
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11.0, 10.5, 10.0, 9.0, 8.0, 7.1, 7.0 or later
18 Feb 2018
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Introduction
The toolset is seperated into 2 categories. One to operate on vectors3 and one to operate on 4x4 transformation matrices.
Every pixel can be worked on independently because each can have its own vector and matrix data.
Vector
Vector data is expected to be in the layer rgb.
(r, g, b) = (x, y, z)
Operations like vector addition, substraction, multiplication and division can be done with a standard merge or merge expression node.
Vector_magnitude
Vector_Normalized
Vector_Dot
Vector_Cross
Vector_Apply_Matrix
Matrix
Matrix data is expected to be in the layers; matrix0, matrix1, matrix2 and matrix3.
Layers are automatically created by the nodes.
The transformation matrix is stored as followed:
matrix0: [0, 1, 2, 3,
matrix1: 0, 1, 2, 3,
matrix2: 0, 1, 2, 3,
matrix3: 0, 1, 2, 3]
Matrix_Identity
Matrix_Invert
Matrix_Product
Matrix_Transform
Matrix_Translate
Matrix_Rotate
Matrix_Scale
Matrix_Transpose
Matrix_Determinant
Matrix_3x3_det
Matrix_2x2_det
Vector operators
Vector_Magnitude
Returns the magnitude of a vector. In other words, the vector's length.
The resulted output is repeated to fill up the output vector.
input: vector
output: vector
Vector_Normalize
Returns the normalized vector.
Scaling the vector so that its length equal 1.
input: vector
output: vector
Vector_Dot
Returns the dot product between 2 vectors.
The resulted output is repeated to fill up the output vector.
inputs: vectorA, vectorB
output: vector
Vector_Cross
Returns the cross product between 2 vectors.
input: vectorA, vectorB
output: vector
Vector_Apply_Matrix
Returns a new vector resulted by the input vector multiplied by the input matrix.
inputs: vector, matrix
output: vector
Matrix operators
Matrix_Identity
Returns an 4x4 identity matrix.
The input bg is used to give a format to the matrix.
input: bg
ouput: matrix
Matrix_Invert
Returns the inverted input 4x4 matrix.
input: matrix
output: matrix
Matrix_Product
Returns the dot product of matrixB * matrixA.
The matrix order is very important as switching A and B will give different results.
inputs: matrixB, matrixA
output: matrix
Matrix_Transform
Retuns the input 4x4 matrix transformed by the the node's knobs.
If no matrix is given, the transformations will be made on a identity matrix.
input: matrix
output: matrix
Matrix_Translate
Returns the input 4x4 matrix translated by the input vector.
inputs: matrix, vector
output: matrix
Matrix_Rotate
Returns the input 4x4 matrix rotated by the input vector.
inputs: matrix, vector
output: matrix
The rotation unit knob specify the rotation unit(degrees or radians) of the input vector.
The rotation order knob specify the order in which the axes are rotated
Matrix_Scale
Returns the input 4x4 matrix scaled by the input vector.
inputs: matrix, vector
output: matrix
Matrix_Transpose
Returns the input 4x4 matrix transposed.
Values of the matrix are mirrored diagonally.
inputs: matrix
output: matrix
Matrix_Determinant
Returns the determinant of the input 4x4 matrix.
The resulted output is repeated to fill up the output vector.
inputs: matrix
output: vector
Matrix_3x3_det
Returns the determinant of the input 3x3 matrix.
The resulted output is repeated to fill up the output vector.
Utility operator used by the Matrix_Determinant and Matrix_Invert operators.
inputs: matrix
output: vector
Matrix_2x2_det
Returns the determinant of the input 2x2 matrix.
The resulted output is repeated to fill up the output vector.
Utility operator used by the Matrix_3x3_det, Matrix_Determinant and Matrix_Invert operators.
inputs: matrix
output: vector
Comments
We should combine our toolsets, I have one slightly similar for Vector operations only. http://www.nukepedia.com/toolsets/other/vectortools, though I'm missing a few of yours.
You have a great toolset and some very useful tutorials on your website. Its something that i aim to do with mine once i have finished building my other tools which use this one.
I love the idea of having a centralised place for math operators and mine does not cover 2D vectors yet or their 3x3 matrix either.
I am still new to nukepedia so i am not sure how a collab would work but i am all for it.
I can start the project today although i will be on vacation for 3 weeks starting tomorrow so i wont be able to update before i come back.
https://github.com/mapoga/nuke-vector-matrix
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