Swizzling (computer graphics)

Vector computation used in computer graphics

Not to be confused with Pointer swizzling.

In computer graphics, swizzles are a class of operations that transform vectors by rearranging components.^[1] Swizzles can also project from a vector of one dimensionality to a vector of another dimensionality, such as taking a three-dimensional vector and creating a two-dimensional or five-dimensional vector using components from the original vector.^[2] For example, if A = {1,2,3,4}, where the components are x, y, z, and w respectively, one could compute B = A.wwxy, whereupon B would equal {4,4,1,2}. Additionally, one could create a two-dimensional vector with A.wx or a five-dimensional vector with A.xyzwx. Combining vectors and swizzling can be employed in various ways. This is common in GPGPU applications. ^[3]

In terms of linear algebra, this is equivalent to multiplying by a matrix whose rows are standard basis vectors. If $A=(1,2,3,4)^{T}$ {\displaystyle A=(1,2,3,4)^{T}}, then swizzling $A$ {\displaystyle A} as above looks like

A.wwxy={\begin{bmatrix}0&0&0&1\0円&0&0&1\1円&0&0&0\0円&1&0&0\end{bmatrix}}{\begin{bmatrix}1\2円\3円\4円\end{bmatrix}}={\begin{bmatrix}4\4円\1円\2円\end{bmatrix}}.

{\displaystyle A.wwxy={\begin{bmatrix}0&0&0&1\0円&0&0&1\1円&0&0&0\0円&1&0&0\end{bmatrix}}{\begin{bmatrix}1\2円\3円\4円\end{bmatrix}}={\begin{bmatrix}4\4円\1円\2円\end{bmatrix}}.}