Cube-Map

One method to renormalize the vectors is to use a cube map texture. Cube map texturing is a form of texture mapping that uses a 3D direction vector built from the texture coordinates (s, t, r) to access a texture that consists of six square 2D images arranged like the faces of a cube [10].

Figure 5: Cube Map

[Directional Access] ]

[RGB Coded Normalization Faces

In order to normalize a vector, the cube map can be thought as a way to store a look-up table indexed by a direction vector (Figure 5(a)). This means that vectors of varying length which point in the same direction do not change the lookup result. The normalization given in Formula 4 is precomputed for discrete values of $\vec{v}$ and stored in the cube map.

$$\vec{v}^{\prime}=\frac{\vec{v}}{\left\Vert \vec{v}\right\Vert }=\... ...{\vec{v}_{x}^{2}+\vec{v}<tex2html_comment_mark>46 _{y}^{2}+\vec{v}_{z}^{2}}}%%$$ (4)

Since parts of the render pipeline work only with positive values, the signed vector components must be range compressed from $[-1,1]$ to $[0,1]$ and stored as colors (Figure 5(b)).