Projection

As no scaling is performed during (shear/warp) projection to the base plane and nearest-neighbor interpolation is used, voxels are projected onto integer coordinates within the base plane. Assuming that $z$ is the main viewing axis, and thus the base plane is the $xy$-plane, the projected position (index within the image buffer) of a voxel $(x,y,z)$ is

$${\bf P}\left( \begin{array}{c} x \\ y \\ z \\ \end{array} \right)= \textrm{offset}[z]+y*width_{baseplane}+x$$

$\textrm{offset}$ is the offset of the voxel with $x=0, y=0$ within a volume slice at depth $z$, $width_{baseplane}$ is the width of the base plane image in pixels. The resulting value can be directly used as an index to access the affected pixel of the base plane.

mailto:mroz@cg.tuwien.ac.at.