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The problem of parallel thread mapping is studied for the case of discreteorthogonal $m$-simplices. The possibility of a $O(1)$ time recursiveblock-space map $\lambda: \mathbb{Z}^m \mapsto \mathbb{Z}^m$ is analyzed fromthe point of view of parallel space efficiency and potential performanceimprovement. The $2$-simplex and $3$-simplex are analyzed as special cases,where constant time maps are found, providing a potential improvement of up to$2\times$ and $6\times$ more efficient than a bounding-box approach,respectively. For the general case it is shown that finding an efficientrecursive parallel space for an $m$-simplex depends of the choice of twoparameters, for which some insights are provided which can lead to a volumethat matches the $m$-simplex for $n>n_0$, making parallel space approximately$m!$ times more efficient than a bounding-box.

Possibilities of Recursive GPU Mapping for Discrete Orthogonal Simplices