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The kd-tree and Bounding Volume Hierarchy (BVH) are well-known datastructures for computing ray-object intersections. Less known is theConstrained Convex Space Partitioning (CCSP), which partitions space and makesthe geometric primitives exactly overlap with the boundaries of its cells.Consequently, it is robust against ill-fitting cells that plague methods withaxis-aligned cells (kd-tree, BVH) and it permits an efficient, stacklesstraversal.  Within computer graphics, CCSPs have received some attention in both 2D and3D, but their construction methods were never directly aimed at minimizingtheir traversal cost -- even having fundamentally opposing goals forDelaunay-type methods. Instead, for an isotropic and translation-invariant raydistribution the traversal cost is minimized by minimizing the weight: thetotal boundary size of all cells in the structure.  We study the 2D case using triangulations as CCSPs and minimize their totaledge length using a simulated annealing process that allows for topologicalchanges and varying vertex count. Standard Delaunay-based triangulationtechniques show total edge lengths ranging from 10% higher to twice as high asour optimized triangulations for a variety of scenes, with a similar differencein traversal cost when using the triangulations for ray tracing. Compared to aroped kd-tree, our triangulations require less traversal steps for all scenesthat we tested and they are robust against the kd-tree's pathological behaviourwhen geometry becomes misaligned with the world axes. Moreover, the stacklesstraversal strongly outperforms a BVH, which always requires a top-down descentin the hierarchy. In fact, we show several scenes where the number of traversaloperations for our triangulations decreases(!) as the number of geometricprimitives $N$ increases, in contrast to the increasing $\log N$ behaviour of aBVH.

Stackless Ray-Object Intersections Using Approximate Minimum Weight  Triangulations: Results in 2D That Outperform Roped KD-Trees (And Massively  Outperform BVHs)