Abstract In this short paper, we analyze the problem of finding the triangular barycentric coordinates of an interpolated ray hitting a given point. This task, which we term theinverse barycentric displacement problem, is general and useful in geometry processing and computer graphics. Concrete applications of the solution include the construction of displacement maps and texture baking. We derive the set of complete, closed-form solutions and discuss the number and existence of solutions. We close with a discussion of implementation-oriented optimizations and a few example applications.

Micro-meshes (μ-meshes) are a new structured graphics primitive supporting a large increase in geometric fidelity, without commensurate memory and run-time processing costs, consisting of a base mesh enriched by a displacement map. A new generation of GPUs supports this structure with native hardware μ-mesh ray-tracing, that leverages a self-bounding, compressed displacement mapping scheme to achieve these efficiencies. In this paper, we present anautomatic method to convert an existing multi-million triangle mesh into this compact format, unlocking the advantages of the data representation for a large number of scenarios. We identify the requirements for high-quality μ-meshes, and show how existing re-meshing and displacement-map baking tools are ill-suited for their generation. Our method is based on a simplification scheme tailored to the generation of high-quality base meshes , optimized for tessellation and displacement sampling, in conjunction with algorithms for determining displacement vectors to control the direction and range of displacements. We also explore the optimization of μ-meshes for texture maps and the representation of boundaries. We demonstrate our method with extensive batch processing, converting an existing collection of high-resolution scanned models to the micro-mesh representation, providing an open-source reference implementation, and, as additional material, the data and an inspection tool.