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Ray Tracing Harmonic Functions
ACM Transactions on Graphics (SIGGRAPH 2024) The sphere tracing algorithm provides a fast and high-quality strategy for visualizing surfaces encoded by signed distance functions (SDFs), which have become a centerpiece in a wide range of visual computing algorithms. In this paper we introduce a sphere tracing algorithm for a completely different class of functions, harmonic functions, opening up a whole new set of possibilities.
This procedure effectively shows the result of running the Poisson surface reconstruction algorithm of Kazhdan et al. [2006], without requiring any volumetric meshing or linear solves. @article{Gillespie:2024:RTH, author = {Gillespie, Mark and Yang, Denise and Botsch, Mario and Crane, Keenan}, title = {Ray Tracing Harmonic Functions}, journal = {ACM Trans. The resulting image is both higher-quality than the simple triangulation used by most mesh viewers(bottom left), and much simpler to compute than optimizing a mesh-based minimal surface, as originally proposed by de Goes et al.[2011].
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