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Segment Tracing Using Local Lipschitz Bounds
Author(s) -
Galin Eric,
Guérin Eric,
Paris Axel,
Peytavie Adrien
Publication year - 2020
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.13951
Subject(s) - lipschitz continuity , computer science , computation , intersection (aeronautics) , tracing , ray tracing (physics) , algorithm , field (mathematics) , theoretical computer science , mathematics , pure mathematics , physics , quantum mechanics , engineering , aerospace engineering , operating system
We introduce Segment Tracing, a new algorithm that accelerates the classical Sphere Tracing method for computing the intersection between a ray and an implicit surface. Our approach consists in computing the Lipschitz bound locally over a segment to improve the marching step computation and accelerate the overall process. We describe the computation of the Lipschitz bound for different operators and primitives. We demonstrate that our algorithm significantly reduces the number of field function queries compared to previous methods, without the need for additional accelerating data‐structures. Our method can be applied to a vast variety of implicit models ranging from hierarchical procedural objects built from complex primitives, to simulation‐generated implicit surfaces created from many particles.