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Ray/Ribbon Intersections

Published: 27 July 2022 Publication History

Abstract

We present a new ray tracing primitive---a curved ribbon, which is embedded inside a ruled surface. We describe two such surfaces. Ribbons inside doubly ruled bilinear patches can be intersected by solving a quadratic equation. We also consider a singly ruled surface with a directrix defined by a quadratic Bézier curve and a generator---by two linearly interpolated bitangent vectors. Intersecting such a surface requires solving a cubic equation, but it provides more fine-tuned control of the ribbon shape.
These two primitives are smooth, composable, and allow fast non-iterative intersections. These are the first primitives that possess all such properties simultaneously.

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cover image Proceedings of the ACM on Computer Graphics and Interactive Techniques
Proceedings of the ACM on Computer Graphics and Interactive Techniques  Volume 5, Issue 3
July 2022
198 pages
EISSN:2577-6193
DOI:10.1145/3552302
Issue’s Table of Contents
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Publication History

Published: 27 July 2022
Published in PACMCGIT Volume 5, Issue 3

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Author Tags

  1. Cauchy's bounds
  2. GPU
  3. Ray tracing
  4. algebraic equations
  5. bilinear patches
  6. higher-order surfaces
  7. ruled surfaces

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