Robust Ray–Surface Intersections for Algebraic Surfaces

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dc.contributor.authorSzente, Péter
dc.contributor.authorKarikó, Csongor Csanád
dc.contributor.authorValasek, Gábor
dc.date.accessioned2026-04-20T08:46:48Z
dc.date.available2026-04-20T08:46:48Z
dc.date.issued2026
dc.description.abstractWe present a robust method for rendering algebraic surfaces on the GPU using only single-precision arithmetic. While fitting the surface function to a polynomial along the view ray is efficient, it typically suffers from numerical instability even at moderate degrees. We address this by employing error-free transforms to emulate higher precision without the performance cost of standard double-precision types. We show that the resulting polynomial fit can supply data for inferring directional Lipschitz bounds and we propose a new lower and upper bound on Bézier functions. Additionally, we propose a modification to Yuksel’s bracketed Newton method that uses the fitted polynomial solely to isolate monotonous segments, while the final root refinement relies on bisection of the original implicit function. This strategy ensures numerical stability and register efficiency on consumer graphics hardware. We demonstrate our results on rendering various degree algebraic surfaces.
dc.description.sectionheadersRendering Representations & GPU Pipelines
dc.description.seriesinformationEurographics 2026 - Short Papers
dc.identifier.doi10.2312/egs.20261027
dc.identifier.isbn978-3-03868-299-8
dc.identifier.issn2309-5059
dc.identifier.pages4 pages
dc.identifier.urihttps://diglib.eg.org/handle/10.2312/egs20261027
dc.identifier.urihttps://doi.org/10.2312/egs.20261027
dc.publisherThe Eurographics Association
dc.rightsCC-BY-4.0
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subjectComputer graphics
dc.subjectRasterization
dc.titleRobust Ray–Surface Intersections for Algebraic Surfaces
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