Exploiting Budan-Fourier and Vincent's Theorems for Ray Tracing 3D Bézier Curves

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dc.contributor.authorReshetov, Alexanderen_US
dc.contributor.editorVlastimil Havran and Karthik Vaiyanathanen_US
dc.date.accessioned2017-12-06T19:47:29Z
dc.date.available2017-12-06T19:47:29Z
dc.date.issued2017
dc.description.abstractWe present a new approach to finding ray-cubic Bézier curve intersections by leveraging recent achievements in polynomial studies. Compared with the state-of-the-art adaptive linearization, it increases performance by 5-50 times, while also improving the accuracy by 1000X. Our algorithm quickly eliminates parts of the curve for which the distance to the given ray is guaranteed to be bigger than a model-specific threshold (maximum curve's half-width). We then reduce the interval with the isolated distance minimum even further and apply a single iteration of a non-linear root-finding technique (Ridders' method).en_US
dc.description.sectionheadersRay Traversal and Intersection
dc.description.seriesinformationEurographics/ ACM SIGGRAPH Symposium on High Performance Graphics
dc.identifier.doi10.1145/3105762.3105783
dc.identifier.isbn978-1-4503-5101-0
dc.identifier.issn2079-8679
dc.identifier.urihttps://doi.org/10.1145/3105762.3105783
dc.identifier.urihttps://diglib.eg.org:443/handle/10.1145/3105762-3105783
dc.publisherACMen_US
dc.subjectComputing methodologies
dc.subjectRay tracing
dc.subjectParametric curve and surface models
dc.subjectBézier curves
dc.subjectray tracing
dc.subjecthair and fur rendering
dc.subjectpolynomial roots
dc.subjectBudan
dc.subjectFourier theorem
dc.subjectVincent's theorem
dc.subjectVCA
dc.subjectVAG
dc.subjectVAS
dc.titleExploiting Budan-Fourier and Vincent's Theorems for Ray Tracing 3D Bézier Curvesen_US
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High-Performance Graphics 2017