Reshetov, AlexanderVlastimil Havran and Karthik Vaiyanathan2017-12-062017-12-062017978-1-4503-5101-02079-8679https://doi.org/10.1145/3105762.3105783https://diglib.eg.org:443/handle/10.1145/3105762-3105783We 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).Computing methodologiesRay tracingParametric curve and surface modelsBézier curvesray tracinghair and fur renderingpolynomial rootsBudanFourier theoremVincent's theoremVCAVAGVAS10.1145/3105762.3105783