Reshetov, AlexanderJosef SpjutMarc StammingerVictor Zordan2023-01-232023-01-2320222577-6193https://doi.org/10.1145/3543862https://diglib.eg.org:443/handle/10.1145/3543862We 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.CCS Concepts: Computing methodologies -> Ray tracing; Parametric curve and surface models Additional KeyWords and Phrases: Ray tracing, higher-order surfaces, bilinear patches, ruled surfaces, algebraic equations, Cauchy's bounds, GPUComputing methodologiesRay tracingParametric curve and surface models Additional KeyWords and PhrasesRay tracinghigherorder surfacesbilinear patchesruled surfacesalgebraic equationsCauchy's boundsGPU10.1145/3543862