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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