Ray tracing objects defined by sweeping planar cubic splines
ACM Transactions on Graphics (TOG)
New Techniques for Ray Tracing Procedurally Defined Objects
ACM Transactions on Graphics (TOG)
An improved illumination model for shaded display
Communications of the ACM
Computer Vision
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
Ray tracing algebraic surfaces
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Ray tracing parametric patches
SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques
Polynomial real root isolation using Descarte's rule of signs
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
An updated cross-indexed guide to the ray-tracing literature
ACM SIGGRAPH Computer Graphics
Corrigendum: Ray tracing generalized cylinders
ACM Transactions on Graphics (TOG)
Modeling generalized cylinders via Fourier morphing
ACM Transactions on Graphics (TOG)
Approximate envelope reconstruction for moving solids
Mathematical Methods for Curves and Surfaces
Computation of rotation minimizing frames
ACM Transactions on Graphics (TOG)
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An algorithm is presented for ray tracing generalized cylinders, that is, objects defined by sweeping a two-dimensional contour along a three-dimensional trajectory. The contour can be any 'well-behaved' curve in the sense that it is continuous, and that the points where the tangent is horizontal or vertical can be determined, the trajectory can be any spline curve. First a definition is given of generalized cylinders in terms of the Frenet frame of the trajectory. Then the main problem in ray tracing these objects, the computation of the intersection points with a ray, is reduced to the problem of intersecting two two-dimensional curves. This problem is solved by a subdivision algorithm. The three-dimensional normal at the intersection point closest to the eye point, necessary to perform shading, is obtained by transforming the two-dimensional normal at the corresponding intersection point of the two two-dimensional curves. In this way it is possible to obtain highly realistic images for a very broad class of objects.