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1 November 1992 Recursive division of interrogation offset surfaces
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Proceedings Volume 1830, Curves and Surfaces in Computer Vision and Graphics III; (1992) https://doi.org/10.1117/12.131741
Event: Applications in Optical Science and Engineering, 1992, Boston, MA, United States
Abstract
For surfaces, such as Bezier or B-splines, or NURBS with positive weights, which are defined by networks of control points and for which identifiable pieces of surface are known to lie within the convex hull of a subset of the control points, recursive division is one of the most robust interrogation techniques available, guaranteeing except in very singular circumstances to find all components of the intersection. Offset surfaces, used where an object has a small non-zero thickness, and to determine cutter center loci where a cutting point must lie on a given surface, have not had this option. This paper describes a technique for applying recursive division interrogation to offset surfaces, where the offset is either constant or a function of surface normal. Sections I and II recapitulate the standard theory of recursive subdivision interrogation and the definition of offset surfaces. Section III explores the concept of procedural interface, and section IV introduces that of a Quantized Hull. Sections V to VII suggest a naive method of recursive division interrogation, discover why it does not work, and show how it may be salvaged.
© (1992) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Malcolm Sabin "Recursive division of interrogation offset surfaces", Proc. SPIE 1830, Curves and Surfaces in Computer Vision and Graphics III, (1 November 1992); https://doi.org/10.1117/12.131741
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