NDLI: Algorithm 783: Pcp2Nurb—smooth free-form surfacing with linearly trimmed bicubic B-splines

Content Provider	ACM Digital Library
Author	Peters, Jörg
Copyright Year	1998
Abstract	Unrestricted control polyhedra facilitate modeling free-form surfaces of arbitrary topology and local patch-layout by allowing $\textit{n}-sided,$ possibly nonplanar, facets and $\textit{m}-valent$ vertices. By cutting off edges and corners, the smoothing of an unrestricted control polyhedron can be reduced to the smoothing of a planar-cut polyhedron. A planar-cut polyhedron is a generalization of the well-known tensor-product control structure. The routine Pcp2Nurb in turn translates planar-cut polyhedra to a collection of four-sided linearly trimmed bicubic B-splines and untrimmed biquadratic B-splines. The routine can thus serve as central building block for overcoming topological constraints in the mathematical modeling of smooth surfaces that are stored, transmitted, and rendered using only the standard representation in industry. Specifically, on input of a nine-point subnet of a planar-cut polyhedron, the routine outputs a trimmed bicubic NURBS patch. If the subnet does not have geometrically redundant edges, this patch joins smoothly with patches from adjacent subnets as a four-sided piece of a regular $\textit{C1}$ surface. The patch integrates smoothly with untrimmed biquadratic tensor-product surfaces derived from subnets with tensor-product structure. Sharp features can be retained in this representation by using geometrically redundant edges in the planar-cut polyhedron. The resulting surface follows the outlines of the planar-cut polyhedron in the manner traditional tensor-product splines follow the outline of their rectilinear control polyhedron. In particular, it stays in the local convex hull of the planar-cut polyhedron.
Starting Page	261
Ending Page	267
Page Count	7
File Format	PDF
ISSN	00983500
e-ISSN	15577295
DOI	10.1145/292395.292399
Volume Number	24
Issue Number	3
Journal	ACM Transactions on Mathematical Software (TOMS)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1998-09-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	$\textit{C1}$ surface Matlab NURBS Arbitrary patch layout Arbitrary surface topology Biquadratic tensor-product B-splines Free-form surface Planar-cut polyhedron Trimmed bicubic B-splines
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Software

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Algorithm 783: Pcp2Nurb—smooth free-form surfacing with linearly trimmed bicubic B-splines

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Algorithm 783: Pcp2Nurb—smooth free-form surfacing with linearly trimmed bicubic B-splines