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ABSTRACT
Named after the title, the PCCM transformation is a simple, explicit algorithm that creates large, smoothly joining bicubic Nurbs patches from a refined Catmull-Clark subdivision mesh. The resulting patches are maximally large in the sense that one patch corresponds to one quadrilateral facet of the initial, coarsest quadrilateral mesh before subdivision. The patches join parametrically C2 and agree with the Catmull-Clark limit surface except in the immediate neighborhood of extraordinary mesh nodes; in such a neighborhood they join at least with tangent continuity and interpolate the limit of the extraordinary mesh node. The PCCM transformation integrates naturally with array-based implementations of subdivision surfaces.
REFERENCES
Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.
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E. Catmull and J. Clark. Recursively generated B-spline sur-faces on arbitrary topological meshes. Computer Aided De-sign, 10:350-355, Oct 1978.
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OpenGL Foundation. http://trant.sgi.com/opengl/docs/man pages/hardcopy/GL/html/glu/nurbssurface.html.
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A. H. Nasri and J. Peters. Computing volumes of solids en-closed by recursive subdivision surfaces. Comp. Gr. Forum, 16(3), September 1997.
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D. Zorin. Implementing subdivision and multiresolution meshes. Chapter 6 of Course notes 37 of SIGGRAPH 99, Aug 1999.
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INDEX TERMS
Primary Classification:
I.
Computing Methodologies
I.3
COMPUTER GRAPHICS
I.3.5
Computational Geometry and Object Modeling
Subjects:
Splines
Additional Classification:
G.
Mathematics of Computing
G.1
NUMERICAL ANALYSIS
G.1.1
Interpolation
Subjects:
Smoothing
I.
Computing Methodologies
I.3
COMPUTER GRAPHICS
I.3.5
Computational Geometry and Object Modeling
Subjects:
Curve, surface, solid, and object representations;
Geometric algorithms, languages, and systems
I.3.6
Methodology and Techniques
Subjects:
Graphics data structures and data types
J.
Computer Applications
General Terms:
Design,
Measurement,
Performance,
Theory
Keywords:
CAD,
curves & surfaces,
geometric modeling
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