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Subdivision Surfaces (SDS)
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Idea: smoothly subdivide [unterteilen] a polygonal mesh several times;
always use the same subdivision and smoothing procedure
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Demo with Cinema 4D and Maya
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Advantages:
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virtually unrestricted topology (as opposed to spline surfaces)
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editing by standard polygon-based tools
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the optimum balance of smoothness and polygon number can be found by applying
subdivision more or less often
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Example for modeling process: start from frontal and lateral images
of a head, use them as background pictures in the corresponding 3D views
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Extensions:
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Creases [Knicke] at vertices or edges
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Hierarchical editing (demo with Maya)
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Zoo of subdivision methods. Demo with Amapi.
Computation rules.
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Doo-Sabin
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Catmull-Clark: standard method in current 3D software. After the first
subdivision, the mesh consists completely of quadrangles [Vierecke].
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Loop: works on triangular meshes
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Butterfly: works on triangular meshes. This method interpolates among
the original vertices instead of approximating them.
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Problems
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Vertices with a "wrong" number of neighbors (technical term: valence) remain
as "extraordinary vertices" and may become visible due to distorsion around
them.
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Vertices with a large number of neighbors may cause the surface to oscillate.