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The Subdivision Surfaces

The Subdivision Surfaces. Graduate School of Software Hyo Min Ahn tamimi@lycos.co.kr. 2. 1. 2. 1. 1. 1. (. (. (. (. (. (. ). ). ). ). ). ). C. C. C. C. C. C. Face split (primal type) Vertex split (dual type). Loop Scheme. Approximating, triangular meshes.

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The Subdivision Surfaces

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  1. The Subdivision Surfaces Graduate School of Software Hyo Min Ahn tamimi@lycos.co.kr

  2. 2 1 2 1 1 1 ( ( ( ( ( ( ) ) ) ) ) ) C C C C C C Face split (primal type) Vertex split (dual type)

  3. Loop Scheme • Approximating, triangular meshes. • For as proposed by Warren. For can be used

  4. Loop Scheme • Boundary edge

  5. Butterfly Scheme • Interpolating, triangular meshes. • The limit surface of original butterfly scheme is not -continuous at extraordinary points of valence

  6. Butterfly Scheme • Symmetric 8-point Butterfly SS

  7. Modified Butterfly Scheme • Interpolating, triangular meshes. • - continuous surfaces for arbitrary meshes

  8. Modified Butterfly Scheme • The edge connects two vertices of valence 6

  9. Modified Butterfly Scheme • The edge connects a K-vertex and a 6-vertex

  10. Modified Butterfly Scheme • The edge connects two extraordinary vertices • We take the average of the values computed using the appropriate scheme of the previous paragraph for each endpoint. • Boundary edge • 1-dimensional 4 point scheme

  11. Catmull-Clark Scheme • Approximating, quadrilateral meshes. • except the extraordinary vertices, where they are

  12. Catmull-Clark Scheme

  13. Catmull-Clark Scheme • Extraordinary vertices

  14. Kobbelt Scheme • sdfsd

  15. Doo-Sabin Scheme • quadrilateral meshes.

  16. Doo-Sabin Scheme • irregular

  17. P’3 P0 P3 P’’3 P’’0 P’0 P’2 P’’1 P’’2 P1 P2 P’1 Mid-Edge Scheme

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