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Semi-regular Quadrilateral-only Remeshing from Simplified Base Domains

Semi-regular Quadrilateral-only Remeshing from Simplified Base Domains. Published in Eurographics 2009 報告者 : 丁琨桓. Introducion. Polygonal models can be categorized as irregular or (semi)regular determined by structural properties of the mesh connectivity.

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Semi-regular Quadrilateral-only Remeshing from Simplified Base Domains

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  1. Semi-regular Quadrilateral-only Remeshing from Simplified Base Domains Published in Eurographics 2009 報告者:丁琨桓

  2. Introducion • Polygonal models can be categorized as irregular or (semi)regular determined by structural properties of the mesh connectivity. • For a quad mesh, a completely regular mesh is defined to be one where all vertices have valence 4.

  3. Semi-regular mesh • Semi-regular表示該網格結構是透過細分(Subdivision)技術產生 • Catmull-Clark Subdivision 連接N邊形的中心點和每一個邊的中心點

  4. Algorithm • Step1: splits an input mesh into a quad-only mesh

  5. Algorithm • Step2: deletion operators

  6. Algorithm • Step3: map the original geometry to the base domain and refined

  7. Algorithm • Step4: the vertices are reprojected to the original surface

  8. Splits an input mesh • Catmull-Clark subdivision Splitting the polygonal mesh based on Catmull-Clark subdivision rules yields quad-only elements

  9. Deletion Operators • Quadrilateral mesh simplification. In ACM SIGGRAPH Asia(2008). • This techniques describe various simplification operators, as well as weighting functions for the automated prioritization of element deletions. Low Resolution High

  10. Keyframe Meshes • Mc is the current simplified mesh. • the Hausdorff distance between Mc and Km, is greater than a specified distance d. • the projection of Km onto Mc has flipped elements. Km Km+1 Original mesh KM Keyframe Meshes stack

  11. Downward Projection

  12. Downward Projection

  13. Downward Projection • (α,β,γ) is the barycentric coordinates of p,on the sub-triangle t of the quad q. • are computed for each vertex q.vi on t’

  14. Hierarchical Keyframe Mapping • A new mesh the projection of Km onto Km-1 a b c

  15. Hierarchical Keyframe Mapping • Movement vector • are the neighboring quads of • C(q) computes the centroid of quad q • . returns the normal of evaluated at v.

  16. Hierarchical Keyframe Mapping • returns the normal of evaluated at the projection of v. • <n1,n2> is the inner product of the two vectors • The movement vector is projected and scaled, α=0.5,and is reprojected onto Km-1 • iterative ray-casting and relaxation of the vertices of Km over Km-1 until inverted elements are resolved

  17. Adaptive Resampling • Competing fronts for coarse-to-fine surface reconstruction. Computer Graphics (2006). • Ballooning scheme that improves element quality and area approximation.

  18. Adaptive Resampling

  19. Feature Preservation • The simplification operators maintain feature edge loops, annotated as important structures on the original mesh. • During the adaptive resampling method, annotated feature points are not allowed to move.

  20. Result Fertility Moai Pensatore Venus times (simplification (I), keyframe mapping (II), adaptive remesh (III)

  21. Result

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