An Incremental Approach to Feature Aligned Quad Dominant Remeshing

1. An Incremental Approach to Feature Aligned Quad Dominant Remeshing ACM Symposium on Solid and Physical Modeling 2008 報告者:丁琨桓

2. Outline • Quad remeshing paper • Relax operation

3. Introduction • 3D models of objects is now being used in more and more application fields ranging from Computer Graphics and Computer Aided Design. • Earlier algorithms for 3D reconstruction have focussed on the generation of highly detailed but unstructured triangle meshes

4. Introduction • [Variational Shape Approximation,2004] • quad meshes provide a better surface approximation well-shaped quad mesh

5. Introduction • This paper present a new algorithm which turns an unstructured triangle mesh into a quad-dominant mesh. • Quad mesh with edges aligned to the principal directions.

6. Algorithm

7. Principal Direction Estimation • This paper use the methods proposed in [Restricted Delaunay Triangulations and Normal Cycle,2003] and [Robust Principal Curvatures on Multiple Scales,2006] to estimate the principal directions at the vertices of the input mesh.

8. Principal Direction Estimation Robust Principal Curvatures on Multiple Scales,2006 Restricted Delaunay Triangulations and Normal Cycle,2003

9. Initial Mesh Generation • The starting configuration is crucial for incremental optimization. • This paper use the method proposed in [Robust feature classification and editing, 2007] which produces meshes with the vertex density adapted to the local curvature.

10. Initial Mesh Generation meshes with the vertex density adapted to the local curvature

11. Optimized triangle mesh • Original Mesh :M Initial Mesh Generation :M' • Sliding the vertices of M' over M such that the edges of M' become aligned to the pricipal direction fields of M. • After relocation, project the vertices of M'back to the nearest point of M after every iteration.

12. Optimized triangle mesh • Apply a local remeshing procedure to preserve a good mesh quality. • Use a variant of the connectivity update procedure described in [A remeshing approach tomultiresolution modeling,2004]. Original remeshing

13. Optimized triangle mesh • Collapse edges that have become shorter than some threshold • Flip edges if the maximum inner angle of one of the adjacent triangles is above some threshold

14. Quad Mesh Generation • An edge is removed if the quality ofthe resulting face is superior to the quality of the two faces. • The quality of a face is measured by its rectangularity. the quality of the two faces

15. Result Principal Direction Initial Mesh Generation Optimized triangle mesh Quad Mesh Generation

16. Result Hand model remeshed with the principal direction field

17. Result

18. Conclusion • The approach is simple, and produces quad-dominant meshes that show a very good alignment to geometric features. • T-vertices provide more flexibility in order to improve the alignment and the shape of the faces.

19. Relax operation 半規則四角網格模型 細分模型 分群結果 基底模型 原始模型 Relax operation

20. Relax operation • 增加四角片規則度 • 將每一個頂點調整移動到其相鄰點的中心點位置 • 分群區塊邊界上的點不調整 移動到其相鄰點的中心點位置 區塊邊界上的點不調整

21. Relax operation 無relaxtion relaxtion

22. Relax operation 無relaxtion relaxtion