1. Quads and Friends Kenshi Takayama

2. General Planar Quadrilateral Mesh Design Using Conjugate Direction Field goal: planar quad (PQ) mesh design – application: architectural glass structures key challenge: Conjugate Direction Field (CDF) design (warning: very hard to read for non-experts  ) Liu, Xu, Wang, Zhu, Guo, Chen, Wang MSRA, Univ. Sci. Tech. China, Peking Univ.

5. Workflow input triangular mesh initial CDFoptimized CDF output PQ mesh : user constraints on mesh directions

6. Comparison input mesh & direction constraint quad mesh from direction fields (non-planar) after planarization conjugate direction field (proposed) 4-RoSy field [Bommes09]

7. Comparison proposed [Bommes09] + planarization cannot preserve original shape!

8. Connectivity Editing for Quadrilateral Meshes goal: improve the quality of quad meshes by manual editing of connectivity Peng, Zhang, Kobayashi, Wonka Arizona State Univ., Oregon State Univ., KAUST beforeafter

9. Basic Operations Atomic Semantic Operations – combination of Basic Operations 3-5 pair movementgeneration/removal of 3-5 pair inverse

10. Pair-wise Movement Operations – combination of Atomic Semantic Operations 5 pages of theoretical analysis – quite complicated, actually...

13. Simple Quad Domains for Field Aligned Mesh Parametrization goal: modify input quad mesh such that its separatrices become simple – separatrix := consecutive edges connecting two irregular vertices  resulting in simpler domains Tarini, Puppo, Panozzo, Pietroni, Cignoni ISTI-CNR, Univ. dell’Insubria, Univ. di Genova originalmodified

14. applications: – regular remeshing – texture mapping – GPU computation (e.g., Poisson solver) workflow: – step 1: changing the separatrices’ connectivity – step 2: remeshing and smoothing

16. step 2: remeshing and smoothing – basically use one of the existing methods (unpolished writing...  ) results

18. Boundary Aligned Smooth 3D Cross-Frame Field extension of surface symmetry field to volumes applications: – hexahedral meshing – (texture synthesis?) Huang, Tong, Wei, Bao State Key Lab of CAD&CG (Zhejiang Univ.), Michigan State Univ. Surface [Palacios11] Volume (proposed)

19. ・・ ・

21. technical details: – alignment with surface normals – nonlinear optimization on tetrahedral mesh results