Quads and Friends Kenshi Takayama. General Planar Quadrilateral Mesh Design Using Conjugate Direction Field goal: planar quad (PQ) mesh design – application:

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Presentation transcript:

Quads and Friends Kenshi Takayama

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.

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

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

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

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

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

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

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

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

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

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)

・・・

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