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Quads and FriendsKenshi TakayamaGeneral Planar Quadrilateral Mesh Design Using Conjugate Direction Fieldgoal: planar quad (PQ) mesh designapplication: architectural glass structures

key challenge: Conjugate Direction Field (CDF) design(warning: very hard to read for non-experts)Liu, Xu, Wang, Zhu, Guo, Chen, WangMSRA, Univ. Sci. Tech. China, Peking Univ.

Workflow

input triangular meshinitial CDFoptimized CDFoutput PQ mesh: user constraints on mesh directionsComparison

input mesh & direction constraintquad mesh from direction fields (non-planar)after planarizationconjugate direction field (proposed)4-RoSy field[Bommes09]Comparison

proposed[Bommes09] + planarizationcannot preserve original shape!7Connectivity Editing for Quadrilateral Meshesgoal: improve the quality of quad meshes by manual editing of connectivityPeng, Zhang, Kobayashi, WonkaArizona State Univ., Oregon State Univ., KAUST

beforeafterBasic Operations

Atomic Semantic Operationscombination of Basic Operations

3-5 pair movementgeneration/removal of 3-5 pairinversePair-wise Movement Operationscombination of Atomic Semantic Operations

5 pages of theoretical analysisquite complicated, actually...

Simple Quad Domains for Field Aligned Mesh Parametrizationgoal: modify input quad mesh such that its separatrices become simpleseparatrix := consecutive edges connecting two irregular vertices resulting in simpler domains

Tarini, Puppo, Panozzo, Pietroni, CignoniISTI-CNR, Univ. dellInsubria, Univ. di Genova

originalmodified

applications:regular remeshingtexture mappingGPU computation (e.g., Poisson solver)workflow:step 1: changing the separatrices connectivitystep 2: remeshing and smoothing

step 2: remeshing and smoothingbasically use one of the existing methods

(unpolished writing...)

results

Boundary Aligned Smooth 3D Cross-Frame Fieldextension of surface symmetry field to volumes

applications:hexahedral meshing(texture synthesis?)Huang, Tong, Wei, BaoState Key Lab of CAD&CG (Zhejiang Univ.), Michigan State Univ.

Surface[Palacios11]Volume(proposed)

technical details:alignment with surface normalsnonlinear optimization on tetrahedral meshresults