Data-driven interactive quadrangulation

Representing digital objects with structured meshes that embed a coarse block decomposition is a relevant problem in applications like computer animation, physically-based simulation and Computer Aided Design (CAD). One of the key ingredients to produce coarse block structures is to achieve a good alignment between the mesh singularities (i.e., the corners of each block). In this paper we improve on the polycube-based meshing pipeline to produce both surface and volumetric coarse block-structured meshes of general shapes. To this aim we add a new step in the pipeline. Our goal is to optimize the positions of the polycube corners to produce as coarse as possible base complexes. We rely on re-mapping the positions of the corners on an integer grid and then using integer numerical programming to reach the optimal. To the best of our knowledge this is the first attempt to solve the singularity misalignment problem directly in polycube space. Previous methods for polycube generation did not specifically address this issue. Our corner optimization strategy is efficient and requires a negligible extra running time for the meshing pipeline. In the paper we show that our optimized polycubes produce coarser block structured surface and volumetric meshes if compared with previous approaches. They also induce higher quality hexahedral meshes and are better suited for spline fitting because they reduce the number of splines necessary to cover the domain, thus improving both the efficiency and the overall level of smoothness throughout the volume

Section: Related Workmentioning

confidence: 99%

Polycube Simplification for Coarse Layouts of Surfaces and Volumes

Cherchi

Livesu

Scateni

2016

“…Quad layouts may also be obtained from quad meshes via base complex simplification [BLK11; TPP*11]. Besides fully automatic methods, interactive user‐guided layout generation tools [TPSS13; CK14a; MTP*15] have been proposed as well.…”

Section: Related Workmentioning

confidence: 99%

Layout Embedding via Combinatorial Optimization

Born

Schmidt

Kobbelt

2021

Figure 1: We embed a given layout connectivity (left, visualized as a coarse mesh for illustration) into a target surface with prescribed landmark positions (center left) by successively embedding edges as shortest paths in an optimized order. Previous methods choose a greedy sequence of locally optimal decisions, which can lead to severe topological artifacts (center right) due to accidental blocking of subsequently inserted paths. Our branch-and-bound method globally optimizes over all possible edge insertion sequences to find an embedding of shortest total path length, which yields the expected homotopy class (right).

“…Our spirit in this work is also shared by some prior work on interactive quad remeshing [TPSHSH13, CK14, MTP∗15, JTPSH15, ESCK16] where the user expresses through intuitive interfaces her particular application‐specific intent that would otherwise not be captured by automatic algorithms. We believe similar tools for hex meshing to be valuable, but to our knowledge, no such attempt has been reported so far in the literature.…”

Section: Related Workmentioning

confidence: 99%

Dual Sheet Meshing: An Interactive Approach to Robust Hexahedralization

Takayama

2019

Self Cite

The combinatorial dual of a hex mesh induces a collection of mutually intersecting surfaces (dual sheets). Inspired by Campen et al.'s work on quad meshing [CBK12, CK14], we propose to directly generate such dual sheets so that, as long as the volume is properly partitioned by the dual sheets, we are guaranteed to arrive at a valid all‐hex mesh topology. Since automatically generating dual sheets seems much harder than the 2D counterpart, we chose to leave the task to the user; our system is equipped with a few simple 3D modeling tools for interactively designing dual sheets. Dual sheets are represented as implicit surfaces in our approach, greatly simplifying many of the computational steps such as finding intersections and analyzing topology. We also propose a simple algorithm for primalizing the dual graph where each dual cell, often enclosing singular edges, gets mapped onto a reference polyhedron via harmonic parameterization. Preservation of sharp features is simply achieved by modifying the boundary conditions. We demonstrate the feasibility of our approach through various modeling examples.