Compatible quadrangulation by sketching

Abstract

Mesh quadrangulation has received increasing attention in the past decade. While previous works have mostly focused on producing a high quality quad mesh of a single model, the connectivity of the quadrangulation is typically difficult to control and varies among models even with similar shapes. In this paper, we propose a novel interactive framework for quadrangulating a set of models collectively with compatible connectivity. Furthermore, we demonstrate its application to 3D mesh morphing. In our approach, the user interactively sketches a skeleton within each model, and our method automatically computes compatible base domains for all models from these skeletons, on which the models are parameterized. With this novel parameterization, it is very easy to generate a pleasing and smooth 3D morphing sequence among these compatible models. The method yields quadrangulation with comparable quality to existing approaches, but greatly simplifies compatible re-meshing among a group of topologically equivalent models, in particular characters and animals models, with direct applications in shape blending and morphing.

Restricted Trivariate Polycube Splines for Volumetric Data Modeling

“…M; P ; M & IR 3 . The polycube P can be constructed either manually [19], [20], [29] or automatically [21], [22]. These techniques also provide the boundary mapping g from the polycube boundary surface (denoted as @P ) to the boundary of M (@M).…”

“…Along the following two directions, we would like to also explore volumetric mapping techniques for parameterization with higher quality: 1) We can use more complicated/general parametric domains such as manifold domains (directly represented by tetrahedral meshes), polytubes [29], and so forth, which may more flexibly approximate the shape and yield lower distortion. However, on such domains, it becomes more challenging to construct regular splines providing the same favorable features of RTP-splines.…”

Scaffolding skeletons using spherical Voronoi diagrams: Feasibility, regularity and symmetry

“…Still the stitching process might leave some triangular patches at the joints. [24] and [26] proposed a scaffolding technique that generates a pure-quad mesh by extruding boxes emanating from cubes positioned at the joints. In [24] the subdivision of the cubes is modeled with an Integer Linear Program, for which a solution might fail to exist when there are cycles in the skeleton.…”

“…"Lids" [24, Figure 6] are introduced as a workaround. [26] also introduces extra quads around joints [26,Figure 4].…”

“…A scaffold can be used to generate a surface, either by subdivision as in [4], or as initial patchwork for a spline surface [7,16] (see Figure 1). It is used as an intermediate step in the extraction of a quad layout on a given triangular mesh [5,24], and for compatible quadrangulation [26]. An application we present here is the polygonization of skeleton-based implicit surfaces into quad-dominant meshes.…”