Scale‐Invariant Directional Alignment of Surface Parametrizations

Given a seamless parametrization of a surface as input we construct a non-conforming T-mesh aligned with it. A modified version of the motorcycle graph is employed for this purpose, in which traces do not stop at the first collision. We solve an integer linear program to assign integers to the arcs of this T-mesh. By carefully constraining this quantization, the result implies a coarse conforming quad layout whose separatrices deviate less than a user given bound from the directions prescribed by the seamless input parametrization.

Section: Resultsmentioning

confidence: 99%

Quad Layouts via Constrained T‐Mesh Quantization

Lyon

Campen

Kobbelt

2021

“…To assess our method in the context of other fully‐automatic quadrangulation techniques, we compare the results generated using our approach to those obtained using the curvature‐based field synthesis methods presented by B ommes et al [BZK09], C ampen et al [CIE∗16] and M arcias et al [MPP∗13]. For our comparison, we use the implementations and default parameters which were kindly provided by the respective authors.…”

Section: Resultsmentioning

confidence: 99%

Learning Direction Fields for Quad Mesh Generation

Dielen

Lim

Lyon

et al. 2021

Self Cite

State of the art quadrangulation methods are able to reliably and robustly convert triangle meshes into quad meshes. Most of these methods rely on a dense direction field that is used to align a parametrization from which a quad mesh can be extracted. In this context, the aforementioned direction field is of particular importance, as it plays a key role in determining the structure of the generated quad mesh. If there are no user‐provided directions available, the direction field is usually interpolated from a subset of principal curvature directions. To this end, a number of heuristics that aim to identify significant surface regions have been proposed. Unfortunately, the resulting fields often fail to capture the structure found in meshes created by human experts. This is due to the fact that experienced designers can leverage their domain knowledge in order to optimize a mesh for a specific application. In the context of physics simulation, for example, a designer might prefer an alignment and local refinement that facilitates a more accurate numerical simulation. Similarly, a character artist may prefer an alignment that makes the resulting mesh easier to animate. Crucially, this higher level domain knowledge cannot be easily extracted from local curvature information alone. Motivated by this issue, we propose a data‐driven approach to the computation of direction fields that allows us to mimic the structure found in existing meshes, which could originate from human experts or other sources. More specifically, we make use of a neural network that aggregates global and local shape information in order to compute a direction field that can be used to guide a parametrization‐based quad meshing method. Our approach is a first step towards addressing this challenging problem with a fully automatic learning‐based method. We show that compared to classical techniques our data‐driven approach combined with a robust model‐driven method, is able to produce results that more closely exhibit the ground truth structure of a synthetic dataset (i.e. a manually designed quad mesh template fitted to a variety of human body types in a set of different poses).

“…Instead of enforcing specific points to be connected by isocurves, one can enforce isocurves to form cyclic loops rather than spirals or helices around parts of an object [BLK11]. This can be achieved using a variation, or special case, of connection constraints, with a = b and the path p forming a closed loop [CIE∗16, 4.3]:…”

Section: Seamless Parametrizationsmentioning

confidence: 99%

Exact Constraint Satisfaction for Truly Seamless Parametrization

Mandad

Campen

2019

In the field of global surface parametrization a recent focus has been on so‐called seamless parametrization. This term refers to parametrization approaches which, while using an atlas of charts to enable the handling of surfaces of arbitrary topology, relate the parametrization across the cuts between charts via transition functions from special classes of transformations. This effectively makes the cuts invisible to applications which are invariant to these specific transformations in some sense. In actual implementations of these parametrization approaches, however, these restrictions are obeyed only approximately; errors stem from the tolerances of numerical solvers employed and, ultimately, from the limited accuracy of floating point arithmetic. In practice, robustness issues arise from these flaws in the seamlessness of a parametrization, no matter how small. We present a robust global algorithm that turns a given approximately seamless parametrization into an exactly seamless one ‐ that still is representable by standard floating point numbers. It supports common practically relevant additional constraints regarding boundary and feature curve alignment or isocurve connectivity, and ensures that these are likewise fulfilled exactly. This allows subsequent algorithms to operate robustly on the resulting truly seamless parametrization. We believe that the core of our method will furthermore be of benefit in a broader range of applications involving linearly constrained numerical optimization.