Quad Layout Embedding via Aligned Parameterization

This paper introduces a new approach to automatically generate pure quadrilateral patch layouts on manifold meshes. The algorithm is based on a careful construction of a singularity graph of a given input frame field or a given periodic global parameterization. A pure quadrilateral patch layout is then derived as a constrained minimum weight perfect matching of that graph. The resulting layout is optimal relative to a balance between coarseness and geometric feature alignment. We formulate the problem of finding pure quadrilateral patch layouts as a global optimization problem related to a well‐known concept in graph theory. The main advantage of the new method is its simplicity and its computation speed. Patch layouts generated by the present algorithm are high quality and are very competitive compared to current state of the art.

Section: Related Workmentioning

confidence: 99%

Perfect Matching Quad Layouts for Manifold Meshes

Razaflndrazaka

Reitebuch

Polthier

2015

“…We believe the quadrilateral patch layout could be further optimized by using the technique proposed by [CK14b]. As patches have integer sizes that are globally consistent along shared edges, this procedure produces a proper quadrangulation.…”

Section: Quadrangulationmentioning

confidence: 99%

Tracing Field‐Coherent Quad Layouts

Pietroni

Puppo

Marcias

et al. 2016

Given a cross field over a triangulated surface we present a practical and robust method to compute a field aligned coarse quad layout over the surface. The method works directly on a triangle mesh without requiring any parametrization and it is based on a new technique for tracing field-coherent geodesic paths directly on a triangle mesh, and on a new relaxed formulation of a binary LP problem, which allows us to extract both conforming quad layouts and coarser layouts containing t-junctions. Our method is easy to implement, very robust, and, being directly based on the input cross field, it is able to generate better aligned layouts, even with complicated fields containing many singularities. We show results on a number of datasets and comparisons with state-of-the-art methods

“…In some scenarios [CK14b] it is clear from the context how they shall be fixed, so this information is readily available. In some scenarios [CK14b] it is clear from the context how they shall be fixed, so this information is readily available.…”

Section: Fairest N-direction Fieldmentioning

confidence: 99%

“…This implies a much harder optimization problem with discrete degrees of freedom [CK14b]. For instance: how many turns does the field make between two directional constraints?…”

Section: Fairest N-direction Field With Directional Constraintsmentioning

confidence: 99%

“…If the constraint topology is unknown, a term + k N 2π (effectively representing a free matching and period jump) needs to be added for each directional constraint, where k is an integer variable to be optimized per constraint [CK14b]. The optimization can then still be performed using a simple sparse linear system solve.…”

Section: Fairest N-direction Field With Directional Constraintsmentioning

confidence: 99%

See 1 more Smart Citation

Directional Field Synthesis, Design, and Processing

Vaxman

Campen

Diamanti

et al. 2016

103

SummaryDirection fields and vector fields play an increasingly important role in computer graphics and geometry processing. The synthesis of directional fields on surfaces, or other spatial domains, is a fundamental step in numerous applications, such as mesh generation, deformation, texture mapping, and many more. The wide range of applications resulted in definitions for many types of directional fields: from vector and tensor fields, over line and cross fields, to frame and vector-set fields. Depending on the application at hand, researchers have used various notions of objectives and constraints to synthesize such fields. These notions are defined in terms of fairness, feature alignment, symmetry, or field topology, to mention just a few. To facilitate these objectives, various representations, discretizations, and optimization strategies have been developed. These choices come with varying strengths and weaknesses. This course provides a systematic overview of directional field synthesis for graphics applications, the challenges it poses, and the methods developed in recent years to address these challenges. PrerequisitesThe audience should have some prior experience with triangle mesh representation of geometric models, and a working knowledge of vector calculus, linear algebra, and general computer graphics fundamentals. Some familiarity with the basics of differential geometry and numerical optimization are helpful, but not required. Intended AudienceThe course targets researchers and developers who seek to understand the concepts and technologies used in direction field and vector field synthesis, learn about the most recent developments, and discern how this powerful tool, which has had impact in a variety of research and application areas, might benefit their area of work. Participants will get a broad overview, and obtain the knowledge on how to choose the proper combination of techniques for many relevant tasks. SourcesThese notes are largely based on the following state-of-the-art report by the lecturers. It has been extended to include updates on the most recent developments. • The course was subsequently given at SIGGRAPH Asia 2016, including demos and real-time coding sessions. The entire course, including the notes, the presentation slides, and the demos, is provided in the following open-source GitHub repository: https://github.com/avaxman/DirectionalFieldSynthesis Further ReadingBeing a relatively young and developing topic, no textbooks covering the various aspects of directional field synthesis in the context of computer graphics and geometry processing are available. The notes of a recent course on vector field processing offer another perspective on parts of the topic, with a focus on the discrete differential geometry aspects:• F. Her current interests are in geometry processing and modeling, specifically on vector field design, surface parametrizations, and inter-surface mappings. David Bommes RWTH Aachen University, GermanyDavid Bommes is an assistant professor in the Computer Science ...