130 research outputs found
Htex: Per-Halfedge Texturing for Arbitrary Mesh Topologies
We introduce per-halfedge texturing (Htex) a GPU-friendly method for
texturing arbitrary polygon-meshes without an explicit parameterization. Htex
builds upon the insight that halfedges encode an intrinsic triangulation for
polygon meshes, where each halfedge spans a unique triangle with direct
adjacency information. Rather than storing a separate texture per face of the
input mesh as is done by previous parameterization-free texturing methods, Htex
stores a square texture for each halfedge and its twin. We show that this
simple change from face to halfedge induces two important properties for high
performance parameterization-free texturing. First, Htex natively supports
arbitrary polygons without requiring dedicated code for, e.g, non-quad faces.
Second, Htex leads to a straightforward and efficient GPU implementation that
uses only three texture-fetches per halfedge to produce continuous texturing
across the entire mesh. We demonstrate the effectiveness of Htex by rendering
production assets in real time
Hierarchical Riesz bases for Hs(Omega), 1 < s < 5/2
On arbitrary polygonal domains , we construct hierarchical Riesz bases for Sobolev spaces . In contrast to an earlier construction by Dahmen, Oswald, and Shi (1994), our bases will be of Lagrange instead of Hermite type, by which we extend the range of stability from to . Since the latter range includes , with respect to the present basis, the stiffness matrices of fourth-order elliptic problems are uniformly well-conditioned
Quad Meshing
Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi-regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this State of the Art Report, we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrization, and remeshing
Global parametrization of range image sets
We present a method to globally parameterize a surface represented by height maps over a set of planes (range images). In contrast to other parametrization techniques, we do not start with a manifold mesh. The parametrization we compute defines a manifold structure, it is seamless and globally smooth, can be aligned to geometric features and shows good quality in terms of angle and area preservation, comparable to current parametrization techniques for meshes. Computing such global seamless parametrization makes it possible to perform quad remeshing, texture mapping and texture synthesis and many other types of geometry processing operations. Our approach is based on a formulation of the Poisson equation on a manifold structure defined for the surface by the range images. Construction of such global parametrization requires only a way to project surface data onto a set of planes, and can be applied directly to implicit surfaces, nonmanifold surfaces, very large meshes, and collections of range scans. We demonstrate application of our technique to all these geometry types
Learning quadrangulated patches for 3D shape parameterization and completion
We propose a novel 3D shape parameterization by surface patches, that are
oriented by 3D mesh quadrangulation of the shape. By encoding 3D surface detail
on local patches, we learn a patch dictionary that identifies principal surface
features of the shape. Unlike previous methods, we are able to encode surface
patches of variable size as determined by the user. We propose novel methods
for dictionary learning and patch reconstruction based on the query of a noisy
input patch with holes. We evaluate the patch dictionary towards various
applications in 3D shape inpainting, denoising and compression. Our method is
able to predict missing vertices and inpaint moderately sized holes. We
demonstrate a complete pipeline for reconstructing the 3D mesh from the patch
encoding. We validate our shape parameterization and reconstruction methods on
both synthetic shapes and real world scans. We show that our patch dictionary
performs successful shape completion of complicated surface textures.Comment: To be presented at International Conference on 3D Vision 2017, 201
Connectivity Control for Quad-Dominant Meshes
abstract: Quad-dominant (QD) meshes, i.e., three-dimensional, 2-manifold polygonal meshes comprising mostly four-sided faces (i.e., quads), are a popular choice for many applications such as polygonal shape modeling, computer animation, base meshes for spline and subdivision surface, simulation, and architectural design. This thesis investigates the topic of connectivity control, i.e., exploring different choices of mesh connectivity to represent the same 3D shape or surface. One key concept of QD mesh connectivity is the distinction between regular and irregular elements: a vertex with valence 4 is regular; otherwise, it is irregular. In a similar sense, a face with four sides is regular; otherwise, it is irregular. For QD meshes, the placement of irregular elements is especially important since it largely determines the achievable geometric quality of the final mesh.
Traditionally, the research on QD meshes focuses on the automatic generation of pure quadrilateral or QD meshes from a given surface. Explicit control of the placement of irregular elements can only be achieved indirectly. To fill this gap, in this thesis, we make the following contributions. First, we formulate the theoretical background about the fundamental combinatorial properties of irregular elements in QD meshes. Second, we develop algorithms for the explicit control of irregular elements and the exhaustive enumeration of QD mesh connectivities. Finally, we demonstrate the importance of connectivity control for QD meshes in a wide range of applications.Dissertation/ThesisDoctoral Dissertation Computer Science 201
Quadrilateral Meshes with Bounded Minimum Angle
This paper presents an algorithm that utilizes a quadtree to construct a strictly convex quadrilateral mesh for a simple polygonal region in which no newly created angle is smaller than . This is the first known result, to the best of our knowledge, on quadrilateral mesh generation with a provable guarantee on the minimum angle
Quadrilateral Meshes with Bounded Minimum Angle
This paper presents an algorithm that utilizes a quadtree to construct a strictly convex quadrilateral mesh for a simple polygonal region in which no newly created angle is smaller than . This is the first known result, to the best of our knowledge, on quadrilateral mesh generation with a provable guarantee on the minimum angle
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