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- David Bommes, Henrik Zimmer, Leif Kobbelt
- ACM Trans. Graph.
- 2009

We present a novel method for quadrangulating a given triangle mesh. After constructing an as smooth as possible symmetric cross field satisfying a sparse set of directional constraints (to capture the geometric structure of the surface), the mesh is cut open in order to enable a low distortion unfolding. Then a seamless globally smooth parametrization is… (More)

- David Bommes, Marcel Campen, Hans-Christian Ebke, Pierre Alliez, Leif Kobbelt
- ACM Trans. Graph.
- 2013

Quadrilateral remeshing approaches based on global parametrization enable many desirable mesh properties. Two of the most important ones are (1) high regularity due to explicit control over irregular vertices and (2) smooth distribution of distortion achieved by convex variational formulations. Apart from these strengths, state-of-the-art techniques suffer… (More)

- David Bommes, Timm Lempfer, Leif Kobbelt
- Comput. Graph. Forum
- 2011

We introduce a fully automatic algorithm which optimizes the high-level structure of a given quadrilateral mesh to achieve a coarser quadrangular base complex. Such a topological optimization is highly desirable, since state-of-the-art quadrangulation techniques lead to meshes which have an appropriate singularity distribution and an anisotropic element… (More)

- David Bommes, Bruno Lévy, +4 authors Denis Zorin
- Comput. Graph. Forum
- 2013

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… (More)

- Marcel Campen, David Bommes, Leif Kobbelt
- ACM Trans. Graph.
- 2012

We present a theoretical framework and practical method for the automatic construction of simple, all-quadrilateral patch layouts on manifold surfaces. The resulting layouts are coarse, surface-embedded cell complexes well adapted to the geometric structure, hence they are ideally suited as domains and base complexes for surface parameterization, spline… (More)

- David Bommes, Leif Kobbelt
- VMV
- 2007

We present an algorithm for the efficient and accurate computation of geodesic distance fields on triangle meshes. We generalize the algorithm originally proposed by Surazhsky et al. [1]. While the original algorithm is able to compute geodesic distances to isolated points on the mesh only, our generalization can handle arbitrary, possibly open, polygons on… (More)

- Hans-Christian Ebke, David Bommes, Marcel Campen, Leif Kobbelt
- ACM Trans. Graph.
- 2013

The most popular and actively researched class of quad remeshing techniques is the family of <i>parametrization based quad meshing methods</i>. They all strive to generate an <i>integer-grid map</i>, i.e. a parametrization of the input surface into R<sup>2</sup> such that the canonical grid of integer iso-lines forms a quad mesh when mapped back onto the… (More)

- Mario Botsch, David Bommes, Leif Kobbelt
- IMA Conference on the Mathematics of Surfaces
- 2005

The use of polygonal mesh representations for freeform geometry enables the formulation of many important geometry processing tasks as the solution of one or several linear systems. As a consequence, the key ingredient for efficient algorithms is a fast procedure to solve linear systems. A large class of standard problems can further be shown to lead more… (More)

- Henrik Zimmer, Marcel Campen, David Bommes, Leif Kobbelt
- Comput. Graph. Forum
- 2012

Figure 1: Point-folding structure built from pyramidal elements according to a triangulated free-form base surface. Although almost all base triangles are non-similar, thanks to rationalization only 21 mold dies are necessary to produce the 270 elements. Abstract In mechanical engineering and architecture, structural elements with low material consumption… (More)

- Mario Botsch, David Bommes, Christoph Vogel, Leif Kobbelt
- 12th Pacific Conference on Computer Graphics and…
- 2004

In an increasing number of applications triangle meshes represent a flexible and efficient alternative to traditional NURBS-based surface representations. Especially in engineering applications it is crucial to guarantee that a prescribed approximation tolerance to a given reference geometry is respected for any combination of geometric algorithms that are… (More)