Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement

The typical goal of surface remeshing consists in finding a mesh that is (1) geometrically faithful to the original geometry, (2) as coarse as possible to obtain a low-complexity representation and (3) free of bad elements that would hamper the desired application. In this paper, we design an algorithm to address all three optimization goals simultaneously. The user specifies desired bounds on approximation error {\delta}, minimal interior angle {\theta} and maximum mesh complexity N (number of vertices). Since such a desired mesh might not even exist, our optimization framework treats only the approximation error bound {\delta} as a hard constraint and the other two criteria as optimization goals. More specifically, we iteratively perform carefully prioritized local operators, whenever they do not violate the approximation error bound and improve the mesh otherwise. In this way our optimization framework greedily searches for the coarsest mesh with minimal interior angle above {\theta} and approximation error bounded by {\delta}. Fast runtime is enabled by a local approximation error estimation, while implicit feature preservation is obtained by specifically designed vertex relocation operators. Experiments show that our approach delivers high-quality meshes with implicitly preserved features and better balances between geometric fidelity, mesh complexity and element quality than the state-of-the-art.Comment: 14 pages, 20 figures. Submitted to IEEE Transactions on Visualization and Computer Graphic

Применение сервис-ориентированной архитектуры при интеграции систем управления технологическими процессами

Отражен опыт применения сервис-ориентированной архитектуры при создании автоматизированных систем управления технологическими процессами и их интеграции на ОАО "НПК "Уралвагонзавод"

Quadrilateral surface mesh generation for animation and simulation

Besides triangle meshes, quadrilateral meshes are the most prominent discrete representation of surfaces embedded in 3D. Especially in sophisticated applications like for instance animation and simulation, they are often preferred due to their tensor-product nature, which induces several practical advantages. In contrast to their wide area of application, the available generation algorithms for high-quality quadrilateral meshes are still nonsatisfying compared to their triangle mesh counterparts. The main reason consists in the intrinsically more difficult topology, which requires global instead of local considerations. This thesis is devoted to novel algorithms that are specifically designed for the practical requirements in animation and simulation. First we will discuss important quality criteria, stemming from these applications. It turns out that, although the goal of both application areas is quite diverse, the quality criteria, which characterize a high-quality quad mesh, are identical. Apart from topological regularity, applications benefit from quadrilaterals with low distortion, well chosen curvature alignment to achieve good approximation and a coarse patch-structure in order to enable powerful mapping techniques as well as multi-level solver. Based on mixed-integer optimization and graph theory we propose carefully designed algorithms that are able to generate high-quality quadmeshes with the aforementioned properties in a fully automatic manner. Furthermore, the designer or engineer is still equipped with maximal control by the possibility of interactively influencing the automatic solution by means of additional high-level constraints

Quadrilateral surface mesh generation for animation and simulation

Besides triangle meshes, quadrilateral meshes are the most prominent discrete representation of surfaces embedded in 3D. Especially in sophisticated applications like for instance animation and simulation, they are often preferred due to their tensor-product nature, which induces several practical advantages. In contrast to their wide area of application, the available generation algorithms for high-quality quadrilateral meshes are still nonsatisfying compared to their triangle mesh counterparts. The main reason consists in the intrinsically more difficult topology, which requires global instead of local considerations. This thesis is devoted to novel algorithms that are specifically designed for the practical requirements in animation and simulation. First we will discuss important quality criteria, stemming from these applications. It turns out that, although the goal of both application areas is quite diverse, the quality criteria, which characterize a high-quality quad mesh, are identical. Apart from topological regularity, applications benefit from quadrilaterals with low distortion, well chosen curvature alignment to achieve good approximation and a coarse patch-structure in order to enable powerful mapping techniques as well as multi-level solver. Based on mixed-integer optimization and graph theory we propose carefully designed algorithms that are able to generate high-quality quadmeshes with the aforementioned properties in a fully automatic manner. Furthermore, the designer or engineer is still equipped with maximal control by the possibility of interactively influencing the automatic solution by means of additional high-level constraints

Accurate Computation of Geodesic Distance Fields for Polygonal Curves on Triangle Meshes Abstract

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 the mesh to define the zero set of the distance field. Our extensions integrate naturally into the base algorithm and consequently maintain all its nice properties. For most geometry processing algorithms, the exact geodesic distance information is sampled at the mesh vertices and the resulting piecewise linear interpolant is used as an approximation to the true distance field. The quality of this approximation strongly depends on the structure of the mesh and the location of the medial axis of the distance field. Hence our second contribution is a simple adaptive refinement scheme, which inserts new vertices at critical locations on the mesh such that the final piecewise linear interpolant is guaranteed to be a faithful approximation to the true geodesic distance field.

Algebraic Representations for Volumetric Frame Fields

Field-guided parametrization methods have proven effective for quad meshing of surfaces; these methods compute smooth cross fields to guide the meshing process and then integrate the fields to construct a discrete mesh. A key challenge in extending these methods to three dimensions, however, is representation of field values. Whereas cross fields can be represented by tangent vector fields that form a linear space, the 3D analog---an octahedral frame field---takes values in a nonlinear manifold. In this work, we describe the space of octahedral frames in the language of differential and algebraic geometry. With this understanding, we develop geometry-aware tools for optimization of octahedral fields, namely geodesic stepping and exact projection via semidefinite relaxation. Our algebraic approach not only provides an elegant and mathematically-sound description of the space of octahedral frames but also suggests a generalization to frames whose three axes scale independently, better capturing the singular behavior we expect to see in volumetric frame fields. These new odeco frames, so-called as they are represented by orthogonally decomposable tensors, also admit a semidefinite program--based projection operator. Our description of the spaces of octahedral and odeco frames suggests computing frame fields via manifold-based optimization algorithms; we show that these algorithms efficiently produce high-quality fields while maintaining stability and smoothness.Comment: 17 pages, 20 figure