8 research outputs found
Gap Processing for Adaptive Maximal Poisson-Disk Sampling
In this paper, we study the generation of maximal Poisson-disk sets with
varying radii. First, we present a geometric analysis of gaps in such disk
sets. This analysis is the basis for maximal and adaptive sampling in Euclidean
space and on manifolds. Second, we propose efficient algorithms and data
structures to detect gaps and update gaps when disks are inserted, deleted,
moved, or have their radius changed. We build on the concepts of the regular
triangulation and the power diagram. Third, we will show how our analysis can
make a contribution to the state-of-the-art in surface remeshing.Comment: 16 pages. ACM Transactions on Graphics, 201
基于重心Delaunay三角剖分的蓝噪声点采样算法
为了生成带有高质量蓝噪声性质的采样分布,提出一种基于重心Delaunay三角剖分的点采样算法.该算法将Delaunay三角剖分与1-邻域三角片重心相结合,迭代地将每个采样点移至其1-邻域三角片的重心处并更新采样点之间的拓扑连接关系;重心通过给定的密度函数计算得出.实验结果表明,本文算法在运行效率与鲁棒性方面均有一定优势.国家自然科学基金(61472332);;福建省自然科学基金(2018J01104
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
VoroCrust: Voronoi Meshing Without Clipping
Polyhedral meshes are increasingly becoming an attractive option with
particular advantages over traditional meshes for certain applications. What
has been missing is a robust polyhedral meshing algorithm that can handle broad
classes of domains exhibiting arbitrarily curved boundaries and sharp features.
In addition, the power of primal-dual mesh pairs, exemplified by
Voronoi-Delaunay meshes, has been recognized as an important ingredient in
numerous formulations. The VoroCrust algorithm is the first provably-correct
algorithm for conforming polyhedral Voronoi meshing for non-convex and
non-manifold domains with guarantees on the quality of both surface and volume
elements. A robust refinement process estimates a suitable sizing field that
enables the careful placement of Voronoi seeds across the surface circumventing
the need for clipping and avoiding its many drawbacks. The algorithm has the
flexibility of filling the interior by either structured or random samples,
while preserving all sharp features in the output mesh. We demonstrate the
capabilities of the algorithm on a variety of models and compare against
state-of-the-art polyhedral meshing methods based on clipped Voronoi cells
establishing the clear advantage of VoroCrust output.Comment: 18 pages (including appendix), 18 figures. Version without compressed
images available on https://www.dropbox.com/s/qc6sot1gaujundy/VoroCrust.pdf.
Supplemental materials available on
https://www.dropbox.com/s/6p72h1e2ivw6kj3/VoroCrust_supplemental_materials.pd