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

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

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

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

TOWARDS A COMPUTATIONAL MODEL OF RETINAL STRUCTURE AND BEHAVIOR

Human vision is our most important sensory system, allowing us to perceive our surroundings. It is an extremely complex process that starts with light entering the eye and ends inside of the brain, with most of its mechanisms still to be explained. When we observe a scene, the optics of the eye focus an image on the retina, where light signals are processed and sent all the way to the visual cortex of the brain, enabling our visual sensation. The progress of retinal research, especially on the topography of photoreceptors, is often tied to the progress of retinal imaging systems. The latest adaptive optics techniques have been essential for the study of the photoreceptors and their spatial characteristics, leading to discoveries that challenge the existing theories on color sensation. The organization of the retina is associated with various perceptive phenomena, some of them are straightforward and strictly related to visual performance like visual acuity or contrast sensitivity, but some of them are more difficult to analyze and test and can be related to the submosaics of the three classes of cone photoreceptors, like how the huge interpersonal differences between the ratio of different cone classes result in negligible differences in color sensation, suggesting the presence of compensation mechanisms in some stage of the visual system. In this dissertation will be discussed and addressed issues regarding the spatial organization of the photoreceptors in the human retina. A computational model has been developed, organized into a modular pipeline of extensible methods each simulating a different stage of visual processing. It does so by creating a model of spatial distribution of cones inside of a retina, then applying descriptive statistics for each photoreceptor to contribute to the creation of a graphical representation, based on a behavioral model that determines the absorption of photoreceptors. These apparent color stimuli are reconstructed in a representation of the observed scene. The model allows the testing of different parameters regulating the photoreceptor's topography, in order to formulate hypothesis on the perceptual differences arising from variations in spatial organization