We introduce the Hierarchical Poisson Disk Sampling Multi-Triangulation (HPDS-MT) of surfaces, a novel structure that combines the power of multi-triangulation (MT) with the benefits of Hierarchical Poisson Disk Sampling (HPDS). MT is a general framework for representing surfaces through variable resolution triangle meshes, while HPDS is a well-spaced random distribution with blue noise characteristics. The distinguishing feature of the HPDS-MT is its ability to extract adaptive meshes whose triangles are guaranteed to have good shape quality. The key idea behind the HPDS-MT is a preprocessed hierarchy of points, which is used in the construction of a MT via incremental simplification. In addition to proving theoretical properties on the shape quality of the triangle meshes extracted by the HPDS-MT, we provide an implementation that computes the HPDS-MT with high accuracy. Our results confirm the theoretical guarantees and outperform similar methods. We also prove that the Hausdorff distance between the original surface and any (extracted) adaptive mesh is bounded by the sampling distribution of the radii of Poisson-disks over the surface. Finally, we illustrate the advantages of the HPDS-MT in some typical problems of geometry processing.

Abstract Structured light scanning is ubiquituous in 3D acquisition. It is capable of capturing high geometric detail at a low cost under a variety of challenging scene conditions. Recent methods have demonstrated robustness in the presence of artifacts due to global illumination, such as inter‐reflections and sub‐surface scattering, as well as imperfections caused by projector defocus. For comparing approaches, however, the quantitative evaluation of structured lighting schemes is hindered by the challenges in obtaining ground truth data, resulting in a poor understanding for these methods across a wide range of shapes, materials, and lighting configurations. In this paper, we present a benchmark to study the performance of structured lighting algorithms in the presence of errors caused due to the above properties of the scene. In order to do this, we construct a synthetic structured lighting scanner that uses advanced physically based rendering techniques to simulate the point cloud acquisition process. We show that, under conditions similar to that of a real scanner, our synthetic scanner replicates the same artifacts found in the output of a real scanner. Using this synthetic scanner, we perform a quantitative evaluation of four different structured lighting techniques – gray‐code patterns, micro‐phase shifting, ensemble codes, and unstructured light scanning. The evaluation, performed on a variety of scenes, demonstrate that no one method is capable of adequately handling all sources of error – each method is appropriate for addressing distinct sources of error.

Abstract Performances of actual mesh compression algorithms vary significantly depending on the type of model it encodes. These methods rely on prior assumptions on the mesh to be efficient, such as regular connectivity, simple topology and similarity between its elements. However, these priors are implicit in usual schemes, harming their suitability for specific models. In particular, connectivity‐driven schemes are difficult to generalize to higher dimensions and to handle topological singularities. GEncode is a new single‐rate, geometry‐driven compression scheme where prior knowledge of the mesh is plugged into the coder in an explicit manner. It encodes meshes of arbitrary dimension without topological restrictions, but can incorporate topological properties, such as manifoldness, to improve the compression ratio. Prior knowledge of the geometry is taken as an input of the algorithm, represented by a function of the local geometry. This suits particularly well for scanned and remeshed models, where exact geometric priors are available. Compression results surfaces and volumes are competitive with existing schemes.