Static 3D Triangle Mesh Compression Overview

3D triangle meshes are extremely used to model discrete surfaces, and almost always represented with two tables: one for geometry and another for connectivity. While the raw size of a triangle mesh is of around 200 bits per vertex, by coding cleverly (and separately) those two distinct kinds of information it is possible to achieve compression ratios of 15:1 or more. Different techniques must be used depending on whether single-rate vs. progressive bitstreams are sought; and, in the latter case, on whether or not hierarchically nested meshes are desirable during reconstructio

Mesh Compression

Embodiments described herein improve the lossless compression ratio of the Corto codec. An example mesh used for 3D graphics rendering may have many vertices, where each vertex coordinate is composed of X,Y integer pixel position coordinates, and Z is a floating point depth coordinate whose value ranges from 0 (close) to 1 (far). The depth value is coded as a “half float” 16 bit value

Sparse operator compression of higher-order elliptic operators with rough coefficients

We introduce the sparse operator compression to compress a self-adjoint higher-order elliptic operator with rough coefficients and various boundary conditions. The operator compression is achieved by using localized basis functions, which are energy-minimizing functions on local patches. On a regular mesh with mesh size $h$, the localized basis functions have supports of diameter $O(h\log(1/h))$ and give optimal compression rate of the solution operator. We show that by using localized basis functions with supports of diameter $O(h\log(1/h))$, our method achieves the optimal compression rate of the solution operator. From the perspective of the generalized finite element method to solve elliptic equations, the localized basis functions have the optimal convergence rate $O(h^k)$ for a $(2k)$th-order elliptic problem in the energy norm. From the perspective of the sparse PCA, our results show that a large set of Mat\'{e}rn covariance functions can be approximated by a rank-$n$ operator with a localized basis and with the optimal accuracy

Efficient 3D data compression through parameterization of free-form surface patches

This paper presents a new method for 3D data compression based on parameterization of surface patches. The technique is applied to data that can be defined as single valued functions; this is the case for 3D patches obtained using standard 3D scanners. The method defines a number of mesh cutting planes and the intersection of planes on the mesh defines a set of sampling points. These points contain an explicit structure that allows us to define parametrically both x and y coordinates. The z values are interpolated using high degree polynomials and results show that compressions over 99% are achieved while preserving the quality of the mesh

Convergence Study for Rock Unconfined Compression Test Using Discrete Element Method

Mesh convergence is a vital issue that needs to be addressed in a numerical model. This study investigated the effects of mesh element number on the Discrete Element Method (DEM) to granite rock response under compression loading. This study used the 3D finite-element code LS-DYNA to model the Unconfined Compression Test (UCT) numerical simulation. Models with five different mesh types were conducted for convergence mesh, namely normal mesh, fine mesh, super fine mesh, coarse mesh, and super coarse mesh. The mesh convergence of rock media has been conducted using DEM and steel plates simulated using the Finite Element Method (FEM). The DEM-FEM numerical analysis is compared with the results obtained from the experimental test. The best mesh was obtained as the simulation could reproduce the stress-strain curve trends, the failure behaviour and compression strength observed in the experimental test. The normal mesh was selected as the best mesh type in this study based on the comparisons that have been made. This study shows that the DEM-FEM numerical simulation can represent granite rock and can be used for further study based on mesh convergence

Journal Staff

We investigate the mesh colors method for per-face parameterization for texture-mapping of geometry, implemented in the game engine Frostbite 3, for the purpose of evaluating the method compared to traditional texture-mapping in a real-time application. Traditional UV-mapping often causes discontinuities which commonly results in visible seams in the end results. If any change is done to the vertex positions or the topology a remapping of the UV-map has to be done. Mesh colors aims to avoid these problems by skipping the transformation to 2D space as in UV-mapping, and associating color samples directly with the geometry of a mesh. The implementation was done in Frostbite 3 in C++ and HLSL shader code, and rendered with the DirectX graphics API. The results show that mesh colors is a viable alternative in a real-time renderer. Though not as fast as regular UV-mapped textures due to lack of hardware accelerated filtering operations, mesh colors is a realistic alternative for special cases where regular texture-mapping would be cumbersome to work with or produce sub-par results. Possible areas of future research are efficient data structures suitable to handle data insertion dynamically, compression of mesh colors data, and mesh colors in the context of mesh LOD generation