A topological comparison of surface extraction algorithms

In many application areas, it is useful to convert the discrete information stored in the nodes of a regular grid into a continuous boundary model. Isosurface extraction algorithms di er on how the discrete information in the grid is generated, on what information does the grid store and on the properties of the output surface.Preprin

A topological comparison of surface extraction algorithms

In many application areas, it is useful to convert the discrete information stored in the nodes of a regular grid into a continuous boundary model. Isosurface extraction algorithms differ on how the discrete information in the grid is generated, on what information does the grid store and on the properties of the output surface. Recent algorithms offer different solutions for the disambiguation problem and for controlling the final topology. Based on a number of properties of the grid’s grey cells and of the reconstruction algorithms, a characterization of several surface extraction strategies is proposed. The classification presented shows the inherent limitations of the different algorithms concerning global topology control and reconstruction of local features like thin portions of the volume and almost non-manifold regions. These limitations can be observed and are illustrated with some practical examples. We review in light of this classification some of the relevant papers in the literature, and see that they cluster in some areas of the proposed hierarchy, making a case for where it might be more interesting to focus in future research.Preprin

Non-Uniform Offsetting and its Applications in Laser Path Planning of Sterolithography Machine

Laser path planning is an important step in solid freeform fabrication processes such as Stereolithography (SLA). An important consideration in the laser path planning is to compensate the shape of laser beam. Currently the compensation is divided into two steps, Z-compensation and X-Y compensation, and the shape of laser beam is assumed to be uniform for the whole platform. In this research, we present a sampling based non-uniform offsetting method which accounts for the different shapes of laser beam at various locations. We discuss the related steps and algorithms. We demonstrate its effectiveness by using various test cases. Besides improving the accuracy of SLA machine, non-uniform offsetting can also be applied to address other accuracy issues caused by thermal and structural variationsMechanical Engineerin

GPU-based Adaptive Surface Reconstruction for Real-time SPH Fluids

We propose a GPU-based adaptive surface reconstruction algorithm for Smoothed-Particle Hydrodynamics (SPH) fluids. The adaptive surface is reconstructed from 3-level grids as proposed by [Akinci13]. The novel part of our algorithm is a pattern based approach for crack filling, which is recognized as the most challengeable part of building adaptive surfaces. Unlike prior CPU-based approaches [Shu95, Shekhar96, Westermann99, Akinci13] that detect and fill cracks according to some criteria during program running that were slow and unrobust, all the possible crack patterns are analyzed and defined in advance and later, during program running, the cracks are detected and filled according to the patterns. Our approach is thus robust, GPU-friendly, and easy to implement. Results obtained show that our algorithm can produce surface meshes of almost the same quality as those produced by the conventional Marching Cubes method, with significantly reduced computation time and memory usage

Solid modelling for manufacturing: from Voelcker's boundary evaluation to discrete paradigms

Herb Voelcker and his research team laid the foundations of Solid Modelling, on which Computer-Aided Design is based. He founded the ambitious Production Automation Project, that included Constructive Solid Geometry (CSG) as the basic 3D geometric representation. CSG trees were compact and robust, saving a memory space that was scarce in those times. But the main computational problem was Boundary Evaluation: the process of converting CSG trees to Boundary Representations (BReps) with explicit faces, edges and vertices for manufacturing and visualization purposes. This paper presents some glimpses of the history and evolution of some ideas that started with Herb Voelcker. We briefly describe the path from “localization and boundary evaluation” to “localization and printing”, with many intermediate steps driven by hardware, software and new mathematical tools: voxel and volume representations, triangle meshes, and many others, observing also that in some applications, voxel models no longer require Boundary Evaluation. In this last case, we consider the current research challenges and discuss several avenues for further research.Project TIN2017-88515-C2-1-R funded by MCIN/AEI/10.13039/501100011033/FEDER‘‘A way to make Europe’’Peer ReviewedPostprint (published version

Effects of Aerial LiDAR Data Density on the Accuracy of Building Reconstruction

Previous work has identified a positive relationship between the density of aerial LiDAR input for building reconstruction and the accuracy of the resulting reconstructed models. We hypothesize a point of diminished returns at which higher data density no longer contributes meaningfully to higher accuracy in the end product. We investigate this relationship by subsampling a high-density dataset from the City of Surrey, BC to different densities and inputting each subsampled dataset to reconstruction using two different reconstruction methods. We then determine the accuracy of reconstruction based on manually created reference data, in terms of both 2D footprint accuracy and 3D model accuracy. We find that there is no quantitative evidence for meaningfully improved output accuracy from densities higher than 4 p/m2 for either method, although aesthetic improvements at higher point cloud densities are noted for one method

Watertight and 2-Manifold Surface Meshes Using Dual Contouring With Tetrahedral Decomposition of Grid Cubes

The Dual Contouring algorithm (DC) is a grid-based process used to generate surface meshes from volumetric data. The advantage of DC is that it can reproduce sharp features by inserting vertices anywhere inside the grid cube, as opposed to the Marching Cubes (MC) algorithm that can insert vertices only on the grid edges. However, DC is unable to guarantee 2-manifold and watertight meshes due to the fact that it produces only one vertex for each grid cube. We present a modified Dual Contouring algorithm that is capable of overcoming this limitation. Our method decomposes an ambiguous grid cube into a maximum of twelve tetrahedral cells; we introduce novel polygon generation rules that produce 2-manifold and watertight surface meshes. We have applied our proposed method on realistic data, and a comparison of the results of our proposed method with results from traditional DC shows the effectiveness of our method

08221 Abstracts Collection -- Geometric Modeling

From May 26 to May 30 2008 the Dagstuhl Seminar 08221 ``Geometric Modeling\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available