A Simple Plane Patcher Algorithm (original) (raw)

Carving for topology simplification of polygonal meshes

Computer-aided Design, 2010

The topological complexity of polygonal meshes has a large impact on the performance of various geometric processing algorithms, such as rendering and collision detection algorithms. Several approaches for simplifying topology have been discussed in the literature. These methods operate locally on models, which makes their effect on the topology hard to predict and analyze. Most existing methods tend to exhibit several disturbing artifacts, such as shrinking of the input and splitting of its components. We propose a novel top-down approach for topology simplification that avoids most problems that are common in existing methods. We start with a simple, genus-zero mesh that bounds the input and gradually introduce topologic features by a series of carving operations. This process yields a multiresolution stream of meshes with increasing topologic level of detail. We further present a carving algorithm that is based on constrained Delaunay tetrahedralization. The algorithm first constructs the tetrahedral mesh of the complement of the input with respect to its convex hull. It then proceeds to eliminate tetrahedra in a prioritized manner. We present quality results for two families of meshes that are difficult to simplify by all existing methods known to us: topologically complex meshes and highly clustered meshes.

Surface Generation and Cartesian Mesh Support

2004

This document serves the final report for the grant titled "Surface Generation and Cartesian Mesh Support". This completed work was in algorithmic research into automatically generating surface triangulations from CAD geometries. NASA's OVERFLOW and Cavt3D simulation packages use surface triangulations as an underlying geometry description and the ability to automatically generate these from CAD files (without translation) substantially reduces both the wall-clock time and expertise required to get geometry out of CAD and into mesh generation. This surface meshing was exercised greatly during the Shuttle investigation during the last year with success. The secondary efforts performed in this grant involve work on a visualization system cut-cell handling for Cartesian Meshes with embedded boundaries.

Overlaying Surface Meshes, Part I: Algorithms

International Journal of Computational Geometry & Applications, 2004

We describe an efficient and robust algorithm for computing a common refinement of two meshes modeling the'same surface of arbitrary shape by overlaying them on lop of each other. A common refinement is an important data structure for transferring data between meshes that have different combinatorial structures. Our algorithm is optimal in time and space, with linear complexity, and is robust even with inexact computations, through the techniques of error analysis, detection of topological inconsistencies, and automatic resolution of such inconsistencies. We present the verification and some further enhancement of robustness in Part II.

An algorithm for intersecting and trimming parametric meshes

Proceedings SIBGRAPI'98. International Symposium on Computer Graphics, Image Processing, and Vision (Cat. No.98EX237), 1998

We present an algorithm for intersecting nite-element meshes de ned on parametric surface patches. The intersection curves are modeled precisely and both meshes are adjusted to the newly formed borders. The algorithm is part of an interactive shell modeling program, which has been used in the design of large o shore oil structures. We a void unacceptable interaction delays by using a variant of the DCEL data structure that stores topological entities in spatial indexing trees instead of linked lists. These trees speed up the intersection computations required to determine points of the trimming curves, and also allows mesh reconstruction using only local queries.

Progressive Gap Closing for MeshRepairing

Advances in Modelling, Animation and Rendering, 2002

Modern 3D acquisition and modeling tools generate high-quality, detailed geometric models. However, in order to cope with the associated complexity, several mesh decimation methods have been developed in the recent years. On the other hand, a common problem of geometric modeling tools is the generation of consistent three-dimensional meshes. Most of these programs output meshes containing degenerate faces, T-vertices, narrow gaps and cracks. Applying well-established decimation methods to such meshes results in severe artifacts due to lack of consistent connectivity information. The industrial relevance of this problem is emphasized by the fact that as an output of most of the commercial CAD/CAM and other modeling tools, the user usually gets consistent meshes only for separate polygonal patches as opposed to the whole mesh. In this paper we propose a solution, which interprets the above issue as a mesh boundary decimation task. As suggested by Garland and Heckbert [4] and Popović and Hoppe [12], adding a vertex pair contraction operation enables to join unconnected regions of the mesh. In addition to this and the usual edge-collapse operation, we introduce a new vertex-edge collapse operation. This provides extra support for closing gaps and stitching together the boundaries of triangle patches lying in near proximity to each other. In our method, the decimation process is error controlled and conducted in a progressive manner in terms of the error. Therefore, the user is enabled to visually inspect and interactively influence the procedure.

Efficient and Robust Algorithm for Overlaying Nonmatching Surface Meshes

2001

This paper describes an efficient and robust algorithm for computing a common refinement of two meshes modeling a common surface of arbitrary shape by overlaying them on top of each other. A common refinement is an important data structure for transferring data between meshes that have different topological structures. Our algorithm is optimal in time and space, with linear complexity. Special treatments are introduced to handle discretization and rounding errors and to ensure robustness with imprecise computations. It also addresses the additional complexities caused by degeneracies, sharp edges, sharp corners, and nonmatching boundaries. The algorithm has been implemented and demonstrated to be robust for complex geometries from real-world applications.

Interactive cuttingof 3D surface meshes

2000

Engineers and scientists from many fields are using three-dimensional reconstruction for visualization and analysis of physical and abstract data. Beyond observingthe recreated objects in artificial space, it is desirable to develop methods that allow one to interactively manipulate and alter the geometry in an intuitive and efficient manner. In the case of medical data, a baseline interactive task would be