A method of triangular surface mesh smoothing is presented to improve angle quality by extending the original optimal Delaunay triangulation (ODT) to surface meshes. The mesh quality is improved by solving a quadratic optimization problem that minimizes the approximated interpolation error between a parabolic function and its piecewise linear interpolation defined on the mesh. A suboptimal problem is derived to guarantee a unique, analytic solution that is significantly faster with little loss in accuracy as compared to the optimal one. In addition to the quality-improving capability, the proposed method has been adapted to remove noise while faithfully preserving sharp features such as edges and corners of a mesh. Numerous experiments are included to demonstrate the performance of the method.
Three-dimensional shape-based descriptors have been widely used in object recognition and database retrieval. In the current work, we present a novel method called compact Shape-DNA (cShape-DNA) to describe the shape of a triangular surface mesh. While the original Shape-DNA technique provides an effective and isometric-invariant descriptor for surface shapes, the number of eigenvalues used is typically large. To further reduce the space and time consumptions, especially for large-scale database applications, it is of great interest to find a more compact way to describe an arbitrary surface shape. In the present approach, the standard Shape-DNA is first computed from the given mesh and then processed by surface area-based normalization and line subtraction. The proposed cShape-DNA descriptor is composed of some low frequencies of the discrete Fourier transform of the processed Shape-DNA. Several experiments are shown to illustrate the effectiveness and efficiency of the cShape-DNA method on 3D shape analysis, particularly on shape comparison and classification.
Despite its great success in improving the quality of a tetrahedral mesh, the original optimal Delaunay triangulation (ODT) is designed to move only inner vertices and thus cannot handle input meshes containing “bad” triangles on boundaries. In the current work, we present an integrated approach called boundary-optimized Delaunay triangulation (B-ODT) to smooth (improve) a tetrahedral mesh. In our method, both inner and boundary vertices are repositioned by analytically minimizing the
error between a paraboloid function and its piecewise linear interpolation over the neighborhood of each vertex. In addition to the guaranteed volume-preserving property, the proposed algorithm can be readily adapted to preserve sharp features in the original mesh. A number of experiments are included to demonstrate the performance of our method.
In this paper we present a new software toolkit for generating and optimizing surface and volumetric meshes from three-dimensional (3D) biomedical imaging data, targeted at image-based finite element analysis of some biomedical activities in a single material domain. Our toolkit includes a series of geometric processing algorithms including surface re-meshing and quality-guaranteed tetrahedral mesh generation and optimization. All methods described have been encapsulated into a user-friendly graphical interface for easy manipulation and informative visualization of biomedical images and mesh models. Numerous examples are presented to demonstrate the effectiveness and efficiency of the described methods and toolkit.
In this paper, we propose an effective solution to reconstruct solid models of existing objects. Specifically, we convert the model reconstruction problem into the issue of feature parameter extraction, and thereby design diverse methods to extract the parameters of basic design features from input surface meshes. After extracting the feature parameters, the corresponding features are constructed. By performing modeling operations on those features, the final solid model is constructed, and meanwhile the complete history of the model building operations is recorded. By introducing the concepts of “feature,” “constraint,” and “modeling history” into the reconstruction process, the design intent is captured and hence represented in the reconstructed model. As a result, the model is geometrically accurate and topologically consistent, and moreover it is flexibly editable, which makes it convenient to carry out model redesign and modification for the innovation applications. A variety of experimental results demonstrate the effectiveness and robustness of this solution.
Novel approaches for generating and comparing flexible (non-rigid) molecular surface meshes are
developed. The mesh-generating method is fast and memory-efficient. The resulting meshes are smooth and
accurate, and possess high mesh quality. An isometric-invariant shape descriptor based on the Laplace-
Beltrami operator is then explored for mesh comparing. The new shape descriptor is more powerful in discriminating
different surface shapes but rely only on a small set of signature values. The shape descriptor is
applied to shape comparison between molecules with deformed structures. The proposed methods are implemented
into a program that can be used as a stand-alone software tool or as a plug-in to other existing
molecular modeling tools. Particularly, the code is encapsulated into a software toolkit with a user-friendly
graphical interface developed by the authors.
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