Kjellander has reported an algorithm for fairing uniform parametric cubic splines. Poliakoff extended Kjellander’s algorithm to non-uniform case. However, they merely changed the bad point’s position, and neglected the smoothing of tangent at bad point. In this paper, we present a fairing algorithm that both changed point’s position and its corresponding tangent vector. The new algorithm possesses the minimum property of energy. We also proved Poliakoff’s fairing algorithm is a deduction of our fairing algorithm. Several fairing examples are given in this paper.

Many graphics and computer-aided design applications require that the polygonal meshes used in geometric computing have the properties of not only 2-manifold but also are orientable. In this paper, by collecting previous work scattered in the topology and geometry literature, we rigorously present a theoretical basis for orientable polygonal surface representation from a modern point of view. Based on the presented basis, we propose a new combinatorial data structure that can guarantee the property of orientable 2-manifolds and is primal/dual efficient. Comparisons with other widely used data structures are also presented in terms of time and space efficiency.

A meshless simulation system is presented for elastic deformation driven by skeleton in this paper. In this system, we propose a new method for calculating node rotation while applying a similar technique with stiffness warping to tackle the nonlinear large deformation. In our method, all node rotations are evaluated from sampling points in attached skeleton by constructing and solving the diffusion partial differential equation. The experiments indicated that the method can enhance the stability of the dynamics and avoid fussy sub-step calculation in static deformation edition. Moreover, rational deformation results for the area around the skeleton joints can be simulated without user interaction by adopting the simplified technique.

Motivated by the conception of Lee et al.(2005)’s mesh saliency and Chen (2005)’s contextual discontinuities, a novel adaptive smoothing approach is proposed for noise removal and feature preservation. Mesh saliency is employed as a multiscale measure to detect contextual discontinuity for feature preserving and control of the smoothing speed. The proposed method is similar to the bilateral filter method. Comparative results demonstrate the simplicity and efficiency of the presented method, which makes it an excellent solution for smoothing 3D noisy meshes.

The purpose of this study is to develop a Web-based on-machine mould identification and measurement system. The Web-based mould identification system matches obtained vision information with CAD database. Developed Web-based system is to exchange messages between a server and a client by making of ActiveX control, and the result of mould identification is shown on Web-browser at remote site. For effective feature classification and extraction, the signature method is used to make meaningful information from obtained image data. For on-machine measurement of the matched mould, inspection database is constructed from CAD database using developed inspection planning methods. The results are simulated and analyzed using developed system to verify the effectiveness of the proposed methods.

Empirical mode decomposition (EMD) is an adaptive and approximately orthogonal filtering process that reflects human’s visual mechanism of differentiating textures. In this paper, we present a modified 2D EMD algorithm using the FastRBF and an appropriate number of iterations in the shifting process (SP), then apply it to texture classification. Rotation-invariant texture feature vectors are extracted using auto-registration and circular regions of magnitude spectra of 2D fast Fourier transform (FFT). In the experiments, we employ a Bayesion classifier to classify a set of 15 distinct natural textures selected from the Brodatz album. The experimental results, based on different testing datasets for images with different orientations, show the effectiveness of the proposed classification scheme.

Computing the distance between two convex polygons is often a basic step to the algorithms of collision detection and path planning. Now, the lowest time complexity algorithm takes O(logm+logn) time to compute the minimum distance between two disjoint convex polygons P and Q, where n and m are the number of the polygons’ edges respectively. This paper discusses the location relations of outer Voronoi diagrams of two disjoint convex polygons P and Q, and presents a new O(logm+logn) algorithm to compute the minimum distance between P and Q. The algorithm is simple and easy to implement, and does not need any preprocessing and extra data structures.

The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application, some parametrization results might behave better than others. In this paper, we will propose a method to parametrize a genus-zero mesh so that a surface fitting algorithm with PHT-splines can generate good result. Here the parametrization results are obtained by minimizing discrete harmonic energy subject to spherical constraints. Then some applications are given to illustrate the advantages of our results. Based on PHT-splines, parametric surfaces can be constructed efficiently and adaptively to fit genus-zero meshes after their spherical parametrization has been obtained.