Particle swarm optimization (PSO) is a population based optimization technique to search approximate solutions for extremely difficult or impossible numeric problems. However, PSO may easily get trapped in a local optimum when solving complex multimodal problems. This paper proposes an efficient improved PSO based on prey behavior of fish schooling (FSPSO). Firstly, the fish find better place to prey according to the heuristic water wave which other fish provide, and the heuristic information can be used to enhance the global search ability in PSO. Therefore, the global best particle searches randomly towards several best positions that other particles have experienced. Secondly, the weak fish that cannot move quickly are eaten when the fish schooling are attacked. The decimation of the weak fish can be simulated in PSO to avoid the local optimum and to increase the diversity of the population. Hence, the particles in the immediate vicinity of the global worst particle are replaced by new particles. Finally, the proposed FSPSO is tested on both several standard benchmark functions and a typical NP-complete problem. The results demonstrate that our algorithm achieves remarkable improvements over the basic PSO and even other improved PSOs.

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With the rapid growth of 3D models on the Web, effective methods to retrieve appropriate 3D models are becoming crucial. In this paper, we propose a novel sketch-based 3D model retrieval approach which integrates the skeleton graph and contour feature. Skeleton graph represents the topology structure of the query sketch as well as representative 2D views of 3D models, and contour feature captures their detailed information. Moreover, A hierarchical coarse-to-fine searching strategy is employed in this method. Firstly, a skeleton graph based matching method is used to eliminate those 3D models which are dissimilar to the query sketch. Then, the selected candidate models are refined by measuring the similarity of their contour feature. In addition, we adopt a graph transduction method to improve the ranking order of the retrieved 3D models. The proposed method was tested on the public sketch benchmarks and compared with other leading sketch-based 3D model retrieval methods. The experiment results demonstrate that our approach can accurately retrieve desired 3D models for users and has a superior performance to other state-of-the-art approaches.

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This paper studies the problem to construct a spacelike developable surface possessing a given non-null parametric curve as the line of curvature in Minkowski 3-space. By using Frenet frame to express the surface, we derive the necessary and sufficient conditions when the resulting spacelike developable surface is cylinder, cone or tangent surface. Finally, we give some representative examples.

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Segmenting 3D models into meaningful parts is a fundamental problem in computer graphics. In this paper, we present an algorithm which is guided by the mesh vertices for segmenting a mesh into meaningful sub-meshes. First, a candidate set of feature points is selected to highlight the most significant features of the model. After that, a diversity measure is calculated by using Hausdorff distance. The collection of seed points we defined is a subset of the candidate set. The collection of seed points consists of two parts, namely, the basic point and lucky points. By maximizing the diversity measure between the seed set and candidate set, an appropriate seed point is selected. Based on the collection of seed points, the segmentation process can be guided by these seeds. Because humans generally perceive desirable segmentations at concave regions, and the geodesic distance and curvature are well-known noise sensitive. Considering the above factors, in order to partition the target into meaningful parts, we define a distance function between each pair of mesh vertices. This function is formed by arc length, angular distance and curvature-related correction term. We have tested the method developed in this paper with 3D meshes from the Princeton segmentation benchmark. Moreover, our segmentation method also has been compared with other methods. The experimental results have demonstrated the effectiveness of the proposed segmentation method.

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Surface remeshing aims to produce a high-quality mesh from a given input mesh. In this paper, we present a practical approach to isotropic surface remeshing of triangular meshes in an as-equilateral-as-possible (AEAP) manner. The proposed approach iterates in a two-step manner. In the first step, we optimize the mesh connectivity to reduce the number of irregular vertices. And in the second step, we improve the elements' shape by locally fitting an equilateral triangle separately and globally stitching them to a new mesh with feature constraints. The proposed approach can be effectively used in preprocessing for finite element computations. Experiments are presented to show that our approach is simple and robust, and the remeshed results generate more well-shaped triangles and preserve the features of the original surface, which are favored in many applications.

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A new construction method of dual generalized B-spline functions is presented in this paper. Due to the importance of generalized B-splines, several interesting applications of these dual functions in Computer Aided Manufacturing are also given. The purposes of the paper are as follows: 1) As is known to all, B-spline curves, surfaces and related techniques play important roles in the fields of Computer Aided Geometric Design, Computer Aided Manufacturing and Computer Aided Design for their perfect properties. 2) Recently, on the basis of recursive formula of classical B-spline bases, Juhász and Róth (2013) put forward the generalized B-spline bases, which are generated by monotone increasing and continuous “core” functions. 3) With these flexible “core” functions, generalized B-spline curves and surfaces not only hold almost the same perfect properties which classical B-splines hold but also show more flexibility in practical applications. It is necessary to further study dual generalized B-spline bases. The whole arrangement of the paper is divided into four parts. Firstly, a review of dual bases concluding the construction method is given. Secondly, one fresh method of constructing dual generalized B-spline functions is presented in order to extend their applications. With the help of the dual bases functions, one can easily find the best approximation of any function with expressions of generalized B-spline bases; furthermore, one has no need to consider the orthogonal bases of the corresponding space. After that, several applications of dual generalized B-spline functions in Computer Aided Manufacturing such as least square approximation, curve offsetting and degree reduction are illustrated. Numerical examples show that dual functions greatly simplify these approximation problems. Furthermore, better approximation effects can be achieved by changing core functions which exhibits the effects of "core". The paper not only focuses on the construction of generalized B-spline bases which has never been built before, but also applies the dual bases in the practical applications of Computer Aided Manufacturing. We hope it could be a useful bridge to connect theories and practical applications.

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