Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. In this paper, we extend the mathematical model proposed by Juttler and Felis （Adv. Comput. Math., 17 （2002）, pp. 135-152） based on tensor product algebraic spline surfaces from fixed meshes to adaptive meshes. We start with a tensor product algebraic B-spline surface defined on an initial mesh to fit the given data based on an optimization approach. By measuring the fitting errors over each cell of the mesh, we recursively insert new knots in cells over which the errors are larger than some given threshold, and construct a new algebraic spline surface to better fit the given data locally. The algorithm terminates when the error over each cell is less than the threshold. We provide some examples to demonstrate our algorithm and compare it with Juttler＇s method. Examples suggest that our method is effective and is able to produce reconstruction surfaces of high quality.
In this paper, we propose a new approach to solve the approximate implicitization problem based on RBF networks and MQ quasi-interpolation. This approach possesses the advantages of shape preserving, better smoothness, good approximation behavior and relatively less data etc. Several numerical examples are provided to demonstrate the effectiveness and flexibility of the proposed method.
In general, triangular and quadrilateral elements are commonly applied in two-dimensional finite element methods. If they are used to compute polycrystalline materials, the cost of computation can be quite significant. Polygonal elements can do well in simulation of the materials behavior and provide greater flexibility for the meshing of complex geometries. Hence, the study on the polygonal element is a very useful and necessary part in the finite element method. In this paper, an n-sided polygonal element based on quadratic spline interpolant, denoted by PS2 element, is presented using the triangular area coordinates and the B-net method. The PS2 element is conforming and can exactly model the quadratic field. It is valid for both convex and non-convex polygonal element, and insensitive to mesh distortions. In addition, no mapping or coordinate transformation is required and thus no Jacobian matrix and its inverse are evaluated. Some appropriate examples are employed to evaluate the performance of the proposed element.
We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle dis-tortions. We generate the final spherical mapping by independently establishing two hemisphere parameterizations. The essence of the approach is to reduce spherical parameterization to a planar problem using symmetry analysis of 3D meshes. Experiments and comparisons were undertaken with various non-trivial 3D models, which revealed that our approach is efficient and robust. In particular, our method produces almost isometric parameterizations for the objects close to the sphere.
Jian-ping HUXiu-ping LIUZhi-xun SUXi-quan SHIFeng-shan LIU
Labeling information in a complex irregular region is a useful procedure occurring frequently in sheet metal and the furniture industry which will be beneficial in parts management.A fast code-based labeler(FCBL) is proposed to accomplish this objective in this paper.The region is first discretized,and then encoded by the Freeman encoding technique for providing the 2D regional information by 1D codes with redundancies omitted.We enhance the encoding scheme to make it more suitable for our complex problem.Based on the codes,searching algorithms are designed and can be extended with customized constraints.In addition,by introducing a smart optimal direction estimation,the labeling speed and accuracy of FCBL are significantly improved.Experiments with a large range of real data gained from industrial factories demonstrate the stability and millisecond-level speed of FCBL.The proposed method has been integrated into a shipbuilding CAD system,and plays a very important role in ship parts labeling process.
