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This paper presents a global optimization operator for arbitrary meshes. The global optimization operator is composed of two main terms, one part is the global Laplacian operator of the mesh which keeps the fairness and another is the constraint condition which reserves the fidelity to the mesh. The global optimization operator is formulated as a quadratic optimization problem, which is easily solved by solving a sparse linear system. Our global mesh optimization approach can be effectively used in at least three applications: smoothing the noisy mesh, improving the simplified mesh, and geometric modeling with subdivision-connectivity. Many experimental results are presented to show the applicability and flexibility of the approach. [Copyright &y& Elsevier]

Abstract: Current methods for recognition and interpretation of architectural drawings are limited to either low-level analysis of paper drawings or interpretation of electronic drawings that depicts only high-level design entities. In this paper, we propose a Self-Incremental Axis-Net-based Hierarchical Recognition (SINEHIR) model for automatic recognition and interpretation of real-life complex electronic construction structural drawings. We design and implement a series of integrated algorithms for recognizing dimensions, coordinate systems and structural components. We tested our approach on more than 200 real-life drawings. The results show that the average recognition rate of structural components is about 90%, and the computation time is significantly shorter than manual estimation time. [Copyright &y& Elsevier]

This paper presents an algorithm for reconstructing a triangle mesh surface from a given point cloud. Starting with a seed triangle, the algorithm grows a partially reconstructed triangle mesh by selecting a new point based on an intrinsic property of the point cloud, namely, the sampling uniformity degree. The reconstructed mesh is essentially an approximate minimum-weight triangulation to the point cloud constrained to be on a two-dimensional manifold. Thus, the reconstructed surface has only small topological difference from the surface of the sampled object. Topological correct reconstruction can be guaranteed by adding a post-processing step. [Copyright &y& Elsevier]

This paper addresses the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. The basic idea of the approach is to find the conditions for precise merging of two B-spline curves, and perturb the control points of the curves by constrained optimization subject to satisfying these conditions. To obtain a merged curve without superfluous knots, we present a new knot adjustment algorithm for adjusting the end k knots of a kth order B-spline curve without changing its shape. The more general problem of merging curves to pass through some target points is also discussed. [Copyright &y& Elsevier]

Convolution surface has the advantage of being crease-free and bulge-free over other kinds of implicit surfaces. Among the various types of skeletal elements, line segments can be considered one of the most fundamental as they can approximate curve skeletons. This paper presents analytical solutions for convolving line segments with varying kernels modulated by polynomial weighted functions. We derive the closed-form formulae for most classical kernel functions, namely Gaussian, inverse linear, inverse squared, Cauchy, and quartic functions, and compare their computational complexity. These analytical solutions can be incorporated into existing implicit surface modeling systems for more convenient modeling of generalized cylindrical shapes. We demonstrate their high potentials for modeling and animating branching and tubular organic objects with some examples. We also propose a new competitive kernel function that has a smoothness control parameter. [Copyright &y& Elsevier]

This paper presents an algorithm for extending B-spline curves and surfaces. Based on the unclamping algorithm for B-spline curves, we propose a new algorithm for extending B-spline curves that extrapolates using the recurrence property of the de Boor algorithm. This algorithm provides a nice extension, with maximum continuity, to the original curve segment. Moreover, it can be applied to the extension of B-spline surfaces. Extension to both single and multiple target points/curves are considered in this paper. [Copyright &y& Elsevier]

In this paper, we study the problem of constructing a family of surfaces from a given spatial geodesic curve. We derive a parametric representation for a surface pencil whose members share the same geodesic curve as an isoparametric curve. By utilizing the Frenet trihedron frame along the given geodesic, we express the surface pencil as a linear combination of the components of this local coordinate frame, and derive the necessary and sufficient conditions for the coefficients to satisfy both the geodesic and the isoparametric requirements. We illustrate and verify the method by finding exact surface pencil formulations for some simple surfaces, such as surfaces of revolution and ruled surfaces. Finally, we demonstrate the use of this method in a garment design application. [Copyright &y& Elsevier]