In this paper we develop a novel approach to construct non-stationary subdivision schemes with a tension control parameter which can reproduce functions in a finite-dimensional subspace of exponential polynomials. The construction process is mainly implemented by solving linear systems for primal and dual subdivision schemes respectively, which are based on different parameterizations. We give the theoretical basis for the existence, uniqueness, and refinement rules of schemes proposed in this paper. The convergence and smoothness of the schemes are analyzed as well. Moreover, conics reproducing schemes are analyzed based on our theory, and a new idea that the tensor parameter ωk of the schemes can be adjusted for conics generation is proposed.
Bao-jun LIZhi-ling YUBo-wen YUZhi-xun SUXiu-ping LIU
We present a novel algorithm to reconstruct curves with self-intersections and multiple parts from unorganized strip-shaped points,which may have different local shape scales and sampling densities.We first extract an initial curve,a graph composed of polylines,to model the different structures of the points.Then a least-squares optimization is used to improve the geometric approximation.The initial curve is extracted in three steps:anisotropic farthest point sampling with an adaptable sphere,graph construction followed by non-linear region identification,and edge refinement.Our algorithm produces faithful results for points sampled from non-simple curves without pre-segmenting them.Experiments on many simulated and real data demonstrate the efficiency of our method,and more faithful curves are reconstructed compared to other existing methods.
Yuan-di ZHAO 1,Jun-jie CAO 1,2,Zhi-xun SU 1,Zhi-yang LI 1 (1 School of Mathematical Sciences,Dalian University of Technology,Dalian 116024,China) (2 State Key Laboratory of Structural Analysis for Industrial Equipment,Department of Engineering Mechanics,Dalian University of Technology,Dalian 116024,China)
We propose a robust method for detecting features on triangular meshes by combining normal tensor voting with neighbor supporting. Our method contains two stages: feature detection and feature refinement. First, the normal tensor voting method is modified to detect the initial features, which may include some pseudo features. Then, at the feature refinement stage, a novel salient measure deriving from the idea of neighbor supporting is developed. Benefiting from the integrated reliable salient measure feature, pseudo features can be effectively discriminated from the initially detected features and removed. Compared to previous methods based on the differential geometric property, the main advantage of our method is that it can detect both sharp and weak features. Numerical experiments show that our algorithm is robust, effective, and can produce more accurate results. We also discuss how detected features are incorporated into applications, such as feature-preserving mesh denoising and hole-filling, and present visually appealing results by integrating feature information.
Xiao-chao WANGJun-jie CAOXiu-ping LIUBao-jun LIXi-quan SHIYi-zhen SUN
