The aim of this paper is to lay a algebraic geometry foundation for constructing smoothing interpolants on curved side element. Some interpolation theorems in polynomial space are given. The main results effectively f...The aim of this paper is to lay a algebraic geometry foundation for constructing smoothing interpolants on curved side element. Some interpolation theorems in polynomial space are given. The main results effectively for CAGD are presented.展开更多
As wavelet basis in wavelet analysis is neither arbitrary nor unique,the same signal dealing with different wavelet bases will generate different results.Therefore,how to construct a wavelet basis suitable for the cha...As wavelet basis in wavelet analysis is neither arbitrary nor unique,the same signal dealing with different wavelet bases will generate different results.Therefore,how to construct a wavelet basis suitable for the characteristics of the analyzed signal and solve its algorithm and realization is a fundamental problem which perplexed many researchers.To solve these problems,in accordance with the basic features of the measured millisecond blast vibration signal,a new wavelet basis construction method based on the separation blast vibration signal is proposed,and the feasibility of this method is verified by comparing the practical effect of the newly constructed wavelet with other known wavelets in signal processing.展开更多
This paper presents Symm Sketch—a system for creating symmetric 3D free-form shapes from 2D sketches. The reconstruction task usually separates a 3D symmetric shape into two types of shape components, that is, the se...This paper presents Symm Sketch—a system for creating symmetric 3D free-form shapes from 2D sketches. The reconstruction task usually separates a 3D symmetric shape into two types of shape components, that is, the self-symmetric shape component and the mutual-symmetric shape components. Each type can be created in an intuitive manner. Using a uniform symmetry plane, the user first draws 2D sketch lines for each shape component on a sketching plane. The z-depth information of the hand-drawn input sketches can be calculated using their property of mirror symmetry to generate 3D construction curves. In order to provide more freedom for controlling the local geometric features of the reconstructed free-form shapes(e.g., non-circular crosssections), our modeling system creates each shape component from four construction curves. Using one pair of symmetric curves and one pair of general curves, an improved cross-sectional surface blending scheme is applied to generate a parametric surface for each component. The final symmetric free-form shape is progressively created, and is represented by 3D triangular mesh. Experimental results illustrate that our system can generate complex symmetric free-form shapes effectively and conveniently.展开更多
文摘The aim of this paper is to lay a algebraic geometry foundation for constructing smoothing interpolants on curved side element. Some interpolation theorems in polynomial space are given. The main results effectively for CAGD are presented.
基金Projects(51078043,51278071,51308072)supported by the National Natural Science Foundation of China
文摘As wavelet basis in wavelet analysis is neither arbitrary nor unique,the same signal dealing with different wavelet bases will generate different results.Therefore,how to construct a wavelet basis suitable for the characteristics of the analyzed signal and solve its algorithm and realization is a fundamental problem which perplexed many researchers.To solve these problems,in accordance with the basic features of the measured millisecond blast vibration signal,a new wavelet basis construction method based on the separation blast vibration signal is proposed,and the feasibility of this method is verified by comparing the practical effect of the newly constructed wavelet with other known wavelets in signal processing.
基金supported by the National Natural Science Foundation of China under Grant Nos. 61272309 and 61303138
文摘This paper presents Symm Sketch—a system for creating symmetric 3D free-form shapes from 2D sketches. The reconstruction task usually separates a 3D symmetric shape into two types of shape components, that is, the self-symmetric shape component and the mutual-symmetric shape components. Each type can be created in an intuitive manner. Using a uniform symmetry plane, the user first draws 2D sketch lines for each shape component on a sketching plane. The z-depth information of the hand-drawn input sketches can be calculated using their property of mirror symmetry to generate 3D construction curves. In order to provide more freedom for controlling the local geometric features of the reconstructed free-form shapes(e.g., non-circular crosssections), our modeling system creates each shape component from four construction curves. Using one pair of symmetric curves and one pair of general curves, an improved cross-sectional surface blending scheme is applied to generate a parametric surface for each component. The final symmetric free-form shape is progressively created, and is represented by 3D triangular mesh. Experimental results illustrate that our system can generate complex symmetric free-form shapes effectively and conveniently.
