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Research of Swept Surface and Skinning Surface Based on PDE

Author: GuoYuQing
Tutor: YuZhengSheng
School: Hangzhou University of Electronic Science and Technology
Course: Computer Software and Theory
Keywords: Surface Modeling Differential Equations Swept Surface Shape control Masked surfaces Energy function
CLC: TP391.41
Type: Master's thesis
Year: 2011
Downloads: 13
Quote: 0
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Abstract


Construction surfaces using partial differential equations, as a surface modeling method of computer graphics, construct transitional surfaces, free-form surface, functional surface design is very important. The characteristics of this method is to ask surfaces as a partial solution of the boundary value problem, called Partial Differential Equations natural surface (referred to as PDE surfaces) fairing surface constructed for artistic design and function of surface design. Application PDE methods for surface modeling idea was first presented by the University of Leeds, UK Bloor and J.Wilson, after widespread concern. Twenty years this research has made certain achievements, but there are also some problems. Application of PDE method how to interpolation from scattered points reconstructed surfaces; the PDE surface shape control problem; application the the PDE method construction surface in the design of functional surfaces. In this paper, the theory of PDE to construct surfaces based PDE-based scanning surface construction, and application of PDE optimized 3D ball masked surfaces. The papers completed work as follows: (1) through the study of the scanning surface structure surface methodology, introduced the concept of parameter lines. For a given initial and boundary conditions, we only care about the point values ??of the corresponding parameters, they do not care about the curve expression. Construct a surface model parameters such as line scan surfaces by solving differential equations, and then scanning principle. (2) using the superposition principle in differential equations, PDE-based scanning surfaces divided into two sub-surface part of that base surface and deformation surfaces constructed. Split differential equations and boundary conditions, homogeneous differential equations and non-homogeneous equation corresponding to the base surface and deformation surfaces. The experimental results show that this method to construct the scanning surface easily deformed and shape control. (3) For the boundary information is not very clear or strict surface modeling applications, the paper argues that the surface energy function is then calculated by PDE adjust boundaries in order to optimize the surface. This selection of 3D ball masked surfaces as the object of study, the masked surface structure and application of PDE surfaces optimized adjustment function as an evaluation of the application surface energy, the use of parameters along its gradient opposite direction progressive The iterative method so that the surface energy function of the extreme value, while the boundary curve parameters converge, resulting in the optimization of the masked surfaces. The experimental results show that this method can achieve optimization of the masked surfaces.

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CLC: > Industrial Technology > Automation technology,computer technology > Computing technology,computer technology > Computer applications > Information processing (information processing) > Pattern Recognition and devices > Image recognition device
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