Dynamic axial curve-pair based deformation and its application.

Chan, Man Leung Dunco.Thesis submitted in: Nov 2008.Thesis (M.Phil.)--Chinese University of Hong Kong, 2009.Includes bibliographical references (leaves 87-91).Abstracts in English and Chinese.Abstract --- p.2摘要 --- p.3Acknowledgement --- p.4Content --- p.5List of figures --- p.6Chapter Chapter 1 --- Introduction --- p.9Chapter 1.1 --- Background --- p.9Chapter 1.2 --- Prior work --- p.11Chapter 1.3 --- Objectives --- p.13Chapter 1.4 --- Proposed method --- p.16Chapter 1.5 --- Thesis outline --- p.18Chapter Chapter 2 --- Axial curve-pair deformation --- p.19Chapter 2.1 --- Axial deformation technique --- p.20Chapter 2.1.1 --- Representing objects in axial space --- p.21Chapter 2.1.2 --- Defining the frame --- p.23Chapter 2.2 --- Axial curve-pair deformation technique --- p.24Chapter 2.2.1 --- Framing the curve-pair --- p.25Chapter 2.2.2 --- Construction of orientation curve --- p.26Chapter 2.2.3 --- Manipulation of the axial curve-pair --- p.28Chapter Chapter 3 --- Dynamic axial curve-pair based deformation --- p.32Chapter 3.1 --- The dynamic mass spring model --- p.34Chapter 3.1.1 --- Dynamic NURBS curve --- p.35Chapter 3.1.2 --- Dynamic Free-form deformation --- p.37Chapter 3.1.3 --- Dynamic Axial Curve-pair deformation --- p.38Chapter 3.2 --- The dynamic mass spring model --- p.41Chapter 3.2.1 --- Curve-pair Fitting --- p.41Chapter 3.2.2 --- Construction of dynamic curve-pair --- p.44Chapter 3.2.3 --- The three-degree torsional spring --- p.48Chapter 3.2.4 --- Conserving feature in a twisting deformation --- p.50Chapter 3.2.5 --- Comparison of mass spring model --- p.51Chapter 3.3 --- Internal and external forces --- p.54Chapter 3.3.1 --- Tensile stress --- p.54Chapter 3.3.2 --- Torsional stress --- p.55Chapter 3.3.3 --- External forces --- p.59Chapter 3.4 --- Equations of motion --- p.60Chapter 3.5 --- System solver --- p.63Chapter 3.6 --- Hierarchical representation --- p.67Chapter 3.7 --- Collision detection --- p.72Chapter Chapter 4 --- Implementation and experimental result --- p.75Chapter 4.1 --- Comparison with original mass-spring system --- p.76Chapter 4.2 --- Comparison with dynamic free form deformation --- p.77Chapter 4.3 --- Comparison with the axial curve-pair deformation --- p.78Chapter 4.4 --- Shape restoring power --- p.80Chapter 4.5 --- Applications --- p.81Chapter Chapter 5 --- Conclusion --- p.84Reference --- p.8

Métodos matemáticos e computacionais para modelagem e edição de deformações

Orientador: Jorge StolfiTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Nesta tese, descrevemos primeiramente o algoritmo ECLES (Editing by Constrained LEast Squares), um método geral para edição interativa de objetos definidos por parâmetros sujeitos a restrições lineares ou afins. Neste método, as restrições e as ações de edição do usuário são combinadas usando mínimos quadrados restritos, ao invés da abordagem mais comum de elementos finitos. Usamos aritmética exata para detectar e eliminar redundâncias no conjunto de restrições e evitar falhas devido a erros de arredondamento. O algoritmo ECLES tem diversas aplicações. Entre elas, podemos citar a edição de deformações spline com continuidade C¹. Nesta tese, descrevemos um método interativo de edição de deformações do plano, o algoritmo 2DSD (2D Spline Deformation). As deformações são definidas por splines de grau 5 sobre uma malha triangular arbitrária. Estas deformações são editadas alterando-se as posições dos pontos de controle da malha. O algoritmo ECLES é usado em cada ação de edição do usuário para detectar, de forma robusta e eficiente, o conjunto de restrições de continuidade C¹ que são relevantes, garantindo que não existam redundâncias. Em seguida, como os parâmetros são modificados pelo usuário, o ECLES é chamado para calcular as novas posições dos pontos de controle satisfazendo as restrições e as posições especificadas pelo usuário. A fim de validar nosso método 2DSD, ele foi utilizado como parte de um editor interativo para deformações do espaço 2.5D, o editor PrisMystic. Este editor foi utilizado, principalmente, para deformar modelos tridimensionais de organismos microscópicos não-rígidos de modo a coincidir com imagens reais de microscopia ótica. Também utilizamos o editor para editar modelos de terrenosAbstract: In this thesis, we present the ECLES algorithm (Editing by Constrained LEast Squares), a general method for interactive editing of objects that are defined by parameters subject to linear or affine constraints. In this method, the constraints and the user editing actions are combined using constrained least squares instead of the usual finite element approach. We use exact integer arithmetic in order to detect and eliminate redundancies in the set of constraints and to avoid failures due to rounding errors. The ECLES algorithm has various applications. Among them, we can cite the editing of C¹-continuous spline deformations. In this thesis, we describe an interactive editing method for deformations of the plane, the 2DSD algorithm (2D Spline Deformation). The deformations are defined by splines of degree 5 on an arbitrary triangular mesh. The deformations are edited by changing the positions of its control points. The ECLES algorithm is first used in each user editing action in order to detect, in a robust and efficient way, the set of relevant constraints of C¹ continuity, ensuring that there are no redundancies. Then, as the parameters are changed by the user, ECLES is called to compute the new positions of the control points satisfying the constraints and the positions specified by the user. To validate our 2DSD algorithm, we used it as part of an interactive editor for 2.5D space deformations, the PrisMystic editor. This editor has been used, mainly, to deform 3D models of non-rigid living microscopic organisms as seen in actual optical microscope images. We also used the editor to edit terrain modelsDoutoradoCiência da ComputaçãoDoutora em Ciência da Computação140780/2013-001-P-04554-2013CNPQCAPE

A Survey of Spatial Deformation from a User-Centered Perspective

The spatial deformation methods are a family of modeling and animation techniques for indirectly reshaping an object by warping the surrounding space, with results that are similar to molding a highly malleable substance. They have the virtue of being computationally efficient (and hence interactive) and applicable to a variety of object representations. In this paper we survey the state of the art in spatial deformation. Since manipulating ambient space directly is infeasible, deformations are controlled by tools of varying dimension - points, curves, surfaces and volumes - and it is on this basis that we classify them. Unlike previous surveys that concentrate on providing a single underlying mathematical formalism, we use the user-centered criteria of versatility, ease of use, efficiency and correctness to compare techniques

A new free-form deformation through the control of parametric surfaces

A new free-form deformation method is presented in this paper. The deformation of an object is Á achieved by attaching it to two parametric surfaces, namely the shape surface Suv ( , ) and the height Á surface Huv ( ,). A control point or vertex of object is projected onto the shape surface along its normal and a correspondence between the point and its projection on the shape surface is established. The point is then embedded into the parametric space defined by the shape surface. By regarding the height surface as a displacement function, the directed distance from the sample point to its projection on the shape surface can be further adjusted. The proposed method is independent of the representation of underlying object. Experimental results show that the method is intuitive, easy to control and run fast. Keyword: free-form deformation, shape surface, height surface, B-spline surface 1