Axial deformation with controllable local coordinate frames.

Chow, Yuk Pui.Thesis (M.Phil.)--Chinese University of Hong Kong, 2010.Includes bibliographical references (leaves 83-87).Abstracts in English and Chinese.Chapter 1. --- Introduction --- p.13-16Chapter 1.1. --- Motivation --- p.13Chapter 1.2 --- Objectives --- p.14-15Chapter 1.3 --- Thesis Organization --- p.16Chapter 2. --- Related Works --- p.17-24Chapter 2.1 --- Axial and the Free Form Deformation --- p.17Chapter 2.1.1 --- The Free-Form Deformation --- p.18Chapter 2.1.2 --- The Lattice-based Representation --- p.18Chapter 2.1.3 --- The Axial Deformation --- p.19-20Chapter 2.1.4 --- Curve Pair-based Representation --- p.21-22Chapter 2.2 --- Self Intersection Detection --- p.23-24Chapter 3. --- Axial Deformation with Controllable LCFs --- p.25-46Chapter 3.1 --- Related Methods --- p.25Chapter 3.2 --- Axial Space --- p.26-27Chapter 3.3 --- Definition of Local Coordinate Frame --- p.28-29Chapter 3.4 --- Constructing Axial Curve with LCFs --- p.30Chapter 3.5 --- Point Projection Method --- p.31-32Chapter 3.5.1 --- Optimum Reference Axial Curve Point --- p.33Chapter 3.6 --- Advantages using LCFs in Axial Deformation --- p.34Chapter 3.6.1 --- Deformation with Smooth Interpolated LCFs --- p.34-37Chapter 3.6.2 --- Used in Closed-curve Deformation --- p.38-39Chapter 3.6.3 --- Hierarchy of Axial Curve --- p.40Chapter 3.6.4 --- Applications in Soft Object Deformation --- p.41Chapter 3.7 --- Experiments and Results --- p.42-46Chapter 4. --- Self Intersection Detection of Axial Curve with LCFs --- p.47-76Chapter 4.1 --- Related Works --- p.48-49Chapter 4.2 --- Algorithms for Solving Self-intersection Problem with a set of LCFs --- p.50-51Chapter 4.2.1 --- The Intersection of Two Plane --- p.52Chapter 4.2.1.1 --- Constructing the Normal Plane --- p.53-54Chapter 4.2.1.2 --- A Line Formed by Two Planes Intersection --- p.55-57Chapter 4.2.1.3 --- Problems --- p.58Chapter 4.2.1.4 --- Sphere as Constraint --- p.59-60Chapter 4.2.1.5 --- Intersecting Line between Two Circular Discs --- p.61Chapter 4.2.2 --- Distance between a Mesh Vertex and a Curve Point --- p.62-63Chapter 4.2.2.1 --- Possible Cases of a Line and a Circle --- p.64-66Chapter 4.3 --- Definition Proof --- p.67Chapter 4.3.1 --- Define the Meaning of Self-intersection --- p.67Chapter 4.3.2 --- Cross Product of Two Vectors --- p.68Chapter 4.4 --- Factors Affecting the Accuracy of the Algorithm --- p.69Chapter 4.3.1 --- High Curvature of the Axial Curve --- p.69-70Chapter 4.3.2 --- Mesh Density of an Object. --- p.71-73Chapter 4.5 --- Architecture of the Self Intersection Algorithm --- p.74Chapter 4.6 --- Experimental Results --- p.75- 79Chapter 5. --- Conclusions and Future Development --- p.80-82Chapter 5.1 --- Contribution and Conclusions --- p.80-81Chapter 5.2 --- Limitations and Future Developments --- p.82References --- p.83-8

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

Procesado de geometría en CAGD mediante S-series

El diseño geométrico asistido por ordenador (CAGD) se basa en la representación de entidades geométricas en el estándar nurbs, por lo que se debe obtener una aproximación polinómica o racional de aquellas funciones trascendentes, entidades que no pueden ser expresadas en la base de Bernstein. En principio se podría pensar en una aproximación mediante series de Taylor truncadas. De esta forma se obtendría una buena aproximación alrededor de un punto, pero se precisarían grados muy elevados para errores pequeños y los programas de CAD tienen limitado el grado maximo admisible. Una forma de evitar estos grados elevados seria conectar varios desarrollos de Taylor, pero en este caso aparecerían huecos en la unión de dos expansiones, algo inaceptable en una representación para CAD. En esta tesis se introduce la herramienta matemática básica empleada en este trabajo, las s-series. Estas series resultan de la base s-monomial, basada en expansiones de hermite en un intervalo unitario de la variable. Asimismo, se describen las estrategias para calcular de manera eficiente la aproximación de una entidad mediante s-series. Seguidamente, se comparan las aproximaciones mediante s-series con las basadas en series de poisson. A continuación, se aproxima la clotoide como ejemplo de aplicación de las estrategias de aproximación mediante s-series expuestas. Finalmente, se aplican las s-series a las técnicas de deformación. El objetivo de este capítulo consiste en conseguir una aproximación polinómica Bernstein-Bezier de los objetos deformados

Free-form design using axial curve-pairs

Deformation of 3D shapes usually requires the use of a deformation tool. The freeform deformation technique requires the use of a lattice of control point for deforming anobject. This may require a synchronized movement of the lattice control points in order to obtain the desired effects. The axial deformation technique allows an object to bedeformed by manipulating an axial curve. However, unexpected twist of the object may be obtained. This is a result of the lack of control on the local coordinate frame of thecurve. This paper presents a technique for deforming objects with a set of axial curve-pairs. The use of a curve-pair allows the local coordinate frame to be controlledintuitively. A curve-pair is composed of a primary and an orientation curve. The orientation curve is an approximate offset of the primary curve. A technique is proposed formaintaining the relation between the primary and the orientation curve when the curve-pair is adjusted. By associating a complex 3D object to a curve-pair, the object can bestretched, bended, and twisted intuitively through manipulating the curve-pair. This deformation technique is particularly suitable for manipulating complex shapes (e.g. decorative components) in industrial and aesthetic design, and is also suitable for modelling characters and animals with flexible bodies. Adjusting the curve-pair according tosome motion constraints produces different postures of a character or animal model. This in turn can be used as decorative components for aesthetic design