A Second Order Linear Discontinuous Cut-Cell Discretization for the SN Equations in RZ Geometry

In this dissertation we detail the development, implementation, and testing of a new cut-cell discretization for the discrete ordinates form of the neutron transport equation. This method provides an alternative to homogenization for problems containing material interfaces that do not coincide with mesh boundaries. A line is used to represent the boundary between the two materials in a mixed-cell converting a rectangular mixed-cell into two non-orthogonal, homogeneous cut-cells. The linear-discontinuous Galerkin finite element method (LDGFEM) spatial discretization is used on all of the rectangular cells as well as the non-orthogonal sub-cells. We have implemented our new cut-cell method in a test code which has been used to evaluate its performance relative to homogenization. We begin by developing the equations and methods associated with the LDGFEM discretization of the transport equation in RZ geometry for a homogenous orthogonal mesh. Next we introduce cut-cell meshes and develop a modification to the LDGFEM equations to account for material interfaces. We also develop methods to account for meshing errors encountered when representing curved material interfaces with linear cell faces. Finally we present test problems including manufactured solutions, fixed source, and eigenvalue problems for geometries with curvilinear material interfaces. The results of these test problems show the new cut-cell discretization to be second-order convergent for the scalar flux removed from singularities in the solution, as well as significantly more computationally efficient than homogenization

Virtual prototyping with surface reconstruction and freeform geometric modeling using level-set method

More and more products with complex geometries are being designed and manufactured by computer aided design (CAD) and rapid prototyping (RP) technologies. Freeform surface is a geometrical feature widely used in modern products like car bodies, airfoils and turbine blades as well as in aesthetic artifacts. How to efficiently design and generate digital prototypes with freeform surfaces is an important issue in CAD. This paper presents the development of a Virtual Sculpting system and addresses the issues of surface reconstruction from dexel data structures and freeform geometric modeling using the level-set method from distance field structure. Our virtual sculpting method is based on the metaphor of carving a solid block into a 3D freeform object using a 3D haptic input device integrated with the computer visualization. This dissertation presents the result of the study and consists primarily of four papers --Abstract, page iv

Aspects of the Rover Problem

The basic task of a rover is to move about automonously in an unknown environment. A working rover must have the following three subsystems which interact in various ways: 1) locomotion--the ability to move, 2) perception--the ability to determine the three-dimensional structure of the environment, and 3) navigation--the ability to negotiate the environment. This paper will elucidate the nature of the problem in these areas and survey approaches to solving them while paying attention to real-world issues.MIT Artificial Intelligence Laborator

A Second Order Linear Discontinuous Cut-Cell Discretization for the SN Equations in RZ Geometry

In this dissertation we detail the development, implementation, and testing of a new cut-cell discretization for the discrete ordinates form of the neutron transport equation. This method provides an alternative to homogenization for problems containing material interfaces that do not coincide with mesh boundaries. A line is used to represent the boundary between the two materials in a mixed-cell converting a rectangular mixed-cell into two non-orthogonal, homogeneous cut-cells. The linear-discontinuous Galerkin finite element method (LDGFEM) spatial discretization is used on all of the rectangular cells as well as the non-orthogonal sub-cells. We have implemented our new cut-cell method in a test code which has been used to evaluate its performance relative to homogenization. We begin by developing the equations and methods associated with the LDGFEM discretization of the transport equation in RZ geometry for a homogenous orthogonal mesh. Next we introduce cut-cell meshes and develop a modification to the LDGFEM equations to account for material interfaces. We also develop methods to account for meshing errors encountered when representing curved material interfaces with linear cell faces. Finally we present test problems including manufactured solutions, fixed source, and eigenvalue problems for geometries with curvilinear material interfaces. The results of these test problems show the new cut-cell discretization to be second-order convergent for the scalar flux removed from singularities in the solution, as well as significantly more computationally efficient than homogenization

Geometric Approximations and their Application to Motion Planning

Geometric approximation methods are a preferred solution to handle complexities (such as a large volume or complex features such as concavities) in geometric objects or environments containing them. Complexities often pose a computational bottleneck for applications such as motion planning. Exact resolution of these complexities might introduce other complexities such as unmanageable number of components. Hence, approximation methods provide a way to handle these complexities in a manageable state by trading off some accuracy. In this dissertation, two novel geometric approximation methods are studied: aggregation hierarchy and shape primitive skeleton. The aggregation hierarchy is a hierarchical clustering of polygonal or polyhedral objects. The shape primitive skeleton provides an approximation of bounded space as a skeleton of shape primitives. These methods are further applied to improve the performance of motion planning applications. We evaluate the methods in environments with 2D and 3D objects. The aggregation hierarchy groups nearby objects into individual objects. The hierarchy is created by varying the distance threshold that determines which objects are nearby. This creates levels of detail of the environment. The hierarchy of the obstacle space is then used to create a decom-position of the complementary space (i.e, free space) into a set of sampling regions to improve the efficiency and accuracy of the sampling operation of the sampling based motion planners. Our results show that the method can improve the efficiency (10 − 70% of planning time) of sampling based motion planning algorithms. The shape primitive skeleton inscribes a set of shape primitives (e.g., sphere, boxes) inside a bounded space such that they represent the skeleton or the connectivity of the space. We apply the shape primitive skeletons of the free space and obstacle space in motion planning problems to improve the collision detection operation. Our results also show the use of shape primitive skeleton in both spaces improves the performance of collision detectors (by 20 − 70% of collision detection time) used in motion planning algorithms. In summary, this dissertation evaluates how geometric approximation methods can be applied to improve the performance of motion planning methods, especially, sampling based motion planning method

Artistic Content Representation and Modelling based on Visual Style Features

This thesis aims to understand visual style in the context of computer science, using traditionally intangible artistic properties to enhance existing content manipulation algorithms and develop new content creation methods. The developed algorithms can be used to apply extracted properties to other drawings automatically; transfer a selected style; categorise images based upon perceived style; build 3D models using style features from concept artwork; and other style-based actions that change our perception of an object without changing our ability to recognise it. The research in this thesis aims to provide the style manipulation abilities that are missing from modern digital art creation pipelines

An investigation on the framework of dressing virtual humans

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Realistic human models are widely used in variety of applications. Much research has been carried out on improving realism of virtual humans from various aspects, such as body shapes, hair, and facial expressions and so on. In most occasions, these virtual humans need to wear garments. However, it is time-consuming and tedious to dress a human model using current software packages [Maya2004]. Several methods for dressing virtual humans have been proposed recently [Bourguignon2001, Turquin2004, Turquin2007 and Wang2003B]. The method proposed by Bourguignon et al [Bourguignon2001] can only generate 3D garment contour instead of 3D surface. The method presented by Turquin et al. [Turquin2004, Turquin2007] could generate various kinds of garments from sketches but their garments followed the shape of the body and the side of a garment looked not convincing because of using simple linear interpolation. The method proposed by Wang et al. [Wang2003B] lacked interactivity from users, so users had very limited control on the garment shape.This thesis proposes a framework for dressing virtual humans to obtain convincing dressing results, which overcomes problems existing in previous papers mentioned above by using nonlinear interpolation, level set-based shape modification, feature constraints and so on. Human models used in this thesis are reconstructed from real human body data obtained using a body scanning system. Semantic information is then extracted from human models to assist in generation of 3 dimensional (3D) garments. The proposed framework allows users to dress virtual humans using garment patterns and sketches. The proposed dressing method is based on semantic virtual humans. A semantic human model is a human body with semantic information represented by certain of structure and body features. The semantic human body is reconstructed from body scanned data from a real human body. After segmenting the human model into six parts some key features are extracted. These key features are used as constraints for garment construction.Simple 3D garment patterns are generated using the techniques of sweep and offset. To dress a virtual human, users just choose a garment pattern, which is put on the human body at the default position with a default size automatically. Users are allowed to change simple parameters to specify some sizes of a garment by sketching the desired position on the human body.To enable users to dress virtual humans by their own design styles in an intuitive way, this thesis proposes an approach for garment generation from user-drawn sketches. Users can directly draw sketches around reconstructed human bodies and then generates 3D garments based on user-drawn strokes. Some techniques for generating 3D garments and dressing virtual humans are proposed. The specific focus of the research lies in generation of 3D geometric garments, garment shape modification, local shape modification, garment surface processing and decoration creation. A sketch-based interface has been developed allowing users to draw garment contour representing the front-view shape of a garment, and the system can generate a 3D geometric garment surface accordingly. To improve realism of a garment surface, this thesis presents three methods as follows. Firstly, the procedure of garment vertices generation takes key body features as constraints. Secondly, an optimisation algorithm is carried out after generation of garment vertices to optimise positions of garment vertices. Finally, some mesh processing schemes are applied to further process the garment surface. Then, an elaborate 3D geometric garment surface can be obtained through this series of processing. Finally, this thesis proposes some modification and editing methods. The user-drawn sketches are processed into spline curves, which allow users to modify the existing garment shape by dragging the control points into desired positions. This makes it easy for users to obtain a more satisfactory garment shape compared with the existing one. Three decoration tools including a 3D pen, a brush and an embroidery tool, are provided letting users decorate the garment surface by adding some small 3D details such as brand names, symbols and so on. The prototype of the framework is developed using Microsoft Visual Studio C++,OpenGL and GPU programming

In form

Thesis (S.M.)--Massachusetts Institute of Technology, School of Architecture and Planning, Program in Media Arts and Sciences, 2003.Includes bibliographical references (p. 111-116).Spatial computing is human interaction with a machine in which the machine retains and manipulates referents to real objects and spaces. It is an essential component for making our machines fuller partners in our work and play. This thesis presents a series of experiments in the discipline and analysis of its fundamental properties.Simon Greenwold.S.M