No / We present an explicit polynomial solution method for surface generation. In this case the surface in question is characterized by some boundary configuration whereby the resulting surface conforms to a fourth order linear elliptic Partial Differential Equation, the Euler–Lagrange equation of a quadratic functional defined by a norm. In particular, the paper deals with surfaces generated as explicit Bézier polynomial solutions for the chosen Partial Differential Equation. To present the explicit solution methodologies adopted here we divide the Partial Differential Equations into two groups namely the orthogonal and the non-orthogonal cases. In order to demonstrate our methodology we discuss a series of examples which utilize the explicit solutions to generate smooth surfaces that interpolate a given boundary configuration. We compare the speed of our explicit solution scheme with the solution arising from directly solving the associated linear system.

We present an efficient method for reconstructing complex geometry using an elliptic Partial Differential Equation (PDE) formulation. The integral part of this work is the use of three-dimensional curves within the physical space which act as boundary conditions to solve the PDE. The chosen PDE is solved explicitly for a given general set of curves representing the original shape and thus making the method very efficient. In order to improve the quality of results for shape representation we utilize an automatic parameterization scheme on the chosen curves. With this formulation we discuss our methodology for shape representation using a series of practical examples.

This research develops an analytical scientific approach for investigating the high precision surface generation and the quantitative analysis of the effects of direct factors in precision machining. The research focuses on 3D surface characterization with particular reference to the turning process and associated surface generation. The most important issue for this research is surface functionality which is becoming important in the current engineering industry. The surface functionality should match with the characterization parameters of the machined surface, which can be expressed in formula form as proposed in chapter 4. Modelling and simulation are extensively used in the research. The modelling approach integrates the cutting forces model, thermal mode% vibration model, tool wear model, machining system response model and surface topography model. All of those models are integrated as a whole model. The physical model with such as direct inputs is formed. The major inputs to the model are tooling geometry and the process variables. The outputs from the modelling approach are cutting force, surface texture parameters, dimensional errors, residual stress and material removal rate. MATLAB and Simulink are used as tools to implement the modelling and simulation. According to the simulation results, it is found that the feed rate has the most profound effect on in surface generation. The influence of the vibrations between the cutting tool and the workpiece on the surface roughness may be minimised by the small feed rate and large tool nose radius. Surface functionality simulation has been developed to model and simulate the surface generation in precision turning. The surface functionality simulation model covers the material and tool wear as well. It shows that chip formation is resulted from cutting forces. Cutting trials are conducted to validate the modelling and simulation developed. There are positive results that show the agreement between the simulation and experimental results. The analysis of the results of turning trials and simulations are conducted in order to find out the effects of process variables and tooling characteristics on surface texture and topography and machining instability. From the research, it can be concluded that the investigation on modelling and simulation of precision surfaces generation in precision turning is performed well against the research objectives as proposed. Recommendations for future work are to improve the model parameters identification, including comprehensive tool wear, chip formation and using Neural Networks modelling in the engineering surface construction system.

Turning and milling are the main manufacturing techniques in industry. A great deal of time and money is spent for machining operations. Although most of the time, the tool path of a CNC machine tool is generated by a Computer Aided Manufacturing (CAM) software package, to be sure that the result of the machining operation will be as required, it is necessary to use a simulation software. There are various machining simulation software packages available in the market. However, they are not only expensive, but also specialized for only one of the before mentioned machining techniques. Most of the companies in the industry are small or medium scale ones and, it is not so easy for them to afford a specialized simulation software for that purpose. In this thesis, it is aimed to develop a software package, which will be used to simulate advanced industrial machining processes, including turning and milling. Dexelmodeling, which is generated by ray casting, and sweep plane algorithm withpolygon clipping technique are used forvisualization. For polygon clipping technique, outer surfaces of the resultant workpiece are generated from planar contours. The software is developed in C# programming language and DirectX libraries are utilizedfor visualization purposes. With the aid of this software, it is also aimed to visually confirm the validity of both mill and lathe NC-code, by representing highly accurate 3D displayed results of these simulations.

abstract: The Dual Marching Tetrahedra algorithm is a generalization of the Dual Marching Cubes algorithm, used to build a boundary surface around points which have been assigned a particular scalar density value, such as the data produced by and Magnetic Resonance Imaging or Computed Tomography scanner. This boundary acts as a skin between points which are determined to be "inside" and "outside" of an object. However, the DMT is vague in regards to exactly where each vertex of the boundary should be placed, which will not necessarily produce smooth results. Mesh smoothing algorithms which ignore the DMT data structures may distort the output mesh so that it could incorrectly include or exclude density points. Thus, an algorithm is presented here which is designed to smooth the output mesh, while obeying the underlying data structures of the DMT algorithm. / Dissertation/Thesis / M.S. Computer Science 2011

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Yes / This paper presents a method for interactive design by means of extending the PDE based approach for surface generation. The governing partial differential equation is generalized to arbitrary order allowing complex shapes to be designed as single patch PDE surfaces. Using this technique a designer has the flexibility of creating and manipulating the geometry of shape that satisfying an arbitrary set of boundary conditions. Both the boundary conditions which are defined as curves in 3-space and the spine of the corresponding PDE are utilized as interactive design tools for creating and manipulating geometry intuitively. In order to facilitate interactive design in real time, a compact analytic solution for the chosen arbitrary order PDE is formulated. This solution scheme even in the case of general boundary conditions satisfies exactly the boundary conditions where the resulting surface has an closed form representation allowing real time shape manipulation. In order to enable users to appreciate the powerful shape design and manipulation capability of the method, we present a set of practical examples.

The human cerebral cortex is a highly foliated structure that supports the complex cognitive abilities of humans. The cortex is divided by its cytoarchitectural characteristics that can be approximated by the folding pattern of the cortex. Psychiatric and neurological diseases, such as Huntington's disease or schizophrenias, are often related with structural changes in the cerebral cortex. Detecting structural changes in different regions of cerebral cortex can provide insight into disease biology, progression and response to treatment. The delineation of anatomical regions on the cerebral cortex is time intensive if performed manually, therefore automated methods are needed to perform this delineation. Magnetic Resonance Imaging (MRI) is commonly used to explore the structural change in patients with psychiatric and neurological diseases. This dissertation proposes a fast and reliable method to automatically parcellate the cortical surface generated from MR images. A fully automated pipeline has been built to process MR images and generate cortical surfaces associated with parcellation labels. First, genus zero cortical surfaces for each hemisphere of a subject are generated from MR images. The surface is generated at the parametric boundary between gray matter and white matter. Geometry features are calculated for each cortical surface to as scalar values to drive a multi-resolution spherical registration that can align two cortical surfaces together in the spherical domain. Then, the labels on a subject's cortical surface are evaluated by registering a subject's cortical surface with a population atlas and combining the information of prior probabilities on the atlas with the subject's geometry features. The automated parcellation has been tested on a group of subjects with various cerebral cortex structures. It shows that the proposed method is fast (takes about 3 hours to parcellate at one hemisphere) and accurate (with the weighted average Dice ~0.86). The framework of this dissertation will be as follows: the first chapter is about the introduction, including motivation, background, and significance of the study. The second chapter describes the whole pipeline of the automated surface parcellation and focuses on technical details of every method used in the pipeline. The third chapter presents results achieved in this study and the fourth chapter discusses the results and draws a conclusion.

Surface roughness exists at many length scales-from atomic dimensions to meters. At sub-micron scale, the distribution of roughness is largely dependent on the process that generates the surface through the mechanisms of material removal/addition involved and the process parameters. The focus of the research is to quantitatively characterize the evolution of sub-micron scale surface roughness in the mechanical, chemical and electrochemical material removal techniques and study the influence of roughness on the mechanical behavior of surfaces. High purity aluminum surfaces are subjected to surface dissolution techniques such as electropolishing, chemical etching and anodization. Owing to the lack of sufficient lateral resolution in conventional roughness measurement techniques and appropriate scale independent roughness characterization techniques, the effect sub-micron scale electrochemical inhomogeneities present on the surfaces have on the roughness evolution at various length scales has not been understood. In this work, the power spectral density method of roughness characterization is used to quantitatively evaluate the roughness length scales affected in the surface generation processes as a function of time. Results indicate that in the case of electropolishing, roughness is not uniformly reduced at all length scales. Further, cut-off frequencies are suggested to optimize the electropolishing process. In chemical etching, the nature of roughness produced is found to be dependent on the nature of the starting surface. The nature of surface and sub-surface structures produced in the initial stage of the anodization process, and the transition from a disordered to an ordered structure are studied. In order to study the mechanical behavior of surfaces as a function of surface roughness, a single asperity indentation is modeled using nanoindentation of micropillar produced by focused ion beam machining of aluminum surfaces. Load-displacement curves are constructed to show the transition from a single asperity deformation to bulk deformation as function of indentation depth. Additionally, indentation responses of polymer coated surfaces with varying degree of roughness that were produced by the aforementioned surface generation processes are studied. it is shown how high interface roughness gives rise to high scatter both in loading and unloading portions of the load-displacement curves. Finally, porous alumina surface generated by the anodization process discussed above is indented to simulate a multi-asperity interaction.

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