Surface offsetting is a valuable tool used in Computer Aided Design (CAD). An offset surface is a collection of points that are at a constant distance from another surface. An offset surface is created in CAD by selecting a surface and then specifying the distance that the surface is to be offset. If a surface is selected and a distance of D is specified, then the resulting offset surface should always be distance D from the original surface. The surface offset tool can be used for many applications. Modeling of composites or other layered manufacturing processes rely heavily on offset surfaces. Thin walled parts such as injection molded components are often modeled using the offset tool. Coating processes can also be modeled using the offset tool. Modern CAD systems have surface offsetting tools and are widely used throughout industry. However, CAD systems often fail to produce valid results. The process of surface offsetting can often result in surface self-intersections as well as surface degeneracies. Self-intersections and degeneracies make the surfaces invalid because they are physically impossible to create and CAD systems cannot use these invalid surfaces to represent solid bodies. The surface offset tool is therefore, one of the most challenging CAD tools to implement. The process of avoiding, detecting and removing surface self-intersections is extremely challenging. Much research in the field of CAD is dedicated to the detection and removal of surface self-intersections. However, the methods proposed in the literature all suffer from robustness problems. The purpose of this research is to introduce a method that creates valid offset surfaces and does not suffer from the problem of creating surface self-intersections. This method uses a numerical approach that approximates the offset surface and avoids all self-intersections. Because no self-intersections are created, the method does not require intersection tests of any kind. The value of this method is demonstrated by comparing its results with results from leading CAD systems.

Nanowire heterostructures play a crucial role in nanoscale electronics, i.e., one-dimensional electronics derives benefits from the growth of heterostructures along the nanowire axis. We use first-principles plane-wave calculations within density functional theory with the localized density approximation (LDA) to get information about the structural and electronic properties of bare and hydrogen passivated GaAs/AlAs nanowire heterostructures. We also take into account the reconstruction of the nanowire surfaces. Modeled nanowire heterostructures are constructed using bulk atomic positions along [001] and [111] direction of zinc-blende structures and cutting out wires from this GaAs/AlAs heterostructure crystal with a diameter of 1 nm. We study for the effects of the surface passivation on the band gap and the band offsets for the planar GaAs/AlAs bulk heterostructure system and GaAs/AlAs nanowire heterostructure system. It is possible to control the potential that carriers feel in semiconductor heterostructures. For the planar lattice-matched heterostructures, the macroscopic average of potential of the two materials is constant far from the interface and there is a discontinuity at the interface depending on the composition of the heterostructure. In order to obtain the valence band offset in the heterostructure system, the shift in the macroscopic potential at the interface and the difference between the valence band maximum values of the two constituents must be added. In nanoscale heterostructures, the potential profile presents a more complex picture. The results indicate that while the discontinuity remains close to the planar limit right at the interface, there are fluctuations on the average potential profile beyond the interface developed by the inhomogeneous surface termination, that is, there are variations of the band edges beyond the interface. We report a first-principles study of the electronic properties of surface dangling-bond (SDB) states in hydrogen passivated GaAs/AlAs nanowire heterostructures with a diameter of 1 nm, where the SDB is defined as the defect due to an incomplete passivation of a surface atom. The charge transition levels of SDB states serve as a common energy reference level, such that charge transition level value for group III and V atoms is a constant value and a periodic table atomic property. We have carried out first-principles electronic structure and total energy calculations of aluminum nanowires for a series of different diameters ranging from 3 Angtrom-10 Angstrom, which is cut out from a slab of ideal bulk structure along the [001] direction. First-principles calculations of aluminum nanowires have been carried out within the density-functional theory. We use the norm-conserving pseudopotentials that are shown to yield successful results for ultrathin nanowire regime. Our results show that the number of bands crossing the Fermi level decreases with decreasing wire diameter and all wires studied are metallic.

A tool path generation method for sculptured surfaces defined by triangular meshes is presented in this thesis along with an algorithm that helps determine the best type of cutter geometry to machine a specific surface. Existing tool path planning methods for sculptured surfaces defined by triangular meshes require extensive computer processing power and result in long processing times mainly since surface topology for triangular meshes is not provided. The method presented in this thesis avoids this problem by offsetting each triangular facet individually. The combination of all the individual offsets make up a cutter location surface. A single triangle offsetting results in many more triangles; many of these are redundant, increasing the time required for data handling in subsequent steps. To avoid the large number of triangles, the proposed method creates a bounding space to which the offset surface is limited. The original surface mesh describes the bounding surface of a solid, thus it is continuous with no gaps. Therefore, the resulting bounding spaces are also continuous and without gaps. Applying the boundary space limits the size of the offset surface resulting in a reduction in the number of triangular surfaces generated. The offset surface generation may result in unwanted intersecting triangles. The tool path planning strategy addresses this issue by applying hidden-surface removal algorithms. The cutter locations from the offset surface are obtained using the depth buffer. The simulation and machining results show that the tool paths generated by this process are correct. Furthermore, the time required to generate tool paths is less than the time required by other methods. The second part of this thesis presents a method for selecting an optimal cutter type. Extensive research has been carried out to determine the best cutter size for a given machining operation. However, cutter type selection has not been studied in-depth. This work presents a method for selecting the best cutter type based on the amount of material removed. By comparing the amount of material removed by two cutters at a given cutter location the best cutter can be selected. The results show that the optimal cutter is highly dependent on the surface geometry. For most complex surfaces it was found that a combination of cutters provides the best results.

A tool path generation method for sculptured surfaces defined by triangular meshes is presented in this thesis along with an algorithm that helps determine the best type of cutter geometry to machine a specific surface. Existing tool path planning methods for sculptured surfaces defined by triangular meshes require extensive computer processing power and result in long processing times mainly since surface topology for triangular meshes is not provided. The method presented in this thesis avoids this problem by offsetting each triangular facet individually. The combination of all the individual offsets make up a cutter location surface. A single triangle offsetting results in many more triangles; many of these are redundant, increasing the time required for data handling in subsequent steps. To avoid the large number of triangles, the proposed method creates a bounding space to which the offset surface is limited. The original surface mesh describes the bounding surface of a solid, thus it is continuous with no gaps. Therefore, the resulting bounding spaces are also continuous and without gaps. Applying the boundary space limits the size of the offset surface resulting in a reduction in the number of triangular surfaces generated. The offset surface generation may result in unwanted intersecting triangles. The tool path planning strategy addresses this issue by applying hidden-surface removal algorithms. The cutter locations from the offset surface are obtained using the depth buffer. The simulation and machining results show that the tool paths generated by this process are correct. Furthermore, the time required to generate tool paths is less than the time required by other methods. The second part of this thesis presents a method for selecting an optimal cutter type. Extensive research has been carried out to determine the best cutter size for a given machining operation. However, cutter type selection has not been studied in-depth. This work presents a method for selecting the best cutter type based on the amount of material removed. By comparing the amount of material removed by two cutters at a given cutter location the best cutter can be selected. The results show that the optimal cutter is highly dependent on the surface geometry. For most complex surfaces it was found that a combination of cutters provides the best results.

For producing realistic images, reflection is an important visual effect. Reflections of the environment are important not only for highly reflective objects, such as mirrors, but also for more common objects such as brushed metals and glossy plastics. Generating these reflections accurately at real-time rates for interactive applications, however, is a difficult problem. Previous works in this area have made assumptions that sacrifice accuracy in order to preserve interactivity. I will present an algorithm that tries to handle reflection accurately in the general case for real-time rendering. The algorithm uses a database of prerendered environment maps to render both the original object itself and an additional bidirectional reflection distribution function (BRDF). The algorithm performs image-based rendering in reflection space in order to achieve accurate results. It also uses graphics processing unit (GPU) features to accelerate rendering.

For producing realistic images, reflection is an important visual effect. Reflections of the environment are important not only for highly reflective objects, such as mirrors, but also for more common objects such as brushed metals and glossy plastics. Generating these reflections accurately at real-time rates for interactive applications, however, is a difficult problem. Previous works in this area have made assumptions that sacrifice accuracy in order to preserve interactivity. I will present an algorithm that tries to handle reflection accurately in the general case for real-time rendering. The algorithm uses a database of prerendered environment maps to render both the original object itself and an additional bidirectional reflection distribution function (BRDF). The algorithm performs image-based rendering in reflection space in order to achieve accurate results. It also uses graphics processing unit (GPU) features to accelerate rendering.