Doctor of Philosophy

dissertationWhile boundary representations, such as nonuniform rational B-spline (NURBS) surfaces, have traditionally well served the needs of the modeling community, they have not seen widespread adoption among the wider engineering discipline. There is a common perception that NURBS are slow to evaluate and complex to implement. Whereas computer-aided design commonly deals with surfaces, the engineering community must deal with materials that have thickness. Traditional visualization techniques have avoided NURBS, and there has been little cross-talk between the rich spline approximation community and the larger engineering field. Recently there has been a strong desire to marry the modeling and analysis phases of the iterative design cycle, be it in car design, turbulent flow simulation around an airfoil, or lighting design. Research has demonstrated that employing a single representation throughout the cycle has key advantages. Furthermore, novel manufacturing techniques employing heterogeneous materials require the introduction of volumetric modeling representations. There is little question that fields such as scientific visualization and mechanical engineering could benefit from the powerful approximation properties of splines. In this dissertation, we remove several hurdles to the application of NURBS to problems in engineering and demonstrate how their unique properties can be leveraged to solve problems of interest

Direct Slicing of STEP Based NURBS Models for Solid Freeform Fabrication

Direct slicing of CAD models to generate process planning instructions for solid freeform fabrication may overcome inherent disadvantages of using STL format in terms of the process accuracy, ease of file management, and incorporation of multiple materials. This paper will present the results of our development of a direct slicing algorithm for layered freeform fabrication. The direct slicing algorithm was based on a neutral, international standard (ISO 10303) STEP-formatted NURBS geometric representation and is intended to be independent of any commercial CAD software. The following aspects of the development effort will be presented: 1) Determination of optimal build direction based upon STEP-based NURBS models; 2) Adaptive subdivision of NURBS data for geometric refinement; and 3) Ray-casting slice generation into sets of raster patterns. Feasibility studies applying the direct slicing algorithm to example models and the generation of fabrication planning instructions involving multi-material structures will also be presented.Mechanical Engineerin

Uniform Micro-Patterning of an Arbitrary Surface

According to the literature, creating specific micro-level patterns on some surfaces can significantly reduce friction. To this effect, a method is presented to create a regular pattern of micro-level indentations on any irregular surface. Creating a uniform pattern on a regular surface is possible using commercial CAD software, where regular surface is the surface obtained by extrusion or revolution of a 2D sketch along any curve. But, it is complicated and often incorrect for irregular surfaces. The thesis presents the approach followed to create parameterized regular patterns on arbitrary surfaces. Three different algorithms are presented, each achieving a progressively increased quality solution. The last and best method provides a set of points with their corresponding normals to the surface to enable the creation of the patterning feature. The algorithm reads an STL file, a format neutral output of any CAD software and implements the method on the approximated surface. Each facet surface upon which the pattern has to be created is sliced by planes at specific distances from each other. The intersections of the facets and the planes are calculated and chains are formed from the intersections in each plane. Points are interpolated at the required pitch in different chains formed at the intersection of a single plane and the facets. This procedure is repeated for each plane. Thus, a pattern of points of specified pitch distance that can be as low as microns can be generated. Given specifications of a machine, this method generates the X, Y, and Z translations and the axis rotation angles needed to generate a g-code specific to a micro-milling machine. This code can be used directly for any metal removing process that has to create micro-level indentations on an arbitrary surface. If instead, the features are protrusions on some irregular surface, then the resultant points obtained with the developed approach can be used to apply the pattern at each of the identified locations

On Triangular Splines:CAD and Quadrature

The standard representation of CAD (computer aided design) models is based on the boundary representation (B-reps) with trimmed and (topologically) stitched tensor-product NURBS patches. Due to trimming, this leads to gaps and overlaps in the models. While these can be made arbitrarily small for visualisation and manufacturing purposes, they still pose problems in downstream applications such as (isogeometric) analysis and 3D printing. It is therefore worthwhile to investigate conversion methods which (necessarily approximately) convert these models into water-tight or even smooth representations. After briefly surveying existing conversion methods, we will focus on techniques that convert CAD models into triangular spline surfaces of various levels of continuity. In the second part, we will investigate efficient quadrature rules for triangular spline space