Doctor of Philosophy

dissertationThe medial axis of an object is a shape descriptor that intuitively presents the morphology or structure of the object as well as intrinsic geometric properties of the object’s shape. These properties have made the medial axis a vital ingredient for shape analysis applications, and therefore the computation of which is a fundamental problem in computational geometry. This dissertation presents new methods for accurately computing the 2D medial axis of planar objects bounded by B-spline curves, and the 3D medial axis of objects bounded by B-spline surfaces. The proposed methods for the 3D case are the first techniques that automatically compute the complete medial axis along with its topological structure directly from smooth boundary representations. Our approach is based on the eikonal (grassfire) flow where the boundary is offset along the inward normal direction. As the boundary deforms, different regions start intersecting with each other to create the medial axis. In the generic situation, the (self-) intersection set is born at certain creation-type transition points, then grows and undergoes intermediate transitions at special isolated points, and finally ends at annihilation-type transition points. The intersection set evolves smoothly in between transition points. Our approach first computes and classifies all types of transition points. The medial axis is then computed as a time trace of the evolving intersection set of the boundary using theoretically derived evolution vector fields. This dynamic approach enables accurate tracking of elements of the medial axis as they evolve and thus also enables computation of topological structure of the solution. Accurate computation of geometry and topology of 3D medial axes enables a new graph-theoretic method for shape analysis of objects represented with B-spline surfaces. Structural components are computed via the cycle basis of the graph representing the 1-complex of a 3D medial axis. This enables medial axis based surface segmentation, and structure based surface region selection and modification. We also present a new approach for structural analysis of 3D objects based on scalar functions defined on their surfaces. This approach is enabled by accurate computation of geometry and structure of 2D medial axes of level sets of the scalar functions. Edge curves of the 3D medial axis correspond to a subset of ridges on the bounding surfaces. Ridges are extremal curves of principal curvatures on a surface indicating salient intrinsic features of its shape, and hence are of particular interest as tools for shape analysis. This dissertation presents a new algorithm for accurately extracting all ridges directly from B-spline surfaces. The proposed technique is also extended to accurately extract ridges from isosurfaces of volumetric data using smooth implicit B-spline representations. Accurate ridge curves enable new higher-order methods for surface analysis. We present a new definition of salient regions in order to capture geometrically significant surface regions in the neighborhood of ridges as well as to identify salient segments of ridges

Tracing ridges on B-Spline surfaces

posterWon Best Paper Award at SIAM/ACM Joint Conference on Geometric and Physical Modeling, San Francisco, 200

AIChE 2017 Student Design Competition: Manufacturing facility for Nylon 6 6

A preliminary design and economic analysis was performed for the development of a grass roots manufacturing facility of Nylon 6 6 in Calvert City, Kentucky. Nylon 6 6 is a polymer that is synthesized from Adipic Acid (ADA) and Hexamethylene diamine (HMDA) through polycondensation and step-growth polymerization reactions. The two reactions pursued were batch and continuous processes, in which Nylon 6 6 was sold either in solid pellet or spun fiber form. Additionally, the process yields a byproduct of 1,6 hexanediamine (diamine). The objective of the project was to determine which of the four production methods served as the most economically viable option. The optimum Nylon 6 6 production design is an intricate balance between capital and operating expenses that maximizes revenue and minimizes costs.Given the opportunity to invest in the generation of a grass roots facility, it is our recommendation to proceed with the production of spun Nylon 6 6 fibers using a continuous production process. The economic analysis determined which option was the most economically viable for the company to invest in. From this point, a series of optimization procedures took place to reduce utility and capital costs in an effort to maximize annual profits and reduce the payback period of the project. Through changes in the maximum temperature of the evaporation unit within an acceptable range, capital costs and utility costs were reduced resulting in the lowest PWC. The evaporation unit temperature of 280 degrees Celsius was determined to be the most economical case for this production process, with a capital investment of $13,015,000, a DCFROR of 211$2.40, and an NPV of $17,874,000. It was determined advantageous to continue with project development; therefore, the project is scheduled to be completed and fully operational in June of 2018 and will have a payback period of 1.57 years.The fundamental safety concept for this process was to make the operation inherently safer and to mitigate hazards. The hazardous components present in the process consist of ADA, HMDA, and diamine. The risks associated with these components include possible combustion, irritation to respiratory system and skin, and hazardous release to the environment. To mitigate these risks, it is recommended that the equipment is designed to operate within specified design temperatures and pressures and to implement a Distributed Control System (DCS)

Designing and processing parametric models of steady lattices

Our goal is to facilitate the design, analysis, optimization, and additive manufacturing of a specific class of 3D lattices that may comprise an extremely large number of elements. We target curved lattices that exhibit periodicity and uniform geometric gradations in three directions, along possibly curved axes. We represent a lattice by a simple computer program with a carefully selected set of exposed control parameters that may be used to adjust the overall shape of the lattice, its repetition count in each direction, its microstructure, and its gradation. In our Programmed-Lattice Editor (PLE), a typical lattice is represented by a short program of 10 to 50 statements. We propose a simple API and a few rudimentary GUI tools that automate the creation of the corresponding expressions in the program. The overall shape and gradation of the lattice is controlled by three similarity transformations. This deliberate design choice ensures that the gradation in each direction is regular (i.e., mathematically steady), that each cell can be evaluated directly, without iterations, and that integral properties (such as surface area, volume, center of mass and spherical inertia) can be obtained rapidly without having to calculate them for each individual element of the lattice

Distributed Localization with Grid-based Representations on Digital Elevation Models

It has been demonstrated that grid cells in the brain are encoding physical locations using hexagonally spaced, periodic phase-space representations. We explore how such a representation may be computationally advantageous for related engineering applications. Theories of how the brain decodes from a phase-space representation have been developed based on neuroscience data. However, theories of how sensory information is encoded into this phase space are less certain. Here we show a method for how a navigation-relevant input space such as elevation trajectories may be mapped into a phase-space coordinate system that can be decoded using previously developed theories. We also consider how such an algorithm may then also be mapped onto neuromrophic systems. Just as animals can tell where they are in a local region based on where they have been, our encoding algorithm enables the localization to a position in space by integrating measurements from a trajectory over a map. In this paper, we walk through our approach with simulations using a digital elevation model. © 2022 Public Domain.Public domain articleThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

INTEGRATING MULTIPLE ENGINEERING RESOURCES IN A VIRTUAL ENVIRONMENT FOR REVERSE ENGINEERING LEGACY MECHANICAL PARTS

Reverse engineering is a time-consuming and technically formidable process that is increasingly becoming an economic imperative due to replacement costs. The Multiple Engineering Resources aGent Environment (MERGE) system, introduced in this paper, is a new approach toward reverse engineering whose architecture and modules are driven specifically by the requirements of legacy engineering. Legacy engineering scenarios presume availability of multiple (possibly incomplete or inconsistent) sources of information, lack of digital descriptions of the parts, constrained time restrictions and need for significant domain knowledge expertise. The reverse engineering process must yield modern CAD models capable of driving state-of-the art CAM processes. The MERGE system aims at making the reverse engineering process more effective, using both intuitive interaction and visualization as key components, by enabling quick identification and resolution of inconsistencies among various resources in a unified environment. The MERGE system also aims at simplifying the reverse engineering process by integrating various computational agents to assist the reverse engineer in processing information and in creating the desired CAD models