Geometric constructions using ruler and compass are being solved for thousands of years. Humans are capable of solving these problems without explicit knowledge of the analytical models of geometric primitives present in the scene. On the other hand, most methods for solving these problems on a computer require an analytical model. In this thesis, we introduce a method for solving geometrical constructions with access only to the image of the given geometric construction. The method utilizes Mask R-CNN, a convolutional neural network for detection and segmentation of objects in images and videos. Outputs of the Mask R-CNN are masks and bounding boxes with class labels of detected objects in the input image. In this work, we employ and adapt the Mask R- CNN architecture to solve geometric construction problems from image input. We create a process for computing geometric construction steps from masks obtained from Mask R- CNN and describe how to train the Mask R-CNN model to solve geometric construction problems. However, solving geometric problems this way is challenging, as we have to deal with object detection and construction ambiguity. There is possibly an infinite number of ways to solve a geometric construction problem. Furthermore, the method should be able to solve problems not seen during the...

The limb skeleton of tapirs (Perissodactyla: Tapirus spp.) was traditionally thought to exhibit morphological variation only as a result of changes in body size. Here, we test whether forelimb variation exhibited by Tapirus is solely an artefact of size fluctuations through the tapir fossil record or whether it is influenced by habitat differences. We investigated the forelimb osteology of 12 species of Tapirus using three-dimensional geometric morphometrics on laser surface scans. Aligned shape coordinates were regressed against intrinsic bone size to account for allometry. Taxa of equivalent body mass exhibited significant differences in size-corrected bone shape. Stable carbon isotope values were averaged per species as a proxy for habitat density. Multivariate regressions of the humerus, pisiform, cuneiform, unciform, third and fourth metacarpals revealed no significant influence of size on shape. The lateral carpals (pisiform, cuneiform, unciform) demonstrated variation across the habitat density gradient. Observed variation is likely driven by species in the extinct subgenus Helicotapirus tapirs, which inhabited drier, more open woodland than modern taxa. We conclude that tapir forelimb variation is not exclusively an artefact of body size, with lateral wrist bones displaying notable differences across a habitat density gradient, beyond that resulting from size and phylogenetic effects.

Organic Photovoltaic (OPV) solar cells provide a promising alternative for harnessing solar energy. However, the efficient design of OPV materials that achieve better performance requires support by better-tailored visualization tools than are currently available, which is the goal of this thesis. One promising approach in the OPV field is to control the effective material of the OPV device, which is known as the Bulk-Heterojunction (BHJ) morphology. The BHJ morphology has a complex composition. Current BHJ exploration techniques deal with the morphologies as black boxes with no perception of the photoelectric current in the BHJ morphology. Therefore, this method depends on a trial-and-error approach and does not efficiently characterize complex BHJ morphologies. On the other hand, current state-of-the-art methods for assessing the performance of BHJ morphologies are based on the global quantification of morphological features. Accordingly, scientists in OPV research are still lacking a sufficient understanding of the best material design. To remove these limitations, we propose a new approach for knowledge-assisted visual exploration and analysis in the OPV domain. We develop new techniques for enabling efficient OPV charge transport path analysis. We employ, adapt, and develop techniques from scientific visualization, geometric modeling, clustering, and visual interaction to obtain new designs of visualization tools that are specifically tailored for the needs of OPV scientists. At the molecular scale, the user can use semantic rules to define clusters of atoms with certain geometric properties. At the nanoscale, we propose a novel framework for visual characterization and exploration of local structure-performance correlations. We also propose a new approach for correlating structural features to performance bottlenecks. We employ a visual feedback strategy that allows scientists to make intuitive choices about fabrication parameters. We furthermore propose a visual analysis framework to help answer domain science questions through parameter space exploration for local morphology features. This framework is built on the shape-based clustering of local regions (patches), which for the first time enables local analysis of BHJ morphologies. Using our proposed system, domain experts can interactively create and visualize new BHJ structures of interest at both the molecular and nanoscale levels in a relatively short time.

Sex estimation is one of the most important, and arguably the first, parts of the biological profile that is estimated for purposes of human identification. This study will examine the utility of the distal humerus in sex estimation. The goal of this research is to corroborate the usefulness of the distal humerus in sex estimation and the usefulness of geometric morphometrics in sex estimation, as well as validate metric and visual methods for sex estimation using the distal humerus. Multiple methods of sex estimation are necessary because complete skeletons are rarely found, and often only fragments are discovered. Three methods of sex estimation utilizing the distal humerus are used in this study: epicondylar breadth (n=448), nonmetric traits per Rogers (1999) and Vance et al. (2011 (n=444)), and geometric morphometrics via a Microscribe digitizer and MorphoJ software (n=227). The sample was taken from the William M. Bass Donated Skeletal Collection and was primarily composed of White Americans. The male to female ratio was approximately equal. The results of the metric aspect of the study showed a classification accuracy of 88.84% with low intra-observer and inter-observer error rates. The results of the nonmetric aspect of the study showed a classification accuracy of 77% when all traits were combined with low intra-observer and high inter-observer error rates. The results of the geometric morphometric aspect of the study showed a classification accuracy of 55% for all landmarks, 57% for anterior landmarks, and 63% for posterior landmarks. The results show that not only is the epicondylar breadth a reliable and effective method of sex estimation, it is easily repeatable by other observers. The nonmetric method is useful when epicondylar breadth cannot be measured or when an observer is familiar with the method. The geometric morphometric method is not as strong as the other two methods, but with further research and modifications may become a feasible option for sex estimation using the distal humerus. The author concludes that the distal humerus is sexually dimorphic and can be used to estimate sex accurately.

Yes / Computer aided geometric design is an area where the improvement of surface generation techniques is an everlasting demand since faster and more accurate geometric models are required. Traditional methods for generating surfaces were initially mainly based upon interpolation algorithms. Recently, partial differential equations (PDE) were introduced as a valuable tool for geometric modelling since they offer a number of features from which these areas can benefit. This work summarises the uses given to PDE surfaces as a surface generation technique together

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<p> The aim of this thesis is to construct some smooth Einstein manifolds with nonzero Einstein constant, and then to investigate their topological and geometric properties.</p> <p> In the negative case, we are able to construct conformally compact Einstein metrics on 1. products of an arbitrary closed Einstein manifold and a certain even-dimensional ball bundle over products of Hodge Kähler-Einstein manifolds, 2. certain solid torus bundles over a single Fano Kähler-Einstein manifold. We compute the associated conformal invariants, i.e., the renormalized volume in even dimensions and the conformal anomaly in odd dimensions. As by-products, we obtain many Riemannian manifolds with vanishing Q-curvature.</p> <p> In the positive case, we are able to construct complete Einstein metrics on certain 3-sphere bundles over a Fano Kähler-Einstein manifold. We classify the homeomorphism and diffeomorphism types of the total spaces when the base manifold is the complex projective plane.</p> / Thesis / Doctor of Philosophy (PhD)

Antisymmetry is a striking, yet puzzling form of biological asymmetry. The livebearing fish Xenophallus umbratilis exhibits antisymmetry in the male intromittent organ and provides a system that is well-suited for studying the nature of variation in antisymmetrical traits. Using geometric morphometrics, I test the hypothesis that because the gonopodium is critical to fitness there will not be significant differences in gonopodium shape between the two gonopodial morphs in this species. My results are consistent with this prediction, though I found that gonopodium shape did differ with gonopodium size.

One of the major challenges of implementing additive manufacturing (AM) processes for the purpose of production is the lack of understanding of its underlying process-structure-property relationship. Parts manufactured using AM technologies may be too inconsistent and unreliable to meet the stringent requirements for many industrial applications. The first objective of the present research is to characterize the underlying thermo-physical dynamics of AM process, captured by melt pool signals, and predict porosity during the build. Herein, we propose a novel porosity prediction method based on the temperature distribution of the top surface of the melt pool as the AM part is being built. Advance data analytic and machine learning methods are then used to further analyze the 2D melt pool image streams to identify the patterns of melt pool images and its relationship to porosity. Furthermore, the lack of geometric accuracy of AM parts is a major barrier preventing its use in mission-critical applications. Hence, the second objective of this work is to quantify the geometric deviations of additively manufactured parts from a large data set of laser-scanned coordinates using an unsupervised machine learning approach. The outcomes of this research are: 1) quantifying the link between process conditions and geometric accuracy; and 2) significantly reducing the amount of point cloud data required for characterizing of geometric accuracy.

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