Combinatorial Properties and Recognition of Unit Square Visibility Graphs

Unit square (grid) visibility graphs (USV and USGV, resp.) are described by axis-parallel visibility between unit squares placed (on integer grid coordinates) in the plane. We investigate combinatorial properties of these graph classes and the hardness of variants of the recognition problem, i.e., the problem of representing USGV with fixed visibilities within small area and, for USV, the general recognition problem

New Parameters for Beyond-Planar Graphs

Parameters for graphs appear frequently throughout the history of research in this field. They represent very important measures for the properties of graphs and graph drawings, and are often a main criterion for their classification and their aesthetic perception. In this direction, we provide new results for the following graph parameters: – The segment complexity of trees; – the membership of graphs of bounded vertex degree to certain graph classes; – the maximal complete and complete bipartite graphs contained in certain graph classes beyond-planarity; – the crossing number of graphs; – edge densities for outer-gap-planar graphs and for bipartite gap-planar graphs with certain properties; – edge densities and inclusion relationships for 2-layer graphs, as well as characterizations for complete bipartite graphs in the 2-layer setting

Colored anchored visibility representations in 2D and 3D space

© 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In a visibility representation of a graph G, the vertices are represented by nonoverlapping geometric objects, while the edges are represented as segments that only intersect the geometric objects associated with their end-vertices. Given a set P of n points, an Anchored Visibility Representation of a graph G with n vertices is a visibility representation such that for each vertex v of G, the geometric object representing v contains a point of P. We prove positive and negative results about the existence of anchored visibility representations under various models, both in 2D and in 3D space. We consider the case when the mapping between the vertices and the points is not given and the case when it is only partially given.Peer ReviewedPostprint (author's final draft

1.5. Enhancing Archaeological Data Collection and Student Learning with a Mobile Relational Database

In 2011, the Proyecto de Investigación Arqueológico Regional Ancash (PIARA) inaugurated an archaeological field school that employed a comprehensive digital data collection protocol. Students learned to record data on iPads using our customized relational databases for excavation, human skeletal analysis, and artifact classification. The databases integrated digital media, such as vector drawings and annotated photos. In a final research project, the students used the tablet system to analyze excavation contexts and artifacts, visualize relationships between the data, conduct literature reviews, and present their findings. This chapter discusses how students develop a greater comprehension of archaeological concepts and stronger research skills when they collect and analyze data using a relational database. More precisely, it argues that the database develops more perceptive archaeologists who can immediately recognize and interpret relationships between archaeological materials, contexts, and features. The technology, then, not only aids in-field planning and interpretation, but also cultivates analytical thinking.https://dc.uwm.edu/arthist_mobilizingthepast/1006/thumbnail.jp

Doctor of Philosophy in Computing

dissertationPhysics-based animation has proven to be a powerful tool for creating compelling animations for film and games. Most techniques in graphics are based on methods developed for predictive simulation for engineering applications; however, the goals for graphics applications are dramatically different than the goals of engineering applications. As a result, most physics-based animation tools are difficult for artists to work with, providing little direct control over simulation results. In this thesis, we describe tools for physics-based animation designed with artist needs and expertise in mind. Most materials can be modeled as elastoplastic: they recover from small deformations, but large deformations permanently alter their rest shape. Unfortunately, large plastic deformations, common in graphical applications, cause simulation instabilities if not addressed. Most elastoplastic simulation techniques in graphics rely on a finite-element approach where objects are discretized into a tetrahedral mesh. Using these approaches, maintaining simulation stability during large plastic flows requires remeshing, a complex and computationally expensive process. We introduce a new point-based approach that does not rely on an explicit mesh and avoids the expense of remeshing. Our approach produces comparable results with much lower implementation complexity. Points are a ubiquitous primitive for many effects, so our approach also integrates well with existing artist pipelines. Next, we introduce a new technique for animating stylized images which we call Dynamic Sprites. Artists can use our tool to create digital assets that interact in a natural, but stylized, way in virtual environments. In order to support the types of nonphysical, exaggerated motions often desired by artists, our approach relies on a heavily modified deformable body simulator, equipped with a set of new intuitive controls and an example-based deformation model. Our approach allows artists to specify how the shape of the object should change as it moves and collides in interactive virtual environments. Finally, we introduce a new technique for animating destructive scenes. Our approach is built on the insight that the most important visual aspects of destruction are plastic deformation and fracture. Like with Dynamic Sprites, we use an example-based model of deformation for intuitive artist control. Our simulator treats objects as rigid when computing dynamics but allows them to deform plastically and fracture in between timesteps based on interactions with the other objects. We demonstrate that our approach can efficiently animate the types of destructive scenes common in film and games. These animation techniques are designed to exploit artist expertise to ease creation of complex animations. By using artist-friendly primitives and allowing artists to provide characteristic deformations as input, our techniques enable artists to create more compelling animations, more easily