Counterbalancing for serial order carryover effects in experimental condition orders

Reactions of neural, psychological, and social systems are rarely, if ever, independent of previous inputs and states. The potential for serial order carryover effects from one condition to the next in a sequence of experimental trials makes counterbalancing of condition order an essential part of experimental design. Here, a method is proposed for generating counterbalanced sequences for repeated-measures designs including those with multiple observations of each condition on one participant and self-adjacencies of conditions. Condition ordering is reframed as a graph theory problem. Experimental conditions are represented as vertices in a graph and directed edges between them represent temporal relationships between conditions. A counterbalanced trial order results from traversing an Euler circuit through such a graph in which each edge is traversed exactly once. This method can be generalized to counterbalance for higher order serial order carryover effects as well as to create intentional serial order biases. Modern graph theory provides tools for finding other types of paths through such graph representations, providing a tool for generating experimental condition sequences with useful properties

Symmetry in 3D shapes - analysis and applications to model synthesis

Symmetry is an essential property of a shapes\u27 appearance and presents a source of information for structure-aware deformation and model synthesis. This thesis proposes feature-based methods to detect symmetry and regularity in 3D shapes and demonstrates the utilization of symmetry information for content generation. First, we will introduce two novel feature detection techniques that extract salient keypoints and feature lines for a 3D shape respectively. Further, we will propose a randomized, feature-based approach to detect symmetries and decompose the shape into recurring building blocks. Then, we will present the concept of docking sites that allows us to derive a set of shape operations from an exemplar and will produce similar shapes. This is a key insight of this thesis and opens up a new perspective on inverse procedural modeling. Finally, we will present an interactive, structure-aware deformation technique based entirely on regular patterns.Symmetrie ist eine essentielle Eigenschaft für das Aussehen eines Objekts und bietet eine Informationsquelle für strukturerhaltende Deformation und Modellsynthese. Diese Arbeit beschäftigt sich mit merkmalsbasierter Symmetrieerkennung in 3D-Objekten und der Synthese von 3D-Modellen mittels Symmetrieinformationen. Zunächst stellen wir zwei neue Verfahren zur Merkmalserkennung vor, die hervorstechende Punkte bzw. Linien in 3D-Objekten erkennen. Darauf aufbauend beschreiben wir einen randomisierten, merkmalsbasierten Ansatz zur Symmetrieerkennung, der ein Objekt in sich wiederholende Bausteine zerlegt. Des Weiteren führen wir ein Konzept zur Modifikation von Objekten ein, welches Andockstellen in Geometrie berechnet und zur Generierung von ähnlichen Objekten eingesetzt werden kann. Dieses Konzept eröffnet völlig neue Möglichkeiten für die Ermittlung von prozeduralen Regeln aus Beispielen. Zum Schluss präsentieren wir eine interaktive Technik zur strukturerhaltenden Deformation, welche komplett auf regulären Strukturen basiert

Diamond-based models for scientific visualization

Hierarchical spatial decompositions are a basic modeling tool in a variety of application domains including scientific visualization, finite element analysis and shape modeling and analysis. A popular class of such approaches is based on the regular simplex bisection operator, which bisects simplices (e.g. line segments, triangles, tetrahedra) along the midpoint of a predetermined edge. Regular simplex bisection produces adaptive simplicial meshes of high geometric quality, while simplifying the extraction of crack-free, or conforming, approximations to the original dataset. Efficient multiresolution representations for such models have been achieved in 2D and 3D by clustering sets of simplices sharing the same bisection edge into structures called diamonds. In this thesis, we introduce several diamond-based approaches for scientific visualization. We first formalize the notion of diamonds in arbitrary dimensions in terms of two related simplicial decompositions of hypercubes. This enables us to enumerate the vertices, simplices, parents and children of a diamond. In particular, we identify the number of simplices involved in conforming updates to be factorial in the dimension and group these into a linear number of subclusters of simplices that are generated simultaneously. The latter form the basis for a compact pointerless representation for conforming meshes generated by regular simplex bisection and for efficiently navigating the topological connectivity of these meshes. Secondly, we introduce the supercube as a high-level primitive on such nested meshes based on the atomic units within the underlying triangulation grid. We propose the use of supercubes to associate information with coherent subsets of the full hierarchy and demonstrate the effectiveness of such a representation for modeling multiresolution terrain and volumetric datasets. Next, we introduce Isodiamond Hierarchies, a general framework for spatial access structures on a hierarchy of diamonds that exploits the implicit hierarchical and geometric relationships of the diamond model. We use an isodiamond hierarchy to encode irregular updates to a multiresolution isosurface or interval volume in terms of regular updates to diamonds. Finally, we consider nested hypercubic meshes, such as quadtrees, octrees and their higher dimensional analogues, through the lens of diamond hierarchies. This allows us to determine the relationships involved in generating balanced hypercubic meshes and to propose a compact pointerless representation of such meshes. We also provide a local diamond-based triangulation algorithm to generate high-quality conforming simplicial meshes