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

Succinct Indexes

This thesis defines and designs succinct indexes for several abstract data types (ADTs). The concept is to design auxiliary data structures that ideally occupy asymptotically less space than the information-theoretic lower bound on the space required to encode the given data, and support an extended set of operations using the basic operators defined in the ADT. As opposed to succinct (integrated data/index) encodings, the main advantage of succinct indexes is that we make assumptions only on the ADT through which the main data is accessed, rather than the way in which the data is encoded. This allows more freedom in the encoding of the main data. In this thesis, we present succinct indexes for various data types, namely strings, binary relations, multi-labeled trees and multi-labeled graphs, as well as succinct text indexes. For strings, binary relations and multi-labeled trees, when the operators in the ADTs are supported in constant time, our results are comparable to previous results, while allowing more flexibility in the encoding of the given data. Using our techniques, we improve several previous results. We design succinct representations for strings and binary relations that are more compact than previous results, while supporting access/rank/select operations efficiently. Our high-order entropy compressed text index provides more efficient support for searches than previous results that occupy essentially the same amount of space. Our succinct representation for labeled trees supports more operations than previous results do. We also design the first succinct representations of labeled graphs. To design succinct indexes, we also have some preliminary results on succinct data structure design. We present a theorem that characterizes a permutation as a suffix array, based on which we design succinct text indexes. We design a succinct representation of ordinal trees that supports all the navigational operations supported by various succinct tree representations. In addition, this representation also supports two other encodings schemes of ordinal trees as abstract data types. Finally, we design succinct representations of planar triangulations and planar graphs which support the rank/select of edges in counter clockwise order in addition to other operations supported in previous work, and a succinct representation of k-page graph which supports more efficient navigation than previous results for large values of k

Scalable Realtime Rendering and Interaction with Digital Surface Models of Landscapes and Cities

Interactive, realistic rendering of landscapes and cities differs substantially from classical terrain rendering. Due to the sheer size and detail of the data which need to be processed, realtime rendering (i.e. more than 25 images per second) is only feasible with level of detail (LOD) models. Even the design and implementation of efficient, automatic LOD generation is ambitious for such out-of-core datasets considering the large number of scales that are covered in a single view and the necessity to maintain screen-space accuracy for realistic representation. Moreover, users want to interact with the model based on semantic information which needs to be linked to the LOD model. In this thesis I present LOD schemes for the efficient rendering of 2.5d digital surface models (DSMs) and 3d point-clouds, a method for the automatic derivation of city models from raw DSMs, and an approach allowing semantic interaction with complex LOD models. The hierarchical LOD model for digital surface models is based on a quadtree of precomputed, simplified triangle mesh approximations. The rendering of the proposed model is proved to allow real-time rendering of very large and complex models with pixel-accurate details. Moreover, the necessary preprocessing is scalable and fast. For 3d point clouds, I introduce an LOD scheme based on an octree of hybrid plane-polygon representations. For each LOD, the algorithm detects planar regions in an adequately subsampled point cloud and models them as textured rectangles. The rendering of the resulting hybrid model is an order of magnitude faster than comparable point-based LOD schemes. To automatically derive a city model from a DSM, I propose a constrained mesh simplification. Apart from the geometric distance between simplified and original model, it evaluates constraints based on detected planar structures and their mutual topological relations. The resulting models are much less complex than the original DSM but still represent the characteristic building structures faithfully. Finally, I present a method to combine semantic information with complex geometric models. My approach links the semantic entities to the geometric entities on-the-fly via coarser proxy geometries which carry the semantic information. Thus, semantic information can be layered on top of complex LOD models without an explicit attribution step. All findings are supported by experimental results which demonstrate the practical applicability and efficiency of the methods