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

Real-time Terrain Rendering using Smooth Hardware Optimized Level of Detail

We present a method for real-time level of detail reduction that is able to display high-complexity polygonal surface data. A compact and efficient regular grid representation is used. The method is optimized for modern, low-end consumer 3D graphics cards. We avoid sudden changes of the geometry - also known as 'popping', when reducing the geometry by exploiting the low-level hardware programmability in order to maintain interactive framerates. Terrain models are repolygonized in order to minimizing the visible error. Furthermore, the method minimizes CPU usage during rendering and requires minimal pre-processing. We believe that this is the first time that a smooth level of detail has been implemented in commodity hardware

Dyadic Splines

Dyadic splines are a simple and efficient function representation that supports multiresolution design and analysis. These splines are defined as limits of a process that alternately doubles and perturbs a sequence of points, using B-spline subdivision to smoothly perform the doubling. An interval-query algorithm is presented that efficiently and flexibly evaluates a limit function for points and intervals. Methods are given for fitting these functions to input data, and for minimizing the energy and redundancy of the representation. Several methods are given for designing dyadic splines by controlling the perturbations of the limit process. Several applications are explored, including shape design, synthesis of terrain and other natural forms, and compression

A theoretical reflection on smart shape modeling

This paper presents, as far as the authors are aware, a complete and extended new taxonomy of shape specification modeling techniques and a characterization of shape design systems, all based on the relationship of users’ knowledge to the modeling system they use to generate shapes. In-depth knowledge of this relationship is not usually revealed in the regular university training courses such as bachelor’s, master’s and continuing education. For this reason, we believe that it is necessary to modify the learning process, offering a more global vision of all the currently existing techniques and extending training in those related to algorithmic modeling techniques. We consider the latter to be the most powerful current techniques for modeling complex shapes that cannot be modeled with the usual techniques known to date. Therefore, the most complete training should include everything from the usual geometry to textual programming. This would take us a step further along the way to more powerful design environments. The proposed taxonomy could serve as a guideline to help improve the learning process of students and designers in a complex environment with increasingly powerful requirements and tools. The term “smart” is widely used nowadays, e.g. smart phones, smart cars, smart homes, smart cities... and similar terms such as “smart shape modeling”. Nowadays, the term smart is applied from a marketing point of view, whenever an innovation is used to solve a complex problem. This is the case for what is currently called smart shape modeling. However, in the future; this concept should mean a much better design environment than today. The smart future requires better trained and skilled engineers, architects, designers or technical students. This means that they must be prepared to be able to contribute to the creation of new knowledge, to the use of innovations to solve complex problems of form, and to the extraction of the relevant pieces of intelligence from the growing volume of knowledge and technologies accessible today. Our taxonomy is presented from the point of view of methods that are possibly furthest away from what is considered today as “intelligent shape modeling” to the limit of what is achievable today and which the authors call “Generic Shape Algorithm”. Finally, we discuss the characteristics that a shape modeling system must have to be truly “intelligent”: it must be “proactive” in applying innovative ideas to achieve a solution to a complex problem

The development of GIS to aid conservation of architectural and archaeological sites using digital terrestrial photogrammetry

This thesis is concerned with the creation and implementation of an Architectural/Archaeological information System (A/AIS) by integrating digital terrestrial photogrammetry and CAD facilities as applicable to the requirements of architects, archaeologists and civil engineers. Architects and archaeologists are involved with the measurement, analysis and recording of the historical buildings and monuments. Hard-copy photogrammetric methods supporting such analyses and documentation are well established. But the requirement to interpret, classify and quantitatively process photographs can be time consuming. Also, they have limited application and cannot be re-examined if the information desired is not directly presented and a much more challenging extraction of 3-D coordinates than in a digital photogrammetric environment. The A/AIS has been developed to the point that it can provide a precise and reliable technique for non-contact 3-D measurements. The speed of on-line data acquisition, high degree of automation and adaptability has made this technique a powerful measurement tool with a great number of applications for architectural or archaeological sites. The designed tool (A/AIS) has been successful in producing the expected results in tasks examined for St. Avit Senieur Abbey in France, Strome Castle in Scotland, Gilbert Scott Building of Glasgow University, Hunter Memorial in Glasgow University and Anobanini Rock in Iran. The goals of this research were: to extract, using digital photogrammetric digitising, 3-D coordinates of architectural/archaeological features, to identify an appropriate 3-D model, to import 3-D points/lines into an appropriate 3-D modeller, to generate 3-D objects. to design and implement a prototype architectural Information System using the above 3-D model, to compare this approach to traditional approaches of measuring and archiving required information. An assessment of the contribution of digital photogrammetry, GIS and CAD to the surveying, conservation, recording and documentation of historical buildings and cultural monuments include digital rectification and restitution, feature extraction for the creation of 3-D digital models and the computer visualisation are the focus of this research

Lazy Image Processing: An Investigation into Applications of Lazy Functional Languages to Image Processing

The suitability of lazy functional languages for image processing applications is investigated by writing several image processing algorithms. The evaluation is done from an application programmer's point of view and the criteria include ease of writing and reading, and efficiency. Lazy functional languages are claimed to have the advantages that they are easy to write and read, as well as efficient. This is partly because these languages have mechanisms to improve modularity, such as higher-order functions. Also, they have the feature that no subexpression is evaluated until its value is required. Hence, unnecessary operations are automatically eliminated, and therefore programs can be executed efficiently. In image processing the amount of data handled is generally so large that much programming effort is typically spent in tasks such as managing memory and routine sequencing operations in order to improve efficiency. Therefore, lazy functional languages should be a good tool to write image processing applications. However, little practical or experimental evidence on this subject has been reported, since image processing has mostly been written in imperative languages. The discussion starts from the implementation of simple algorithms such as pointwise and local operations. It is shown that a large number of algorithms can be composed from a small number of higher-order functions. Then geometric transformations are implemented, for which lazy functional languages are considered to be particularly suitable. As for representations of images, lists and hierarchical data structures including binary trees and quadtrees are implemented. Through the discussion, it is demonstrated that the laziness of the languages improves modularity and efficiency. In particular, no pixel calculation is involved unless the user explicitly requests pixels, and consecutive transformations are straightforward and involve no quantisation errors. The other items discussed include: a method to combine pixel images and images expressed as continuous functions. Some benchmarks are also presented

Hierarchical occlusion culling for arbitrarily-meshed height fields

Many graphics applications today have need for high-speed 3-D visualization of height fields. Most of these applications deal with the display of digital terrain models characterized by a simple, but vast, non-overlapping mesh of triangles. A great deal of research has been done to find methods of optimizing such systems. The goal of this work is to establish an algorithm to efficiently preprocess a hierarchical height field model that enables the real-time culling of occluded geometry while still allowing for classic terrain-rendering frameworks. By exploiting the planar-monotone characteristics of height fields, it is possible to create a unique and efficient occlusion culling method that is optimized for terrain rendering and similar applications. Previous work has shown that culling is possible with certain regularly-gridded height field models, but not until now has a system been shown to work with all height fields, regardless of how their meshes are constructed. By freeing the system of meshing restrictions, it is possible to incorporate a number of broader height field algorithms with widely-used applications such as flight simulators, GIS systems, and computer games