An Upper Bound on the Average Size of Silhouettes

It is a widely observed phenomenon in computer graphics that the size of the silhouette of a polyhedron is much smaller than the size of the whole polyhedron. This paper provides, for the first time, theoretical evidence supporting this for a large class of objects, namely for polyhedra that approximate surfaces in some reasonable way; the surfaces may be non-convex and non-differentiable and they may have boundaries. We prove that such polyhedra have silhouettes of expected size $O(\sqrt{n})$ where the average is taken over all points of view and n is the complexity of the polyhedron

View generated database

This document represents the final report for the View Generated Database (VGD) project, NAS7-1066. It documents the work done on the project up to the point at which all project work was terminated due to lack of project funds. The VGD was to provide the capability to accurately represent any real-world object or scene as a computer model. Such models include both an accurate spatial/geometric representation of surfaces of the object or scene, as well as any surface detail present on the object. Applications of such models are numerous, including acquisition and maintenance of work models for tele-autonomous systems, generation of accurate 3-D geometric/photometric models for various 3-D vision systems, and graphical models for realistic rendering of 3-D scenes via computer graphics

Doctor of Philosophy

dissertationWhile boundary representations, such as nonuniform rational B-spline (NURBS) surfaces, have traditionally well served the needs of the modeling community, they have not seen widespread adoption among the wider engineering discipline. There is a common perception that NURBS are slow to evaluate and complex to implement. Whereas computer-aided design commonly deals with surfaces, the engineering community must deal with materials that have thickness. Traditional visualization techniques have avoided NURBS, and there has been little cross-talk between the rich spline approximation community and the larger engineering field. Recently there has been a strong desire to marry the modeling and analysis phases of the iterative design cycle, be it in car design, turbulent flow simulation around an airfoil, or lighting design. Research has demonstrated that employing a single representation throughout the cycle has key advantages. Furthermore, novel manufacturing techniques employing heterogeneous materials require the introduction of volumetric modeling representations. There is little question that fields such as scientific visualization and mechanical engineering could benefit from the powerful approximation properties of splines. In this dissertation, we remove several hurdles to the application of NURBS to problems in engineering and demonstrate how their unique properties can be leveraged to solve problems of interest

Efficient view point selection for silhouettes of convex polyhedra

AbstractSilhouettes of polyhedra are an important primitive in application areas such as machine vision and computer graphics. In this paper, we study how to select view points of convex polyhedra such that the silhouette satisfies certain properties. Specifically, we give algorithms to find all projections of a convex polyhedron such that a given set of edges, faces and/or vertices appear on the silhouette.We present an algorithm to solve this problem in O(k2) time for k edges. For orthogonal projections, we give an improved algorithm that is fully adaptive in the number l of connected components formed by the edges, and has a time complexity of O(klogk+kl). We then generalize this algorithm to edges and/or faces appearing on the silhouette

Conservative From-Point Visibility.

Visibility determination has been an important part of the computer graphics research for several decades. First studies of the visibility were hidden line removal algorithms, and later hidden surface removal algorithms. Today’s visibility determination is mainly concentrated on conservative, object level visibility determination techniques. Conservative methods are used to accelerate the rendering process when some exact visibility determination algorithm is present. The Z-buffer is a typical exact visibility determination algorithm. The Z-buffer algorithm is implemented in practically every modern graphics chip. This thesis concentrates on a subset of conservative visibility determination techniques. These techniques are sometimes called from-point visibility algorithms. They attempt to estimate a set of visible objects as seen from the current viewpoint. These techniques are typically used with real-time graphics applications such as games and virtual environments. Concentration is on the view frustum culling and occlusion culling. View frustum culling discards objects that are outside of the viewable volume. Occlusion culling algorithms try to identify objects that are not visible because they are behind some other objects. Also spatial data structures behind the efficient implementations of view frustum culling and occlusion culling are reviewed. Spatial data structure techniques like maintaining of dynamic scenes and exploiting spatial and temporal coherences are reviewed.1. Introduction.............................................................................................................1 2. Visibility Problem...................................................................................................3 3. Scene Organization...............................................................................................10 3.1. Bounding Volume Hierarchies and Scene Graphs.................................10 3.2. Spatial Data Structures ...............................................................................13 3.3. Regular Grids...............................................................................................14 3.4. Quadtrees and Octrees ...............................................................................15 3.5. KD-Trees.......................................................................................................20 3.6. BSP-Trees......................................................................................................23 3.7. Exploiting Spatial and Temporal Coherence ..........................................27 3.8. Dynamic Scenes...........................................................................................30 3.9. Summary ......................................................................................................34 4. View Frustum Culling .........................................................................................35 4.1. View Frustum Construction ......................................................................36 4.2. View Frustum Test......................................................................................37 4.3. Hierarchical View Frustum Culling .........................................................41 4.4. Optimizations ..............................................................................................42 4.5. Summary ......................................................................................................44 5. Occlusion Culling .................................................................................................45 5.1. Fundamental Concepts...............................................................................45 5.2. Occluder Selection.......................................................................................46 5.3. Hardware Occlusion Queries....................................................................49 5.4. Object-Space Methods ................................................................................50 5.5. Image-Space Methods ................................................................................55 5.6. Summary ......................................................................................................64 6. Conclusion.............................................................................................................66 References .................................................................................................................... 7

Minkowski Sum Construction and other Applications of Arrangements of Geodesic Arcs on the Sphere

We present two exact implementations of efficient output-sensitive algorithms that compute Minkowski sums of two convex polyhedra in 3D. We do not assume general position. Namely, we handle degenerate input, and produce exact results. We provide a tight bound on the exact maximum complexity of Minkowski sums of polytopes in 3D in terms of the number of facets of the summand polytopes. The algorithms employ variants of a data structure that represents arrangements embedded on two-dimensional parametric surfaces in 3D, and they make use of many operations applied to arrangements in these representations. We have developed software components that support the arrangement data-structure variants and the operations applied to them. These software components are generic, as they can be instantiated with any number type. However, our algorithms require only (exact) rational arithmetic. These software components together with exact rational-arithmetic enable a robust, efficient, and elegant implementation of the Minkowski-sum constructions and the related applications. These software components are provided through a package of the Computational Geometry Algorithm Library (CGAL) called Arrangement_on_surface_2. We also present exact implementations of other applications that exploit arrangements of arcs of great circles embedded on the sphere. We use them as basic blocks in an exact implementation of an efficient algorithm that partitions an assembly of polyhedra in 3D with two hands using infinite translations. This application distinctly shows the importance of exact computation, as imprecise computation might result with dismissal of valid partitioning-motions.Comment: A Ph.D. thesis carried out at the Tel-Aviv university. 134 pages long. The advisor was Prof. Dan Halperi

Efficient acquisition, representation and rendering of light fields

In this thesis we discuss the representation of three-dimensional scenes using image data (image-based rendering), and more precisely the so-called light field approach. We start with an up-to-date survey on previous work in this young field of research. Then we propose a light field representation based on image data and additional per-pixel depth values. This enables us to reconstruct arbitrary views of the scene in an efficient way and with high quality. Furtermore, we can use the same representation to determine optimal reference views during the acquisition of a light field. We further present the so-called free form parameterization, which allows for a relatively free placement of reference views. Finally, we demonstrate a prototype of the Lumi-Shelf system, which acquires, transmits, and renders the light field of a dynamic scene at multiple frames per second.Diese Doktorarbeit beschäftigt sich mit der Repräsentierung dreidimensionaler Szenen durch Bilddaten (engl. image-based rendering, deutsch bildbasierte Bildsynthese), speziell mit dem Ansatz des sog. Lichtfelds. Nach einem aktuellen Überblick über bisherige Arbeiten in diesem jungen Forschungsgebiet stellen wir eine Datenrepräsentation vor, die auf Bilddaten mit zusätzlichen Tiefenwerten basiert. Damit sind wir in der Lage, beliebige Ansichten der Szene effizient und in hoher Qualität zu rekonstruieren sowie die optimalen Referenz-Ansichten bei der Akquisition eines Lichtfelds zu bestimmen. Weiterhin präsentieren wir die sog. Freiform-Parametrisierung, die eine relativ freie Anordnung der Referenz-Ansichten erlaubt. Abschließend demonstrieren wir einen Prototyp des Lumishelf-Systems, welches die Aufnahme, Übertragung und Darstellung des Lichtfeldes einer dynamischen Szene mit mehreren Bildern pro Sekunde ermöglicht