Computing the visibility map of fat objects

AbstractWe give an output-sensitive algorithm for computing the visibility map of a set of n constant-complexity convex fat polyhedra or curved objects in 3-space. Our algorithm runs in O((n+k) polylog n) time, where k is the combinatorial complexity of the visibility map. This is the first algorithm for computing the visibility map of fat objects that does not require a depth order on the objects and is faster than the best known algorithm for general objects. It is also the first output-sensitive algorithm for curved objects that does not require a depth order

View space linking, solid node compression and binary space partitioning for visibility determination in 3D walk-throughs

Today\u27s 3D games consumers are expecting more and more quality in their games. To enable high quality graphics at interactive rates, games programmers employ a technique known as hidden surface removal (HSR) or polygon culling. HSR is not just applicable to games; it may also be applied to any application that requires quality and interactive rates, including medical, military and building applications. One such commonly used technique for HSR is the binary space partition (BSP) tree, which is used for 3D ‘walk-throughs’, otherwise known as 3D static environments or first person shooters. Recent developments in 3D accelerated hardware technology do not mean that HSR is becoming redundant; in fact, HSR is increasingly becoming more important to the graphics pipeline. The well established potentially visible sets (PSV) BSP tree algorithm is used as a platform for exploring three enhanced algorithms; View Space Lighting, Solid Node Compression and hardware accelerated occlusion are shown to reducing the amounts of nodes that are traversed in a BSP tree, improving tree travel efficiency. These algorithms are proven (in cases) to improve overall efficiency

Algorithms for fat objects : decompositions and applications

Computational geometry is the branch of theoretical computer science that deals with algorithms and data structures for geometric objects. The most basic geometric objects include points, lines, polygons, and polyhedra. Computational geometry has applications in many areas of computer science, including computer graphics, robotics, and geographic information systems. In many computational-geometry problems, the theoretical worst case is achieved by input that is in some way "unrealistic". This causes situations where the theoretical running time is not a good predictor of the running time in practice. In addition, algorithms must also be designed with the worst-case examples in mind, which causes them to be needlessly complicated. In recent years, realistic input models have been proposed in an attempt to deal with this problem. The usual form such solutions take is to limit some geometric property of the input to a constant. We examine a specific realistic input model in this thesis: the model where objects are restricted to be fat. Intuitively, objects that are more like a ball are more fat, and objects that are more like a long pole are less fat. We look at fat objects in the context of five different problems—two related to decompositions of input objects and three problems suggested by computer graphics. Decompositions of geometric objects are important because they are often used as a preliminary step in other algorithms, since many algorithms can only handle geometric objects that are convex and preferably of low complexity. The two main issues in developing decomposition algorithms are to keep the number of pieces produced by the decomposition small and to compute the decomposition quickly. The main question we address is the following: is it possible to obtain better decompositions for fat objects than for general objects, and/or is it possible to obtain decompositions quickly? These questions are also interesting because most research into fat objects has concerned objects that are convex. We begin by triangulating fat polygons. The problem of triangulating polygons—that is, partitioning them into triangles without adding any vertices—has been solved already, but the only linear-time algorithm is so complicated that it has never been implemented. We propose two algorithms for triangulating fat polygons in linear time that are much simpler. They make use of the observation that a small set of guards placed at points inside a (certain type of) fat polygon is sufficient to see the boundary of such a polygon. We then look at decompositions of fat polyhedra in three dimensions. We show that polyhedra can be decomposed into a linear number of convex pieces if certain fatness restrictions aremet. We also show that if these restrictions are notmet, a quadratic number of pieces may be needed. We also show that if we wish the output to be fat and convex, the restrictions must be much tighter. We then study three computational-geometry problems inspired by computer graphics. First, we study ray-shooting amidst fat objects from two perspectives. This is the problem of preprocessing data into a data structure that can answer which object is first hit by a query ray in a given direction from a given point. We present a new data structure for answering vertical ray-shooting queries—that is, queries where the ray’s direction is fixed—as well as a data structure for answering ray-shooting queries for rays with arbitrary direction. Both structures improve the best known results on these problems. Another problem that is studied in the field of computer graphics is the depth-order problem. We study it in the context of computational geometry. This is the problem of finding an ordering of the objects in the scene from "top" to "bottom", where one object is above the other if they share a point in the projection to the xy-plane and the first object has a higher z-value at that point. We give an algorithm for finding the depth order of a group of fat objects and an algorithm for verifying if a depth order of a group of fat objects is correct. The latter algorithm is useful because the former can return an incorrect order if the objects do not have a depth order (this can happen if the above/below relationship has a cycle in it). The first algorithm improves on the results previously known for fat objects; the second is the first algorithm for verifying depth orders of fat objects. The final problem that we study is the hidden-surface removal problem. In this problem, we wish to find and report the visible portions of a scene from a given viewpoint—this is called the visibility map. The main difficulty in this problem is to find an algorithm whose running time depends in part on the complexity of the output. For example, if all but one of the objects in the input scene are hidden behind one large object, then our algorithm should have a faster running time than if all of the objects are visible and have borders that overlap. We give such an algorithm that improves on the running time of previous algorithms for fat objects. Furthermore, our algorithm is able to handle curved objects and situations where the objects do not have a depth order—two features missing from most other algorithms that perform hidden surface removal

Parallel implementation of a virtual reality system on a transputer architecture

A Virtual Reality is a computer model of an environment, actual or imagined, presented to a user in as realistic a fashion as possible. Stereo goggles may be used to provide the user with a view of the modelled environment from within the environment, while a data-glove is used to interact with the environment. To simulate reality on a computer, the machine has to produce realistic images rapidly. Such a requirement usually necessitates expensive equipment. This thesis presents an implementation of a virtual reality system on a transputer architecture. The system is general, and is intended to provide support for the development of various virtual environments. The three main components of the system are the output device drivers, the input device drivers, and the virtual world kernel. This last component is responsible for the simulation of the virtual world. The rendering system is described in detail. Various methods for implementing the components of the graphics pipeline are discussed. These are then generalised to make use of the facilities provided by the transputer processor for parallel processing. A number of different decomposition techniques are implemented and compared. The emphasis in this section is on the speed at which the world can be rendered, and the interaction latency involved. In the best case, where almost linear speedup is obtained, a world containing over 250 polygons is rendered at 32 frames/second. The bandwidth of the transputer links is the major factor limiting speedup. A description is given of an input device driver which makes use of a powerglove. Techniques for overcoming the limitations of this device, and for interacting with the virtual world, are discussed. The virtual world kernel is designed to make extensive use of the parallel processing facilities provided by transputers. It is capable of providing support for mUltiple worlds concurrently, and for multiple users interacting with these worlds. Two applications are described that were successfully implemented using this system. The design of the system is compared with other recently developed virtual reality systems. Features that are common or advantageous in each of the systems are discussed. The system described in this thesis compares favourably, particularly in its use of parallel processors.KMBT_22

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

Constructing Binary Space Partitions for Orthogonal Rectangles in Practice

The original publication is available at www.springerlink.comIn this paper, we develop a simple technique for constructing a I3inary Space Partition (nSP) for a set of orthogonal rectangles in IR3. OUf algorithm has the novel feature that it tunes its performance to the geometric properties of the rectangles, e.g., their aspect ratios. "Fe have implemented our algorithm and tested its performance on real data scti). V\.Tc have also systematically compared the performance of our algorithm with that of other techniques presented in the literature. Our studies show that our algorithm constructs nsps of near-linear size and small height in practice, has fast running times, and answers queries efficiently. It is a method of choice for constructing BSPs for orthogonal rectangles

Overview of database projects

The use of entity and object oriented data modeling techniques for managing Computer Aided Design (CAD) is explored

Reduced-Order Equivalent-Circuit Models Of Thermal Systems Including Thermal Radiation

We established a general, automatic, and versatile procedure to derive an equivalent circuit for a thermal system using temperature data obtained from FE simulations. The EC topology was deduced from the FE mesh using a robust and general graph-partitioning algorithm. The method was shown to yield models that are independent of the boundary conditions for complicated 3D thermal systems such as an electronic chip. The results are strongly correlated with the geometry, and the EC can be extended to yield variable medium-order models. Moreover, a variety of heat sources and boundary conditions can be accommodated, and the EC models are inherently modular. A reliable method to compute thermal resistors connecting different regions was developed. It appropriately averages several estimates of a thermal resistance where each estimate is obtained using data obtained under different boundary or heating conditions. The concept of fictitious heat sources was used to increase the number of simulation datasets. The method was shown to yield models that are independent of the BCs for complicated 2-D thermal systems such as a 2D cavity. A reliable method to compute thermal resistors connecting different regions was developed. In general, the number of regions required for getting an accurate reduced-order model depends on the complexity of the system to be modeled. We have extended the reduced-order modeling procedure to include a view-factor based thermal radiation heat transfer model by including voltage controlled current sources in the equivalent circuit