In this paper we present a comprehensive flythrough system which

An octree is a well known hierarchical spatial structure which is widely used in Computer Graphics algorithms. One of the most frequent operations is the computation of the octree voxels intersected by a straight line. This has a number of applications, such as ray-object intersection tests speed-up and visualisation of hierarchical density models by ray-casting. Several methods have been proposed to achieve this goal, which differ in the order in which intersected voxels are visited. In this paper we introduce a new top-down parametric method. The main difference with previously proposed methods is related to descent movements, that is, the selection of a child sub-voxel from the current one. This selection, as the algorithm, is based on the parameter of the ray and comprises simple comparisons. The resulting algorithm is easy to implement, and efficient when compared to other related top-down and bottom-up algorithms for octrees. Finally, a comparison with Kelvin's method for binary trees is presented. Keywords: Octree, Binary tree, Ray Tracing, Acceleration Techniques 1

We present an efficient method to automatically compute a smooth approximation of large functional scattered data sets given over arbitrarily shaped planar domains. Our approach is based on the construction of a ¢¤ £-continuous bivariate cubic spline and our method offers optimal approximation order. Both local variation and nonuniform distribution of the data are taken into account by using local polynomial least squares approximations of varying degree. Since we only need to solve small linear systems and no triangulation of the scattered data points is required, the overall complexity of the algorithm is linear in the total number of points. Numerical examples dealing with several real world scattered data sets with up to millions of points demonstrate the efficiency of our method. The resulting spline surface is of high visual quality and can be efficiently evaluated for rendering and modeling. In our implementation we achieve real-time frame rates for typical fly-through sequences and interactive frame rates for recomputing and rendering a locally modified spline surface. CR Categories: G.1.2 [Numerical Analysis]: Approximation— approximation of surfaces, least squares approximation, spline and piecewise polynomial approximation; I.3.3 [Computer Graphics]: Picture/Image Generation—display algorithms, viewing algorithms; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—surface representation, splines; E.4 [Coding

The problem of detecting the visible and hidden areas of a topographic surface from a given viewpoint is well known, and has applications in GIS and other fields. The computational geometry literature is rich with solutions based on a polygonal representation of the surface. This work confronts the problem by working directly on the Digital Elevation Map which represents the terrain surface. We present an algorithm that processes discrete lines of sight from the viewpoint to the surface perimeter, and tests the unit-sized terrain elements along the discrete cross-sections defined by these lines. The algorithm is very efficient, performing O(n) testing operations, consisting of a few additions and no more than one multiplication each, where n is the number of the terrain elements in the map.

Ray casting may be applied to the terrain rendering from DTMs (Digital Terrain Models). In this paper we propose a ray casting method which exploits exact vertical ray coherence. This method not only achieves a good performance, but also allows any set of viewing parameters. To analyze vertical ray coherence property, we define the terms: a ray plane which is perpendicular to the sea-level plane and passes through the COP (center of projection); and the corresponding ray line which is the line of intersection of the ray plane and the projection plane. Vertical ray coherence can be stated as: if two rays pass through the same ray line, they pass over the identical set of points on the DTM base plane. After a ray is cast on the DTM, we can get a good starting point to cast another ray using this property. Our method tries to cover the projection plane with ray lines. Since ray lines are not parallel to each other, it is a difficult task to cover the entire plane. In fact all ray lines in...

This paper is a survey of volume visualization, volume graphics, and volume rendering techniques. It focuses specifically on the use of the voxel representation and volumetric techniques for geometric applications. 1. Introduction Volume data are 3D entities that may have information inside them, might not consist of surfaces and edges, or might be too voluminous to be represented geometrically . Volume visualization is a method of extracting meaningful information from volumetric data using interactive graphics and imaging, and it is concerned with volume data representation, modeling, manipulation, and rendering [49]. Volume data are obtained by sampling, simulation, or modeling techniques. For example, a sequence of 2D slices obtained from Magnetic Resonance Imaging (MRI) or Computed Tomography (CT) is 3D reconstructed into a volume model and visualized for diagnostic purposes or for planning of treatment or surgery. The same technology is often used with industrial CT for non-des...

This dissertation gives accurate and efficient methods for the object-order rendering of discrete objects. Discrete objects are typically represented with a volume raster and rendered with a volume rendering algorithm. However, current object-order volume rendering algorithms suffer from several problems. First, they require that the volume raster be traversed in a strict visibility order, but existing visibility ordering methods do not always correctly order perspective projections of volume rasters. Second, both perspective and orthographic renderings of volume rasters can contain aliasing artifacts, but current object-order techniques have no method for addressing these artifacts. Third, computergenerated animations suffer from temporal aliasing artifacts, which can be addressed by adding motion blur. But currently the only motion-blur method for object-order techniques is super-sampling, which is very expensive. This

We present algorithms for rendering realistic images of large terrains and their implementation on a parallel computer for rapid production of terrain animation sequences. By "large" terrains, we mean the use of datasets too large to be contained in RAM, a fact which significantly influences the design of rendering algorithms, and has not been addressed in most other works on this subject. To achieve a good speed without quality degradation, we use a hybrid ray-casting and projection technique, incorporating quadtree subdivision techniques and filter using precomputed bit masks. Hilbert space-filling curves determine the image pixel rendering order, fully exploiting spatial coherence. A parallel version of the algorithm is presented, based on an architecture implemented on a Meiko parallel computer. The architecture is designed to relieve dataflow bottlenecks caused by slow interprocessor communications, and exploit temporal image coherence. Using our parallel system, incorporating 26 processors, we are able to generate a full color terrain image at video resolution, without noticable aliasing artifacts, every 2 seconds, including I/O and communication overheads. The speedup of the system is linear with the number of processors.

Interactive tridimensional visualization of terrain models can be found in Geographical Information Systems and computer games. Both applications share the need for high performance algorithms that are tailored to produce textured images in interactive time, say at least 5 frames per second. In this paper we propose and analyze the extension of a well known ray casting algorithm to the case where the view plane is not vertical. Three efficient algorithms are presented and compared. Experimental results are shown and conclusions are made.

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