A technique for rendering images Of volumes containing mixtures of materials is presented. The shading model allows both the interior of a material and the boundary between materials to be colored. Image projection is performed by simulating the absorption of light along the ray path to the eye. The algorithms used are designed to avoid artifacts caused by aliasing and quantization and can be efficiently implemented on an image computer. Images from a variety of applications are shown.

ix Acknowledgements x Acknowledgements : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : x Publication History : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : x 1. Introduction 1 1.1 Introduction to Direct Volume Rendering : : : : : : : : : : : : : : : : : : : 2 1.1.1 Volumetric Grids : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 3 1.1.2 Image-space Rendering Algorithms : : : : : : : : : : : : : : : : : : : 4 1.1.3 Object-space Rendering Algorithms : : : : : : : : : : : : : : : : : : 5 1.1.4 Shear Transformations : : : : : : : : : : : : : : : : : : : : : : : : : : 7 1.1.5 Complexity : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 1.2 Motivation for Parallel Direct Volume Rendering : : : : : : : : : : : : : : : 8 1.2.1 Scalability Is Important : : : : : : : : : : : : : : : : : : : : : : : : : 8 1.3 Context for Use : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 9 1.3.1 Distributed Graphical Us...

The discrete space representation of most scientific datasets (pixels, voxels, etc.), generated through instruments or by sampling continuously defined fields, while being simple, is also verbose and structureless. We propose the use of a particular spatial structure, the binary space partitioning tree, or, simply, partitioning tree, as a new representation to perform efficient geometric computation in discretely defined domains. The ease of performing affine transformations, set operations between objects, and correct implementation of transparency (exploiting the visibility ordering inherent to the representation) makes the partitioning tree a good candidate for probing and analyzing medical reconstructions, in such applications as surgery planning and prostheses design. The multiresolution characteristics of the representation can be exploited to perform such operations at interactive rates by smooth variation of the amount of geometry. Application to ultrasound data segmenta...

Surface visualization is very important within scientic visualization. The surfaces depict a value of equal density (an isosurface) or display the surrounds of specied objects within the data. Likewise, in two dimensions contour plots may be used to display the information. Thus similarly, in four dimensions hypersurfaces may be formed around hyperobjects. These surfaces (or contours) are often formed from a set of connected triangles (or lines). These piecewise segments represent the simplest non-degenerate object of that dimension and are named simplices. In four dimensions a simplex is represented by a tetrahedron, which is also known as a 3-simplex. Thus, a continuous n dimensional surface may be represented by a lattice of connected n-1 dimensional simplices. This lattice of connected simplices may be calculated over a set of adjacent n dimensional cubes, via for example the Marching Cubes Algorithm. We propose that the methods of this local-cell tiling method may be usefully-ap...

This paper addresses the problems of (1) representing natural shapes such as mountains, trees and clouds, and (2) computing such a description from image data. In order to solve these problems we must be able to relate natural surfaces to their images; this requires a good model of natural surface shapes. Fractal functions are good a choice for modeling natural surfaces because (1) many physical processes produce a fractal surface shape, (2) fractals are widely used as a graphics tool for generating naturallooking shapes, and (3) a survey of natural imagery has shown that the 3-D fractal surface model, transformed by the image formation process, furnishes an accurate description of both textured and shaded image regions. This characterization of image regions has been shown to be stable over transformations of scale and linear transforms of intensity. Much work has been accomplished that is relevant to computing 3-D information from the image data, and the computation of a 3-D fractal-based representation from actual image data has been demonstrated using an image of a mountain. This example shows the potential of a fractal-based representation for efficiently computing good 3-D representations of natural shapes, including such seemingly-difficult cases as mountains, clumps of leaves and clouds. I

Creating surfaces with intricate small-scale features (microgeometry) and detail is an important task in geometric modeling and computer graphics. We present a model processing method capable of producing a wide variety of complex surface features based on displacement mapping and stochastic geometry. The latter is a branch of mathematics that analyzes and characterizes the statistical properties of spatial structures. The technique has been incorporated into an interactive modeling environment that supports the design of stochastic microgeometries. Additionally a tool has been developed that provides random exploration of the technique’s entire parameter space by generating sample microgeometry over a broad range of values. We demonstrate the effectiveness of our technique by creating diverse, complex surface structures for a variety of geometric models, e.g. arrowheads, candy bars, busts, planets and coral. 1.

Driven by the prospect of three-dimensional rasters as a primary vehicle for future 3D graphics and volumetric imaging, this paper introduces an architecture for real-time rendering of high-resolution volumetric images. The Flipping Cube Architecture utilizes parallel memory organization and a unique data orientation scheme in order to support contention free access to viewing rays. 1.1 Introduction The swift advances in performance, availability and price of computing power, memory, and disk-space are transforming long thought techniques into reality. One typical example to this trend is the revolution taking place in the field of volume graphics. Grasping the feeling of this revolution requires no more than three decades of perspective. The display of computer graphics in the sixties was based on vector drawing devices and an 'object based' approach to scene representation and rendering. A symbolic representation of the scene objects was stored in a display-list and managed by the c...

In two dimensions contour elements surround two dimensional objects, in three dimensions surfaces surround three dimensional objects and in four dimensions hypersurfaces surround hyperobjects. These surfaces can be represented by a collection of connected simplices, hence, continuous n dimensional surfaces can be represented by a lattice of connected n \Gamma 1 dimensional simplices. The lattice of connected simplices can be calculated over a set of adjacent n-dimensional cubes, via for example the Marching Cubes Algorithm. These algorithms are often named local cell tilers. We propose that the local-cell tiling method can be usefully-applied to four dimensions and potentially to N-dimensions. We present an algorithm for the generation of major cases (cases that are topologically invariant under standard geometrical transformations) and introduce the notion of a sub-case which simplifies their representations. Each sub-case can be easily subdivided into simplices for rendering and we describe a backtracking tetrahedronization algorithm for the four dimensional case. An implementation for surfaces from the fourth dimension is presented and we describe and discuss ambiguities inherent within this and related algorithms. 1

Fractals provide an innovative method for generating 3D images of real-world objects by using computational modelling algorithms based on the imperatives of selfsimilarity, scale invariance, and dimensionality. Of the many different types of fractals that have come into limelight since their origin, the family of Mandelbrot Set fractals has eluded both mathematicians and computer scientists alike. And the „true ‟ 3D realization of the Mandelbrot set has been a challenging centre piece of research with its limits extending only to that of the sky. An earlier paper co-authored by us in 2011 explained a method of realizing a „true ‟ 3D simulation of the Mandelbrot set and the rendering of the same onto 3-dimensional space. This paper takes a step further in using this variant of the Mandelbulb as input and outlines a method of the game-enabling of the same Mandelbulb by using direction-oriented vectors that are analogous in function to that of Support Vectors in the Support Vector Graphics (SVG) domain. A real-world application of the same can translate to examples of understanding an entire coast-line set to motion in space by adding 3D-animation enabled elevation to the corresponding fractal image.