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Volume Rendering
, 1988
"... 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 ..."
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Cited by 379 (2 self)
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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.
Piecewise Linear Hypersurfaces using the Marching Cubes Algorithm
, 1999
"... 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 d ..."
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Cited by 5 (0 self)
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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 nondegenerate object of that dimension and are named simplices. In four dimensions a simplex is represented by a tetrahedron, which is also known as a 3simplex. Thus, a continuous n dimensional surface may be represented by a lattice of connected n1 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 localcell tiling method may be usefullyap...
Converting Discrete Images to Partitioning Trees
 IEEE Transactions on Visualization and Computer Graphics
, 1997
"... 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 ..."
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Cited by 4 (1 self)
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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...
Fractalbased description
 Proc. Jnr. Joitu Conf. AH. Inrell
, 1983
"... 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 s ..."
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Cited by 1 (0 self)
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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 3D 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 3D information from the image data, and the computation of a 3D fractalbased representation from actual image data has been demonstrated using an image of a mountain. This example shows the potential of a fractalbased representation for efficiently computing good 3D representations of natural shapes, including such seeminglydifficult cases as mountains, clumps of leaves and clouds. I
Stochastic Microgeometry for Displacement Mapping
"... Creating surfaces with intricate smallscale 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 geometr ..."
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Cited by 1 (1 self)
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Creating surfaces with intricate smallscale 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.
The Flipping Cube: A Device for Rotating 3D Rasters
, 1991
"... Driven by the prospect of threedimensional rasters as a primary vehicle for future 3D graphics and volumetric imaging, this paper introduces an architecture for realtime rendering of highresolution volumetric images. The Flipping Cube Architecture utilizes parallel memory organization and a uniqu ..."
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Cited by 1 (0 self)
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Driven by the prospect of threedimensional rasters as a primary vehicle for future 3D graphics and volumetric imaging, this paper introduces an architecture for realtime rendering of highresolution 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 diskspace 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 displaylist and managed by the c...
Generating Surface Geometry in Higher Dimensions using Local Cell Tilers
, 1998
"... 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 s ..."
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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 ndimensional cubes, via for example the Marching Cubes Algorithm. These algorithms are often named local cell tilers. We propose that the localcell tiling method can be usefullyapplied to four dimensions and potentially to Ndimensions. 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 subcase which simplifies their representations. Each subcase 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
Gameenabling the 3DMandelbulb Fractal by adding Velocityinduced Support Vectors
"... Fractals provide an innovative method for generating 3D images of realworld 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, ..."
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Fractals provide an innovative method for generating 3D images of realworld 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 coauthored by us in 2011 explained a method of realizing a „true ‟ 3D simulation of the Mandelbrot set and the rendering of the same onto 3dimensional space. This paper takes a step further in using this variant of the Mandelbulb as input and outlines a method of the gameenabling of the same Mandelbulb by using directionoriented vectors that are analogous in function to that of Support Vectors in the Support Vector Graphics (SVG) domain. A realworld application of the same can translate to examples of understanding an entire coastline set to motion in space by adding 3Danimation enabled elevation to the corresponding fractal image.