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Adaptive Tesselation of Subdivision Surfaces
, 2003
"... For a variety of reasons subdivision surfaces have developed into a prominent member of the family of freeform shapes. Based on a standard polygonal mesh a modeller can build various kinds of shapes using an arbitrary topology and special geometrical features like creases. However, the interactive d ..."
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Cited by 3 (0 self)
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display of subdivision surfaces in current scenegraph systems based on static levels of detail is unpractical, because of the exponentially increasing number of polygons during the subdivision steps. Therefore, an adaptive algorithm choosing only the necessary quads and triangles is required to obtain
Adaptive Tesselation of Subdivision Surfaces in OpenSG Abstract
"... For a variety of reasons subdivision surfaces have developed into a prominent member of the family of freeform shapes. Based on a standard polygonal mesh modeller can build various kinds of shapes using an arbitrary topology and special geometrical features like creases. However, the interactive dis ..."
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display of subdivision surfaces in current scenegraph systems based on static levels of detail is unpractical, because of the exponentially increasing number of polygons during the subdivision steps. Therefore, an adaptive algorithm choosing only the necessary quads and triangles is required to obtain
Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrams
 ACM Tmns. Graph
, 1985
"... The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms ar ..."
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Cited by 543 (11 self)
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The following problem is discussed: Given n points in the plane (the sites) and an arbitrary query point 4, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the given sites and then locating the query point in one of its regions. Two algorithms are given, one that constructs the Voronoi diagram in O(n log n) time, and another that inserts a new site in O(n) time. Both are based on the use of the Voronoi dual, or Delaunay triangulation, and are simple enough to be of practical value. The simplicity of both algorithms can be attributed to the separation of the geometrical and topological aspects of the problem and to the use of two simple but powerful primitives, a geometric predicate and an operator for manipulating the topology of the diagram. The topology is represented by a new data structure for generalized diagrams, that is, embeddings of graphs in twodimensional manifolds. This structure represents simultaneously an embedding, its dual, and its mirror image. Furthermore, just two operators are sufficient for building and modifying arbitrary diagrams.
ReTiling Polygonal Surfaces
 Computer Graphics
, 1992
"... This paper presents an automatic method of creating surface models at several levels of detail from an original polygonal description of a given object. Representing models at various levels of detail is important for achieving high frame rates in interactive graphics applications and also for speed ..."
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Cited by 448 (3 self)
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curvature and 3) a method of smoothly interpolating between models that represent the same object at different levels of detail. The key notion in the retiling procedure is the creation of an intermediate model called the mutual tessellation of a surface that contains both the vertices from the original
The Lifting Scheme: A Construction Of Second Generation Wavelets
, 1997
"... . We present the lifting scheme, a simple construction of second generation wavelets, wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads to ..."
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Cited by 541 (16 self)
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. We present the lifting scheme, a simple construction of second generation wavelets, wavelets that are not necessarily translates and dilates of one fixed function. Such wavelets can be adapted to intervals, domains, surfaces, weights, and irregular samples. We show how the lifting scheme leads
Footprint evaluation for volume rendering
 Computer Graphics
, 1990
"... This paper presents a forward mapping rendering algorithm to display regular volumetric grids that may not have the same spacings in the three grid directions. It takes advantage of the fact that convolution can be thought of as distributing energy from input samples into space. The renderer calcul ..."
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Cited by 504 (1 self)
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calculates an image plane footprint for each data sample and uses the footprint to spread the sample's energy onto the image plane. A result of the technique is that the forward mapping algorithm can support perspective without excessive cost, and support adaptive resampling of the three
A Survey of Medical Image Registration
, 1998
"... The purpose of this chapter is to present a survey of recent publications concerning medical image registration techniques. These publications will be classified according to a model based on nine salient criteria, the main dichotomy of which is extrinsic versus intrinsic methods The statistics of t ..."
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Cited by 540 (5 self)
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of the classification show definite trends in the evolving registration techniques, which will be discussed. At this moment, the bulk of interesting intrinsic methods is either based on segmented points or surfaces, or on techniques endeavoring to use the full information content of the images involved. Keywords
Implicit Fairing of Irregular Meshes using Diffusion and Curvature Flow
, 1999
"... In this paper, we develop methods to rapidly remove rough features from irregularly triangulated data intended to portray a smooth surface. The main task is to remove undesirable noise and uneven edges while retaining desirable geometric features. The problem arises mainly when creating highfidelit ..."
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Cited by 553 (24 self)
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In this paper, we develop methods to rapidly remove rough features from irregularly triangulated data intended to portray a smooth surface. The main task is to remove undesirable noise and uneven edges while retaining desirable geometric features. The problem arises mainly when creating high
Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
 Biometrika
, 1995
"... Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model determi ..."
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Cited by 1330 (24 self)
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Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model determination, where the dimensionality of the parameter vector is typically not xed. This article proposes a new framework for the construction of reversible Markov chain samplers that jump between parameter subspaces of di ering dimensionality, which is exible and entirely constructive. It should therefore have wide applicability in model determination problems. The methodology is illustrated with applications to multiple changepoint analysis in one and two dimensions, and toaBayesian comparison of binomial experiments.
The Lumigraph
 In Proceedings of SIGGRAPH 96
, 1996
"... This paper discusses a new method for capturing the complete appearanceof both synthetic and real world objects and scenes, representing this information, and then using this representation to render images of the object from new camera positions. Unlike the shape capture process traditionally used ..."
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Cited by 1034 (43 self)
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This paper discusses a new method for capturing the complete appearanceof both synthetic and real world objects and scenes, representing this information, and then using this representation to render images of the object from new camera positions. Unlike the shape capture process traditionally used in computer vision and the rendering process traditionally used in computer graphics, our approach does not rely on geometric representations. Instead we sample and reconstruct a 4D function, which we call a Lumigraph. The Lumigraph is a subset of the complete plenoptic function that describes the flow of light at all positions in all directions. With the Lumigraph, new images of the object can be generated very quickly, independent of the geometric or illumination complexity of the scene or object. The paper discusses a complete working system including the capture of samples, the construction of the Lumigraph, and the subsequent rendering of images from this new representation. 1
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