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36
Convolution Surfaces
, 1991
"... Smoothly blended articulated models are often difficult to construct using current techniques. Our solution in this paper is to extend the surfaces introduced by Blinn [Blinn 1982] by using threedimensional convolution with skeletons composed of polygons or curves. The resulting convolution surfaces ..."
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Cited by 114 (0 self)
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Smoothly blended articulated models are often difficult to construct using current techniques. Our solution in this paper is to extend the surfaces introduced by Blinn [Blinn 1982] by using threedimensional convolution with skeletons composed of polygons or curves. The resulting convolution surfaces permit fluid topology changes, seamless part joins, and efficient implementation.
Efficient Collision Detection for Animation and Robotics
, 1993
"... We present efficient algorithms for collision detection and contact determination between geometric models, described by linear or curved boundaries, undergoing rigid motion. The heart of our collision detection algorithm is a simple and fast incremental method to compute the distance between two ..."
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Cited by 108 (19 self)
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We present efficient algorithms for collision detection and contact determination between geometric models, described by linear or curved boundaries, undergoing rigid motion. The heart of our collision detection algorithm is a simple and fast incremental method to compute the distance between two convex polyhedra. It utilizes convexity to establish some local applicability criteria for verifying the closest features. A preprocessing procedure is used to subdivide each feature's neighboring features to a constant size and thus guarantee expected constant running time for each test. The expected constant time performance is an attribute from exploiting the geometric coherence and locality. Let n be the total number of features, the expected run time is between O( p n) and O(n) ...
An Evaluation of Implicit Surface Tilers
, 1993
"... In recent years, numerous techniques have been developed for the polygonization of implicit surfaces. This article reviews the principal algorithms and provides a framework for identifying their conceptual similarities as well as their practical differences. Particular attention is devoted to the mu ..."
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Cited by 84 (2 self)
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In recent years, numerous techniques have been developed for the polygonization of implicit surfaces. This article reviews the principal algorithms and provides a framework for identifying their conceptual similarities as well as their practical differences. Particular attention is devoted to the much discussed problem of topological ambiguity, with solutions analyzed according to their consistency and correctness. Included in this evaluation are implementation suggestions for various application requirements.
Regularised Marching Tetrahedra: Improved IsoSurface Extraction
 Computers and Graphics
, 1998
"... Marching cubes is a simple and popular method for extracting isosurfaces from implicit functions or discrete threedimensional (3D) data. However, it does not guarantee the surface to be topologically consistent with the data, and it creates triangulations which contain many triangles of poor aspe ..."
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Cited by 53 (7 self)
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Marching cubes is a simple and popular method for extracting isosurfaces from implicit functions or discrete threedimensional (3D) data. However, it does not guarantee the surface to be topologically consistent with the data, and it creates triangulations which contain many triangles of poor aspect ratio. Marching tetrahedra is a variation of marching cubes, which overcomes this topological problem. Improvement in triangle aspect ratio has generally been achieved by mesh simplification, a group of algorithms designed to reduce the large number of triangles. Vertex clustering is one of the simplest of these algorithms, but does not in general maintain the topology of the original mesh. We present a new algorithm, regularised marching tetrahedra, which combines marching tetrahedra and vertex clustering to generate isosurfaces which are topologically consistent with the data and contain a number of triangles appropriate to the sampling resolution (typically 70% fewer than marching tet...
Reconstruction of Topologically Correct and Adaptive Trilinear Isosurfaces
 Computers & Graphics
, 2000
"... The paper goal is to fit trilinear isosurfaces out of volume data, by adopting an adaptive mesh refinement approach and therefore supporting a higher accuracy with respect to standard MC solutions. In order to be correct, adaptive refinement must be applied to a topologically correct initial mesh p ..."
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Cited by 36 (0 self)
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The paper goal is to fit trilinear isosurfaces out of volume data, by adopting an adaptive mesh refinement approach and therefore supporting a higher accuracy with respect to standard MC solutions. In order to be correct, adaptive refinement must be applied to a topologically correct initial mesh patch. For this reason, we designed a new, Exhaustive Look Up Table (ELUT) which encodes multientry patterns for each ambiguous configuration. Following the solution proposed by Natarajan, for each ambiguous configuration we choose, at run time, the actual pattern by evaluating the corresponding set of saddle points. Once the corresponding starting patch has been read from the ELUT, it is adaptively refined to fulfill a userselected accuracy. Refinement is adaptive to ensure that the complexity of the fitted mesh will not become excessive. An evaluation of the results produced on some volume dataset is reported, both in terms of accuracy and complexity of the meshes obtained. Contact autho...
Adaptive Enumeration of Implicit Surfaces with Affine Arithmetic
 Computer Graphics Forum
, 1996
"... . We discuss adaptive enumeration and rendering methods for implicit surfaces, using octrees computed with affine arithmetic, a new tool for range analysis. Affine arithmetic is similar to standard interval arithmetic, but takes into account correlations between operands and subformulas, generally ..."
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Cited by 30 (15 self)
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. We discuss adaptive enumeration and rendering methods for implicit surfaces, using octrees computed with affine arithmetic, a new tool for range analysis. Affine arithmetic is similar to standard interval arithmetic, but takes into account correlations between operands and subformulas, generally providing much tighter bounds for the computed quantities. The resulting octrees are accordingly much smaller, and the rendering faster. We also describe applications of affine arithmetic to intersection and ray tracing of implicit surfaces. keywords: cellular models, interval analysis, rendering, implicit surfaces. 1 Introduction Implicit surfaces have recently become popular in computer graphics and solid modeling. In order to exploit existing hardware and algorithms, it is often necessary to approximate such surfaces by models with simpler geometry, such as polygonal meshes or voxel arrays. Let S be a surface defined implicitly by the equation h(x; y; z) = 0. A simple and general techn...
Simple and Efficient Polygonization of Implicit Surfaces
"... This paper describes a simple and efficient polygonization algorithm that gives a practical way to construct adapted piecewise linear representations of implicit surfaces. The method starts with a coarse uniform polygonal approximation of the surface and subdivides each polygon recursively according ..."
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Cited by 29 (2 self)
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This paper describes a simple and efficient polygonization algorithm that gives a practical way to construct adapted piecewise linear representations of implicit surfaces. The method starts with a coarse uniform polygonal approximation of the surface and subdivides each polygon recursively according to local curvature. In that way, the inherent complexity of the problem is tamed by separating structuring from sampling and reducing part of the full three dimensional search to two dimensions.
Interactive Visualization of Implicit Surfaces with Singularities
 In Proc. Implicit Surfaces '96
, 1997
"... This paper presents work on two methods for interactive visualization of implicit surfaces: physicallybased sampling using particle systems and polygonization followed by physicallybased mesh improvement which explicitly makes use of the surfacedefining equation. While most previous work applie ..."
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Cited by 16 (0 self)
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This paper presents work on two methods for interactive visualization of implicit surfaces: physicallybased sampling using particle systems and polygonization followed by physicallybased mesh improvement which explicitly makes use of the surfacedefining equation. While most previous work applied to bounded manifolds without singularities and without boundary (topological spheres) we broaden the scope of the methods to include surfaces with such features, in particular cusp points and surface selfintersections. These aspects are not (yet) essential for computer graphics modelling with implicit surfaces but they naturally occur in simulations of interest in mathematical visualization. In this paper we use the Kummer family of algebraic surfaces as an example. 1. Introduction Our work is motivated by efforts in the mathematical community for the visualization of implicit algebraic surfaces. Algebraic surfaces and their deformations have been studied for more than one hundred y...
Approximate Conversion of Parametric to Implicit Surfaces
 in Implicit Surfaces'95
, 1996
"... In this paper we present a framework for the approximate conversion of parametric to implicit surfaces. It takes as input a parametric description and generates a piecewise analytic implicit representation. The conversion process consists of three steps: 1) the parametric surface is rasterized int ..."
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Cited by 14 (2 self)
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In this paper we present a framework for the approximate conversion of parametric to implicit surfaces. It takes as input a parametric description and generates a piecewise analytic implicit representation. The conversion process consists of three steps: 1) the parametric surface is rasterized into a volumetric characteristic function. 2) this binary function is converted into a volume array corresponding to samples of a smooth implicit function. 3) this volumetric representation is converted into a multiscale Bspline model. This method is based on wavelet analysis and synthesis techniques and is very general. It can convert to implicit form any geometric object that is suitable for discretization into a characteristic function. 1. Introduction The two main forms of describing the geometry a solid object are the parametric and implicit descriptions. In the parametric description, the solid is specified through its bounding surface, usually in a piecewise manner. In the implic...
Sampling Implicit Objects With PhysicallyBased Particle Systems
 Computers & Graphics
, 1996
"... . After reviewing three classical sampling methods for implicit objects, we describe a new sampling method that is not based on scanning the ambient space. In this method, samples are "randomly" generated using physicallybased particle systems. Introduction In computer graphics, an object is desc ..."
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Cited by 9 (7 self)
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. After reviewing three classical sampling methods for implicit objects, we describe a new sampling method that is not based on scanning the ambient space. In this method, samples are "randomly" generated using physicallybased particle systems. Introduction In computer graphics, an object is described either by a set of sample points or by an analytic scheme that uses mathematical equations to define its geometry and topology. Descriptions based on samples occur in areas such as medical images and terrain models. Analytical descriptions are usually found in applications of geometric modeling, such computeraided design and manufacture. When an object is described by samples, a reconstruction scheme is needed to recover its geometry and topology from the samples. This problem, called structuring, consists of providing a combinatorial structure to the samples in order to (ideally) recover the exact topology of the object and an approximation of its geometry. When the object is describe...