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Polygonization of Implicit Surfaces
, 1988
"... This paper discusses a numerical technique that approximates an implicit surface with a polygonal representation. The implicit function is adaptively sampled as it is surrounded by a spatial partitioning. The partitioning is represented by an octree, which may either converge to the surface or track ..."
Abstract

Cited by 432 (5 self)
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This paper discusses a numerical technique that approximates an implicit surface with a polygonal representation. The implicit function is adaptively sampled as it is surrounded by a spatial partitioning. The partitioning is represented by an octree, which may either converge to the surface
Modelling with Implicit Surfaces that Interpolate
 ACM Transactions on Graphics
, 2002
"... We introduce new techniques for modelling with interpolating implicit surfaces. This form of implicit surface was first used for problems of surface reconstruction [24] and shape transformation [30], but the emphasis of our work is on model creation. These implicit surfaces are described by specify ..."
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Cited by 125 (1 self)
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We introduce new techniques for modelling with interpolating implicit surfaces. This form of implicit surface was first used for problems of surface reconstruction [24] and shape transformation [30], but the emphasis of our work is on model creation. These implicit surfaces are described
Variational Implicit Surfaces
, 1999
"... We introduce a new method of creating smooth implicit surfaces of arbitrary manifold topology. These surfaces are described by specifying locations in 3D through which the surface should pass, and also identifying locations that are interior or exterior to the surface. A 3D implicit function is crea ..."
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Cited by 62 (2 self)
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We introduce a new method of creating smooth implicit surfaces of arbitrary manifold topology. These surfaces are described by specifying locations in 3D through which the surface should pass, and also identifying locations that are interior or exterior to the surface. A 3D implicit function
Optimal polygonization of implicit surfaces
"... In this paper the main definitions of piece regular implicit surfaces, of surfaces curvature, of approximation of piece regular implicit surfaces are introduced. The task of optimal polygonization of piece regular implicit surfaces and some approaches to its solution are given. ..."
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In this paper the main definitions of piece regular implicit surfaces, of surfaces curvature, of approximation of piece regular implicit surfaces are introduced. The task of optimal polygonization of piece regular implicit surfaces and some approaches to its solution are given.
An Implicit Surface Polygonizer
 Graphics Gems IV
, 1994
"... Introduction Some shapes are more readily defined by implicit, rather than parametric, techniques. For example, consider a sphere centered at C with radius r. It can be described parametrically as {P}, where: (P x , P y , P z ) = (C x , C y , C z )+(r cosb cosa, r cosb sina, r sinb), a (0, 2p), b ..."
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Cited by 143 (0 self)
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Introduction Some shapes are more readily defined by implicit, rather than parametric, techniques. For example, consider a sphere centered at C with radius r. It can be described parametrically as {P}, where: (P x , P y , P z ) = (C x , C y , C z )+(r cosb cosa, r cosb sina, r sinb), a (0, 2p), b
Using Particles to Sample and Control Implicit Surfaces
, 1994
"... We present a new particlebased approach to sampling and controlling implicit surfaces. A simple constraint locks a set of particles onto a surface while the particles and the surface move. We use the constraint to make surfaces follow particles, and to make particles follow surfaces. We implement c ..."
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Cited by 256 (3 self)
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We present a new particlebased approach to sampling and controlling implicit surfaces. A simple constraint locks a set of particles onto a surface while the particles and the surface move. We use the constraint to make surfaces follow particles, and to make particles follow surfaces. We implement
Isotopic implicit surface meshing
 STOC'04
, 2004
"... This paper addresses the problem of piecewise linear approximation of implicit surfaces. We first give a criterion ensuring that the zeroset of a smooth function and the one of a piecewise linear approximation of it are isotopic. Then, we deduce from this criterion an implicit surface meshing algor ..."
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Cited by 28 (4 self)
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This paper addresses the problem of piecewise linear approximation of implicit surfaces. We first give a criterion ensuring that the zeroset of a smooth function and the one of a piecewise linear approximation of it are isotopic. Then, we deduce from this criterion an implicit surface meshing
KEYWORDS Trimming Implicit Surfaces
"... Algorithms of trimming implicit surfaces yielding surface sheets and stripes are presented. These twodimensional manifolds with boundaries result from settheoretic operations on an implicit surface and a solid or another implicit surface. The algorithms generate adaptive polygonal approximation of ..."
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Cited by 2 (2 self)
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Algorithms of trimming implicit surfaces yielding surface sheets and stripes are presented. These twodimensional manifolds with boundaries result from settheoretic operations on an implicit surface and a solid or another implicit surface. The algorithms generate adaptive polygonal approximation
Guaranteed Ray Intersections with Implicit Surfaces
, 1989
"... In this paper, we present a robust and mathematically sound rayintersection algorithm for implicit surfaces. The algorithm is guaranteed to numerically find the nearest intersection of the surface with a ray, and is guaranteed not to miss fine features of the surface. It does not require fine tuni ..."
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Cited by 113 (0 self)
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In this paper, we present a robust and mathematically sound rayintersection algorithm for implicit surfaces. The algorithm is guaranteed to numerically find the nearest intersection of the surface with a ray, and is guaranteed not to miss fine features of the surface. It does not require fine
Subdivision Interpolating Implicit Surfaces
, 2003
"... Interpolating implicit surfaces using radial basis functions can directly specify surface points and surface normals with closed form solutions, so they are elegantly used in surface reconstruction and shape morphing. This paper presents subdivision interpolating implicit surfaces, a new progressive ..."
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Cited by 5 (0 self)
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Interpolating implicit surfaces using radial basis functions can directly specify surface points and surface normals with closed form solutions, so they are elegantly used in surface reconstruction and shape morphing. This paper presents subdivision interpolating implicit surfaces, a new
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