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Point Set Surfaces
, 2001
"... We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). We pre ..."
Abstract

Cited by 298 (42 self)
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We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). We
Defining PointSet Surfaces
, 2005
"... The MLS surface [Levin 2003], used for modeling and rendering with point clouds, was originally defined algorithmically as the output of a particular meshless construction. We give a new explicit definition in terms of the critical points of an energy function on lines determined by a vector field. ..."
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Cited by 181 (2 self)
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The MLS surface [Levin 2003], used for modeling and rendering with point clouds, was originally defined algorithmically as the output of a particular meshless construction. We give a new explicit definition in terms of the critical points of an energy function on lines determined by a vector field
Algebraic point set surfaces
 In Proceedings SIGGRAPH ’07
, 2007
"... Figure 1: Illustration of the central features of our algebraic MLS framework. From left to right: efficient handling of very complex point sets, fast mean curvature evaluation and shading, significantly increased stability in regions of high curvature, sharp features with controlled sharpness. Samp ..."
Abstract

Cited by 82 (8 self)
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. Sample positions are partly highlighted. In this paper we present a new Point Set Surface (PSS) definition based on moving least squares (MLS) fitting of algebraic spheres. Our surface representation can be expressed by either a projection procedure or in implicit form. The central advantages of our
Multiresolution Pointset Surfaces
"... Multiresolution representations of 3D surfaces make it possible to concentrate the efforts of a modification at the appropriate level of detail. This paper introduces a multiresolution representation for pointset surfaces. At each level, the point set is smoothed and downsampled, and the geometric ..."
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Cited by 3 (0 self)
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Multiresolution representations of 3D surfaces make it possible to concentrate the efforts of a modification at the appropriate level of detail. This paper introduces a multiresolution representation for pointset surfaces. At each level, the point set is smoothed and downsampled, and the geometric
Point Set Surfaces
"... We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). We pre ..."
Abstract
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We advocate the use of point sets to represent shapes. We provide a definition of a smooth manifold surface from a set of points close to the original surface. The definition is based on local maps from differential geometry, which are approximated by the method of moving least squares (MLS). We
on Point Set Surfaces
"... Over the past several years, pointsampled geometry has gained popularity in graphics and related visual computing areas. Point set surfaces, in particular, have enjoyed a major renaissance in both modeling and rendering. Points have clear advantages over traditional primitives such as triangle mesh ..."
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Over the past several years, pointsampled geometry has gained popularity in graphics and related visual computing areas. Point set surfaces, in particular, have enjoyed a major renaissance in both modeling and rendering. Points have clear advantages over traditional primitives such as triangle
Ray Tracing Point Set Surfaces
, 2003
"... Point set surfaces are a smooth manifold surface approximation from a set of sample points. The surface definition is based on a projection operation that constructs local polynomial approximations and respects a minimum feature size. We present techniques for ray tracing point set surfaces. For the ..."
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Cited by 63 (2 self)
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Point set surfaces are a smooth manifold surface approximation from a set of sample points. The surface definition is based on a projection operation that constructs local polynomial approximations and respects a minimum feature size. We present techniques for ray tracing point set surfaces
The Domain of a Point Set Surface
, 2004
"... It is useful to be able to define a twodimensional pointset surface determined by a point cloud. One popular definition is Levin's MLS surface. This surface is defined on a domain which is a threedimensional subset of R , a narrow region around the input point cloud. If we were to exten ..."
Abstract
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It is useful to be able to define a twodimensional pointset surface determined by a point cloud. One popular definition is Levin's MLS surface. This surface is defined on a domain which is a threedimensional subset of R , a narrow region around the input point cloud. If we were
Point Set Surfaces with Sharp Features
, 2005
"... There are many techniques that reconstruct continuous surfaces from scattered point data coming from laser range scanners. One of the most commonly used representations are Point Set Surfaces (PSS) defined as the set of stationary points of a Moving Least Squares (MLS) projection operator. One inter ..."
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Cited by 1 (0 self)
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There are many techniques that reconstruct continuous surfaces from scattered point data coming from laser range scanners. One of the most commonly used representations are Point Set Surfaces (PSS) defined as the set of stationary points of a Moving Least Squares (MLS) projection operator. One
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