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45
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 244 (36 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 present tools to increase or decrease the density of the points, thus, allowing an adjustment of the spacing among the points to control the fidelity of the representation. To display the point set surface, we introduce a novel point rendering technique. The idea is to evaluate the local maps according to the image resolution. This results in high quality shading effects and smooth silhouettes at interactive frame rates.
Computing and Rendering Point Set Surfaces
, 2002
"... 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). The co ..."
Abstract

Cited by 170 (21 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). The computation of points on the surface is local, which results in an outofcore technique that can handle any point set.
Efficient Simplification of PointSampled Surfaces
, 2002
"... In this paper we introduce, analyze and quantitatively compare a number of surface simplification methods for pointsampled geometry. We have implemented incremental and hierarchical clustering, iterative simplification, and particle simulation algorithms to create approximations of pointbased mode ..."
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Cited by 151 (15 self)
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In this paper we introduce, analyze and quantitatively compare a number of surface simplification methods for pointsampled geometry. We have implemented incremental and hierarchical clustering, iterative simplification, and particle simulation algorithms to create approximations of pointbased models with lower sampling density. All these methods work directly on the point cloud, requiring no intermediate tesselation. We show how local variation estimation and quadric error metrics can be employed to diminish the approximation error and concentrate more samples in regions of high curvature. To compare the quality of the simplified surfaces, we have designed a new method for computing numerical and visual error estimates for pointsampled surfaces. Our algorithms are fast, easy to implement, and create highquality surface approximations, clearly demonstrating the effectiveness of pointbased surface simplification.
Smooth Surface Reconstruction via Natural Neighbour Interpolation of Distance Functions
, 2000
"... We present an algorithm to reconstruct smooth surfaces of arbitrary topology from unorganised sample points and normals. The method uses natural neighbour interpolation, works in any dimension and allows to deal with non uniform samples. The reconstructed surface is a smooth manifold passing through ..."
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Cited by 119 (4 self)
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We present an algorithm to reconstruct smooth surfaces of arbitrary topology from unorganised sample points and normals. The method uses natural neighbour interpolation, works in any dimension and allows to deal with non uniform samples. The reconstructed surface is a smooth manifold passing through all the sample points. This surface is implicitly represented as the zeroset of some pseudodistance function. It can be meshed so as to satisfy a userdefined error bound. Experimental results are presented for surfaces in R³.
Point Based Animation of Elastic, Plastic and Melting Objects
, 2004
"... We present a method for modeling and animating a wide spectrum of volumetric objects, with material properties anywhere in the range from stiff elastic to highly plastic. Both the volume and the surface representation are point based, which allows arbitrarily large deviations form the original sha ..."
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Cited by 93 (12 self)
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We present a method for modeling and animating a wide spectrum of volumetric objects, with material properties anywhere in the range from stiff elastic to highly plastic. Both the volume and the surface representation are point based, which allows arbitrarily large deviations form the original shape. In contrast to previous point based elasticity in computer graphics, our physical model is derived from continuum mechanics, which allows the specification of common material properties such as Young's Modulus and Poisson's Ratio. In each step
On normals and projection operators for surfaces defined by point sets
 IN EUROGRAPHICS SYMP. ON POINTBASED GRAPHICS
, 2004
"... Levin’s MLS projection operator allows defining a surface from a set of points and represents a versatile procedure to generate points on this surface. Practical problems of MLS surfaces are a complicated nonlinear optimization to compute a tangent frame and the (commonly overlooked) fact that the ..."
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Cited by 48 (3 self)
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Levin’s MLS projection operator allows defining a surface from a set of points and represents a versatile procedure to generate points on this surface. Practical problems of MLS surfaces are a complicated nonlinear optimization to compute a tangent frame and the (commonly overlooked) fact that the normal to this tangent frame is not the surface normal. An alternative definition of Point Set Surfaces, inspired by the MLS projection, is the implicit surface version of Adamson & Alexa. We use this surface definition to show how to compute exact surface normals and present simple, efficient projection operators. The exact normal computation also allows computing orthogonal projections.
Smooth meshes for sketchbased freeform modeling
 In Proceedings of the 2003 symposium on Interactive 3D graphics (2003
, 2003
"... This paper describes a framework for introducing visually smooth surfaces into sketchbased freeform modeling systems. An existing sketchbased freeform modeling system generates rough polygonal meshes with uneven triangulations after each operation. Our approach generates a dense, visually smooth p ..."
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Cited by 33 (0 self)
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This paper describes a framework for introducing visually smooth surfaces into sketchbased freeform modeling systems. An existing sketchbased freeform modeling system generates rough polygonal meshes with uneven triangulations after each operation. Our approach generates a dense, visually smooth polygonal mesh by beautifying and refining the original rough mesh. A beautification process generates nearequilateral triangles with a nearuniform distribution of vertices to mask the noise and bad sampling of the uneven mesh. The vertices are distributed on a smoothed surface that approximately interpolates the original mesh. Refinement generates a smooth, dense mesh by subdividing the beautified mesh and moving the vertices to the interpolative surface. The smooth interpolative surface is computed via implicit quadratic surfaces that best fit the mesh locally in a leastsquares sense.
Scalable 3D Video Of dynamic scenes
, 2005
"... In this paper we present a scalable 3D video framework for capturing and rendering dynamic scenes. The acquisition system is based on multiple sparsely placed 3D video bricks, each comprising a projector, two grayscale cameras and a color camera. Relying on structured light with complementary patter ..."
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Cited by 20 (2 self)
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In this paper we present a scalable 3D video framework for capturing and rendering dynamic scenes. The acquisition system is based on multiple sparsely placed 3D video bricks, each comprising a projector, two grayscale cameras and a color camera. Relying on structured light with complementary patterns, texture images and patternaugmented views of the scene are acquired simultaneously by time multiplexed projections and synchronized camera exposures. Using spacetime stereo on the acquired pattern images, highquality depth maps are extracted, whose corresponding surface samples are merged into a viewindependent, pointbased 3D data structure. This representation allows for effective photo consistency enforcement and outlier removal, leading to a significant decrease of visual artifacts and a high resulting rendering quality using EWA volume splatting. Our framework and its viewindependent representation allow for simple and straightforward editing of 3D video. In order to demonstrate its flexibility, we show compositing techniques and spatiotemporal effects.
Contact Handling for Deformable PointBased Objects
, 2004
"... This paper presents an approach to collision detection and response for dynamically deforming pointbased objects. Both the volume of an object and its surface are represented by point sets. In case of a collision, response forces are computed for penetrating surface points and distributed to volume ..."
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Cited by 18 (4 self)
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This paper presents an approach to collision detection and response for dynamically deforming pointbased objects. Both the volume of an object and its surface are represented by point sets. In case of a collision, response forces are computed for penetrating surface points and distributed to volume points which are used for simulating the object dynamics. The decoupling of collision handling and deformation allows for a very stable collision response while maintaining interactive update rates of the dynamic simulation for environments with moderate complexity. Simulation results are presented for elastically and plastically deforming objects with changing topology.