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168
A New VoronoiBased Surface Reconstruction Algorithm
, 2002
"... We describe our experience with a new algorithm for the reconstruction of surfaces from unorganized sample points in R³. The algorithm is the first for this problem with provable guarantees. Given a “good sample” from a smooth surface, the output is guaranteed to be topologically correct and converg ..."
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Cited by 356 (9 self)
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We describe our experience with a new algorithm for the reconstruction of surfaces from unorganized sample points in R³. The algorithm is the first for this problem with provable guarantees. Given a “good sample” from a smooth surface, the output is guaranteed to be topologically correct and convergent to the original surface as the sampling density increases. The definition of a good sample is itself interesting: the required sampling density varies locally, rigorously capturing the intuitive notion that featureless areas can be reconstructed from fewer samples. The output mesh interpolates, rather than approximates, the input points. Our algorithm is based on the threedimensional Voronoi diagram. Given a good program for this fundamental subroutine, the algorithm is quite easy to implement.
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 ..."
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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.
The BallPivoting Algorithm for Surface Reconstruction
 IEEE Transactions on Visualization and Computer Graphics
, 1999
"... The BallPivoting Algorithm (BPA) computes a triangle mesh interpolating a given point cloud. Typically the points are surface samples acquired with multiple range scans of an object. The principle of the BPA is very simple: Three points form a triangle if a ball of a userspecified radius touches ..."
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Cited by 207 (14 self)
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The BallPivoting Algorithm (BPA) computes a triangle mesh interpolating a given point cloud. Typically the points are surface samples acquired with multiple range scans of an object. The principle of the BPA is very simple: Three points form a triangle if a ball of a userspecified radius touches them without containing any other point. Starting with a seed triangle, the ball pivots around an edge (i.e. it revolves around the edge while keeping in contact with the edge's endpoints) until it touches another point, forming another triangle. The process continues until all reachable edges have been tried, and then starts from another seed triangle, until all points have been considered. We applied the BPA to datasets of millions of points representing actual scans of complex 3D objects. The relatively small amount of memory required by the BPA, its time efficiency, and the quality of the results obtained compare favorably with existing techniques.
Painterly Rendering for Animation
 In SIGGRAPH 96 Conference Proceedings
, 1996
"... We present a technique for rendering animations in a painterly style. The difficulty in using existing still frame methods for animation is getting the paint to “stick ” to surfaces rather than randomly change with each frame, while still retaining a handcrafted look. We extend the still frame meth ..."
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Cited by 181 (1 self)
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We present a technique for rendering animations in a painterly style. The difficulty in using existing still frame methods for animation is getting the paint to “stick ” to surfaces rather than randomly change with each frame, while still retaining a handcrafted look. We extend the still frame method to animation by solving two major specific problems of previous techniques. First our method eliminates the “shower door ” effect in which an animation appears as if it were being viewed through textured glass because brush strokes stick to the viewplane not to the animating surfaces. Second, our technique provides for frametoframe coherence in animations so that the resulting frames do not randomly change every frame. To maintain coherence, we model surfaces as 3d particle sets which are rendered as 2d paint brush strokes in screen space much like an artist lays down brush strokes on a canvas. We use geometric and lighting properties of the surfaces to control the appearanceof brush strokes. This powerful combination of using 3d particles, surface lighting information, and rendering 2d brush strokes in screen space gives us the painterly style we desire and forces the brush strokes to stick to animating surfaces. By varying lighting and choosing brush stroke parameters we can create many varied painterly styles. We illustrate the method with images and animated sequences and present specific technical and creative suggestions for achieving different looks.
ParticleBased Fluid Simulation for Interactive Applications
, 2003
"... Realistically animated fluids can add substantial realism to interactive applications such as virtual surgery simulators or computer games. In this paper we propose an interactive method based on Smoothed Particle Hydrodynamics (SPH) to simulate fluids with free surfaces. The method is an extension ..."
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Cited by 180 (9 self)
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Realistically animated fluids can add substantial realism to interactive applications such as virtual surgery simulators or computer games. In this paper we propose an interactive method based on Smoothed Particle Hydrodynamics (SPH) to simulate fluids with free surfaces. The method is an extension of the SPHbased technique by Desbrun to animate highly deformable bodies. We gear the method towards fluid simulation by deriving the force density fields directly from the NavierStokes equation and by adding a term to model surface tension effects. In contrast to Eulerian gridbased approaches, the particlebased approach makes mass conservation equations and convection terms dispensable which reduces the complexity of the simulation. In addition, the particles can directly be used to render the surface of the fluid. We propose methods to track and visualize the free surface using point splatting and marching cubesbased surface reconstruction. Our animation method is fast enough to be used in interactive systems and to allow for user interaction with models consisting of up to 5000 particles.
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 ..."
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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.
Shape modeling with pointsampled geometry
 ACM Transactions on Graphics
, 2003
"... Figure 1: Objects created with our system. (a) boolean operations with scanned geometry, (b) an Octopus modeled by deforming and extruding a sphere, (c) a design study for a Siggraph coffee mug created by boolean operations, freeform deformation and displacement mapping. We present a versatile and ..."
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Cited by 167 (28 self)
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Figure 1: Objects created with our system. (a) boolean operations with scanned geometry, (b) an Octopus modeled by deforming and extruding a sphere, (c) a design study for a Siggraph coffee mug created by boolean operations, freeform deformation and displacement mapping. We present a versatile and complete freeform shape modeling framework for pointsampled geometry. By combining unstructured point clouds with the implicit surface definition of the moving least squares approximation, we obtain a hybrid geometry representation that allows us to exploit the advantages of implicit and parametric surface models. Based on this representation we introduce a shape modeling system that enables the designer to perform large constrained deformations as well as boolean operations on arbitrarily shaped objects. Due to minimum consistency requirements, pointsampled surfaces can easily be restructured on the fly to support extreme geometric deformations during interactive editing. In addition, we show that strict topology control is possible and sharp features can be generated and preserved on pointsampled objects. We demonstrate the effectiveness of our system on a large set of input models, including noisy range scans, irregular point clouds, and sparsely as well as densely sampled models.
FreeForm Shape Design Using Triangulated Surfaces
, 1994
"... We present an approach to modeling with truly mutable yet completely controllable freeform surfaces of arbitrary topology. Surfaces may be pinned down at points and along curves, cut up and smoothly welded back together, and faired and reshaped in the large. This style of control is formulated as a ..."
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Cited by 153 (0 self)
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We present an approach to modeling with truly mutable yet completely controllable freeform surfaces of arbitrary topology. Surfaces may be pinned down at points and along curves, cut up and smoothly welded back together, and faired and reshaped in the large. This style of control is formulated as a constrained shape optimization, with minimization of squared principal curvatures yielding graceful shapes that are free of the parameterization worries accompanying many patchbased approaches. Triangulated point sets are used to approximate these smooth variational surfaces, bridging the gap between patchbased and particlebased representations. Automatic refinement, mesh smoothing, and retriangulation maintain a good computational mesh as the surface shape evolves, and give sample points and surface features much of the freedom to slide around in the surface that oriented particles enjoy. The resulting surface triangulations are constructed and maintained in real time. 1 Introduction ...
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.
Spinimages: A representation for 3d surface matching
, 1997
"... surface registration, object modeling, scene clutter. Dedicated to Dorothy D. Funnell, a believer in higher education. Surface matching is the process that compares surfaces and decides whether they are similar. In threedimensional (3D) computer vision, surface matching plays a prominent role. Sur ..."
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Cited by 115 (4 self)
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surface registration, object modeling, scene clutter. Dedicated to Dorothy D. Funnell, a believer in higher education. Surface matching is the process that compares surfaces and decides whether they are similar. In threedimensional (3D) computer vision, surface matching plays a prominent role. Surface matching can be used for object recognition; by comparing two surfaces, an association between a known object and sensed data is established. By computing the 3D transformation that aligns two surfaces, surface matching can also be used for surface registration. Surface matching is difficult because the coordinate system in which to compare two surfaces is undefined. The typical approach to surface matching is to transform the surfaces being compared into representations where comparison of surfaces is straightforward. Surface matching is further complicated by characteristics of sensed data, including clutter, occlusion and sensor noise. This thesis describes a data level representation of surfaces used for surface matching. In our representation, surface shape is described by a dense collection of oriented points, 3D