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.

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 out-of-core technique that can handle any point set.

In this paper we introduce, analyze and quantitatively compare a number of surface simplification methods for point-sampled geometry. We have implemented incremental and hierarchical clustering, iterative simplification, and particle simulation algorithms to create approximations of point-based 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 point-sampled surfaces. Our algorithms are fast, easy to implement, and create high-quality surface approximations, clearly demonstrating the effectiveness of point-based surface simplification.

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 zero-set of some pseudo-distance function. It can be meshed so as to satisfy a user-defined error bound. Experimental results are presented for surfaces in R³.

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

Abstract not found

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 non-linear 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. Categories and Subject Descriptors (according to ACM CCS): G.1.2 [Numerical Analysis]: Approximation of surfaces and contours I.3.5 [Computer Graphics]: Curve, surface, solid, and object representations

This paper describes a framework for introducing visually smooth surfaces into sketch-based freeform modeling systems. An existing sketch-based 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 near-equilateral triangles with a near-uniform 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 least-squares sense.

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.

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 space-time stereo on the acquired pattern images, high-quality depth maps are extracted, whose corresponding surface samples are merged into a viewindependent, point-based 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 view-independent representation allow for simple and straightforward editing of 3D video. In order to demonstrate its flexibility, we show compositing techniques and spatio-temporal effects.