SGP

A robust statistics approach to curvature estimation on discretely sampled surfaces, namely polygon meshes and point clouds, is presented. The method exhibits accuracy, stability and consistency even for noisy, non-uniformly sampled surfaces with ...

The differential geometry of smooth three-dimensional surfaces can be interpreted from one of two perspectives: in terms of oriented frames located on the surface, or in terms of a pair of associated focal surfaces. These focal surfaces are swept by the ...

Discrete Laplace operators are ubiquitous in applications spanning geometric modeling to simulation. For robustness and efficiency, many applications require discrete operators that retain key structural properties inherent to the continuous setting. ...

We introduce an algorithm for reconstructing watertight surfaces from unoriented point sets. Using the Voronoi diagram of the input point set, we deduce a tensor field whose principal axes and eccentricities locally represent respectively the most ...

In this paper, we describe a system for the reconstruction of deforming geometry from a time sequence of unstructured, noisy point clouds, as produced by recent real-time range scanning devices. Our technique reconstructs both the geometry and dense ...

In this paper we present a high-fidelity surface approximation technique that aims at a faithful reconstruction of piecewise-smooth surfaces from a scattered point set. The presented method builds on the Moving Least-Squares (MLS) projection methodology,...

Reconstruction of surfaces from huge collections of scanned points often requires out-of-core techniques, and most such techniques involve local computations that are not resilient to data errors. We show that a Poisson-based reconstruction scheme, ...

We present a streaming algorithm for reconstructing closed surfaces from large non-uniform point sets based on a geometric convection technique. Assuming that the sample points are organized into slices stacked along one coordinate axis, a triangle mesh ...

In this paper, we consider the problem of reconstructing a shape from unorganized cross-sections. The main motivation for this problem comes from medical imaging applications where cross-sections of human organs are obtained by means of a free hand ...

We present an approach for elastic secondary deformations of shapes described as triangular meshes. The deformations are steered by the simulation of a low number of simple mass-spring sets. The result of this simulation is used to define time-dependent ...

Modeling tasks, such as surface deformation and editing, can be analyzed by observing the local behavior of the surface. We argue that defining a modeling operation by asking for rigidity of the local transformations is useful in various settings. Such ...

In this paper we introduce positive mean value coordinates (PMVC) for mesh deformation. Following the observations of Joshi et al. [JMD*07] we show the advantage of having positive coordinates. The control points of the deformation are the vertices of a ...

This paper presents a novel algorithm for generating a watertight level-set from an octree. We show that the levelset can be efficiently extracted regardless of the topology of the octree or the values assigned to the vertices. The key idea behind our ...

In the field of mesh parameterization, the impact of angular and boundary distortion on parameterization quality have brought forward the need for robust and efficient free boundary angle preserving methods. One of the most prominent approaches in this ...

We present two new Delaunay refinement algorithms, the second an extension of the first. For a given input domain (a set of points in the plane or a planar straight line graph), and a threshold angle α, the Delaunay refinement algorithms compute ...

We present a method for extracting a hierarchical, rigid skeleton from a set of example poses. We then use this skeleton to not only reproduce the example poses, but create new deformations in the same style as the examples. Since rigid skeletons are ...

Developable surfaces are surfaces that can be unfolded into the plane with no distortion. Although ubiquitous in our everyday surroundings, modeling them using existing tools requires significant geometric expertise and time. Our paper simplifies the ...

We propose an algorithm that performs registration of large sets of unstructured point clouds of moving and deforming objects without computing correspondences. Given as input a set of frames with dense spatial and temporal sampling, such as the raw ...

Geometric flows are ubiquitous in mesh processing. Curve and surface evolutions based on functional minimization have been used in the context of surface diffusion, denoising, shape optimization, minimal surfaces, and geodesic paths to mention a few. ...

Many common objects have highly reflective metallic or painted finishes. Their appearance is primarily defined by the distortion the curved shape of the surface introduces in the reflections of surrounding objects.

Reflection lines are commonly used for ...

We propose a constraint-based method for the fairing of surface meshes. The main feature of our approach is that the resulting smoothed surface remains within a prescribed distance to the input mesh. For example, specifying the maximum distance in the ...

This paper introduces a novel technique for joint surface reconstruction and registration. Given a set of roughly aligned noisy point clouds, it outputs a noise-free and watertight solid model. The basic idea of the new technique is to reconstruct a ...

A deformation invariant representation of surfaces, the GPS embedding, is introduced using the eigenvalues and eigenfunctions of the Laplace-Beltrami differential operator. Notably, since the definition of the GPS embedding completely avoids the use of ...

While existing methods for 3D surface approximation use local geometric properties, we propose that more intuitive results can be obtained by considering global shape properties such as symmetry. We modify the Variational Shape Approximation technique ...

This paper presents a new method for reconstructing curves and surfaces from unstructured point clouds, allowing for noise in the data as well as inhomogeneous distribution of the point set. It is based on the observation that the curve/surface is ...

We present an example-based surface reconstruction method for scanned point sets. Our approach uses a database of local shape priors built from a set of given context models that are chosen specifically to match a specific scan. Local neighborhoods of ...

We present two methods for lossy compression of normal vectors through quantization using "base" polyhedra. The first revisits subdivision-based quantization. The second uses fixed-precision barycentric coordinates. For both, we provide fast (de)...

We present algorithms to produce Delaunay meshes from arbitrary triangle meshes by edge flipping and geometrypreserving refinement and prove their correctness. In particular we show that edge flipping serves to reduce mesh surface area, and that a ...