SGP12: Eurographics Symposium on Geometry Processing
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Feature-Preserving Reconstruction of Singular Surfaces
(The Eurographics Association and Blackwell Publishing Ltd., 2012)Reconstructing a surface mesh from a set of discrete point samples is a fundamental problem in geometric modeling. It becomes challenging in presence of 'singularities' such as boundaries, sharp features, and non-manifolds. ... -
Parallel Blue-noise Sampling by Constrained Farthest Point Optimization
(The Eurographics Association and Blackwell Publishing Ltd., 2012)We describe a fast sampling algorithm for generating uniformly-distributed point patterns with good blue noise characteristics. The method, based on constrained farthest point optimization, is provably optimal and may be ... -
Fast and Robust Normal Estimation for Point Clouds with Sharp Features
(The Eurographics Association and Blackwell Publishing Ltd., 2012)This paper presents a new method for estimating normals on unorganized point clouds that preserves sharp features. It is based on a robust version of the Randomized Hough Transform (RHT). We consider the filled Hough ... -
Time-Discrete Geodesics in the Space of Shells
(The Eurographics Association and Blackwell Publishing Ltd., 2012)Building on concepts from continuum mechanics, we offer a computational model for geodesics in the space of thin shells, with a metric that reflects viscous dissipation required to physically deform a thin shell. Different ... -
Can Mean-Curvature Flow be Modified to be Non-singular?
(The Eurographics Association and Blackwell Publishing Ltd., 2012)This work considers the question of whether mean-curvature flow can be modified to avoid the formation of singularities. We analyze the finite-elements discretization and demonstrate why the original flow can result in ... -
Mean Curvature Skeletons
(The Eurographics Association and Blackwell Publishing Ltd., 2012)Inspired by recent developments in contraction-based curve skeleton extraction, we formulate the skeletonization problem via mean curvature flow (MCF). While the classical application of MCF is surface fairing, we take ... -
Stream Surface Parametrization by Flow-Orthogonal Front Lines
(The Eurographics Association and Blackwell Publishing Ltd., 2012)The generation of discrete stream surfaces is an important and challenging task in scientific visualization, which can be considered a particular instance of geometric modeling. The quality of numerically integrated stream ... -
Dihedral Angle Mesh Error: a Fast Perception Correlated Distortion Measure for Fixed Connectivity Triangle Meshes
(The Eurographics Association and Blackwell Publishing Ltd., 2012)In computer graphics, triangle meshes are ubiquitous as a representation of surface models. Processing of this kind of data, such as compression or watermarking, often involves an unwanted distortion of the surface geometry. ... -
Co-Segmentation of 3D Shapes via Subspace Clustering
(The Eurographics Association and Blackwell Publishing Ltd., 2012)We present a novel algorithm for automatically co-segmenting a set of shapes from a common family into consistent parts. Starting from over-segmentations of shapes, our approach generates the segmentations by grouping the ... -
Computing Extremal Quasiconformal Maps
(The Eurographics Association and Blackwell Publishing Ltd., 2012)Conformal maps are widely used in geometry processing applications. They are smooth, preserve angles, and are locally injective by construction. However, conformal maps do not allow for boundary positions to be prescribed. ... -
Growing Least Squares for the Analysis of Manifolds in Scale-Space
(The Eurographics Association and Blackwell Publishing Ltd., 2012)We present a novel approach to the multi-scale analysis of point-sampled manifolds of co-dimension 1. It is based on a variant of Moving Least Squares, whereby the evolution of a geometric descriptor at increasing scales ... -
Radial Symmetry Detection and Shape Characterization with the Multiscale Area Projection Transform
(The Eurographics Association and Blackwell Publishing Ltd., 2012)We present a novel method to characterize 3D surfaces through the computation of a function called (multiscale) area projection transform, measuring the likelihood of points in the 3D space to be center of radial symmetry ... -
Shape-Up: Shaping Discrete Geometry with Projections
(The Eurographics Association and Blackwell Publishing Ltd., 2012)We introduce a unified optimization framework for geometry processing based on shape constraints. These constraints preserve or prescribe the shape of subsets of the points of a geometric data set, such as polygons, one-ring ... -
From A Medial Surface To A Mesh
(The Eurographics Association and Blackwell Publishing Ltd., 2012)Medial surfaces are well-known and interesting surface skeletons. As such, they can describe the topology and the geometry of a 3D closed object. The link between an object and its medial surface is also intuitively ... -
New Bounds on the Size of Optimal Meshes
(The Eurographics Association and Blackwell Publishing Ltd., 2012)The theory of optimal size meshes gives a method for analyzing the output size (number of simplices) of a Delaunay refinement mesh in terms of the integral of a sizing function over the input domain. The input points define ... -
Soft Maps Between Surfaces
(The Eurographics Association and Blackwell Publishing Ltd., 2012)The problem of mapping between two non-isometric surfaces admits ambiguities on both local and global scales. For instance, symmetries can make it possible for multiple maps to be equally acceptable, and stretching, slippage, ... -
Modeling Polyhedral Meshes with Affine Maps
(The Eurographics Association and Blackwell Publishing Ltd., 2012)We offer a framework for editing and modeling of planar meshes, focusing on planar quad, and hexagonaldominant meshes, which are held in high demand in the field of architectural design. Our framework manipulates these ... -
Finding Surface Correspondences Using Symmetry Axis Curves
(The Eurographics Association and Blackwell Publishing Ltd., 2012)In this paper, we propose an automatic algorithm for finding a correspondence map between two 3D surfaces. The key insight is that global reflective symmetry axes are stable, recognizable, semantic features of most real-world ... -
Microtiles: Extracting Building Blocks from Correspondences
(The Eurographics Association and Blackwell Publishing Ltd., 2012)In this paper, we develop a theoretical framework for characterizing shapes by building blocks. We address two questions: First, how do shape correspondences induce building blocks? For this, we introduce a new representation ... -
Smooth Shape-Aware Functions with Controlled Extrema
(The Eurographics Association and Blackwell Publishing Ltd., 2012)Functions that optimize Laplacian-based energies have become popular in geometry processing, e.g. for shape deformation, smoothing, multiscale kernel construction and interpolation. Minimizers of Dirichlet energies, or ...
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