SGP: Eurographics Symposium on Geometry Processing

Permanent URI for this community

https://diglib.eg.org/handle/10.2312/434

Browse

Now showing 1 - 9 of 9

Animation-Aware Quadrangulation
(The Eurographics Association and Blackwell Publishing Ltd., 2013) Marcias, Giorgio; Pietroni, Nico; Panozzo, Daniele; Puppo, Enrico; Sorkine-Hornung, Olga; Yaron Lipman and Hao Zhang
Geometric meshes that model animated characters must be designed while taking into account the deformations that the shape will undergo during animation. We analyze an input sequence of meshes with point-to-point correspondence, and we automatically produce a quadrangular mesh that fits well the input animation. We first analyze the local deformation that the surface undergoes at each point, and we initialize a cross field that remains as aligned as possible to the principal directions of deformation throughout the sequence. We then smooth this cross field based on an energy that uses a weighted combination of the initial field and the local amount of stretch. Finally, we compute a field-aligned quadrangulation with an off-the-shelf method. Our technique is fast and very simple to implement, and it significantly improves the quality of the output quad mesh and its suitability for character animation, compared to creating the quad mesh based on a single pose. We present experimental results and comparisons with a state-of-the-art quadrangulation method, on both sequences from 3D scanning and synthetic sequences obtained by a rough animation of a triangulated model.
CubeCover - Parameterization of 3D Volumes
(The Eurographics Association and Blackwell Publishing Ltd., 2011) Nieser, Matthias; Reitebuch, Ulrich; Polthier, Konrad; Mario Botsch and Scott Schaefer
Despite the success of quad-based 2D surface parameterization methods, effective parameterization algorithms for 3D volumes with cubes, i.e. hexahedral elements, are still missing. CUBECOVER is a first approach for generating a hexahedral tessellation of a given volume with boundary aligned cubes which are guided by a frame field. The input of CUBECOVER is a tetrahedral volume mesh. First, a frame field is designed with manual input from the designer. It guides the interior and boundary layout of the parameterization. Then, the parameterization and the hexahedral mesh are computed so as to align with the given frame field. CUBECOVER has similarities to the QUADCOVER algorithm and extends it from 2D surfaces to 3D volumes. The paper also provides theoretical results for 3D hexahedral parameterizations and analyses topological properties of the appropriate function space.
From A Medial Surface To A Mesh
(The Eurographics Association and Blackwell Publishing Ltd., 2012) Delamé, Thomas; Roudet, Céline; Faudot, Dominique; Eitan Grinspun and Niloy Mitra
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 understood by people. We want to exploit such skeletons to use them in applications like shape creation and shape deformation. For this purpose, we need to define medial surfaces as Shape Representation Models (SRMs). One of the very first task of a SRM is to offer a visualization of the shape it describes. However, achieving this with a medial surface remains a challenging problem. In this paper, we propose a method to build a mesh that approximates an object only described by a medial surface. To do so, we use a volumetric approach based on the construction of an octree. Then, we mesh the boundary of that octree to get a coarse approximation of the object. Finally, we refine this mesh using an original migration algorithm. Quantitative and qualitative studies, on objects coming from digital modeling and laser scans, shows the efficiency of our method in providing high quality surfaces with a reasonable computational complexity.
Incorporating Sharp Features in the General Solid Sweep Framework
(The Eurographics Association and John Wiley & Sons Ltd., 2016) Adsul, Bharat; Machchhar, Jinesh; Sohoni, Milind; Maks Ovsjanikov and Daniele Panozzo
This paper extends a recently proposed robust computational framework for constructing the boundary representation (brep) of the volume swept by a given smooth solid moving along a one parameter family h of rigid motions. Our extension allows the input solid to have sharp features, and thus it is a significant and useful generalization of that work. This naturally requires a precise description of the geometry of the surface generated by the sweep of a sharp edge supported by two intersecting smooth faces. We uncover the geometry along with the related issues like parametrization and singularities via a novel mathematical analysis. Correct trimming of such a surface is achieved by an analysis of the interplay between the cone of normals at a sharp point and its trajectory under h. The overall topology is explained by a key lifting theorem which allows us to compute the adjacency relations amongst entities in the swept volume by relating them to corresponding adjacencies in the input solid. Moreover, global issues related to body-check such as orientation, singularities and self-intersections are efficiently resolved. Examples from a pilot implementation illustrate the efficiency and effectiveness of our framework.
Mesh Statistics for Robust Curvature Estimation
(The Eurographics Association and John Wiley & Sons Ltd., 2016) Váša, Libor; Vaněček, Petr; Prantl, Martin; Skorkovská, Věra; Martínek, Petr; Kolingerová, Ivana; Maks Ovsjanikov and Daniele Panozzo
While it is usually not difficult to compute principal curvatures of a smooth surface of sufficient differentiability, it is a rather difficult task when only a polygonal approximation of the surface is available, because of the inherent ambiguity of such representation. A number of different approaches has been proposed in the past that tackle this problem using various techniques. Most papers tend to focus on a particular method, while an comprehensive comparison of the different approaches is usually missing. We present results of a large experiment, involving both common and recently proposed curvature estimation techniques, applied to triangle meshes of varying properties. It turns out that none of the approaches provides reliable results under all circumstances. Motivated by this observation, we investigate mesh statistics, which can be computed from vertex positions and mesh connectivity information only, and which can help in deciding which estimator will work best for a particular case. Finally, we propose a meta-estimator, which makes a choice between existing algorithms based on the value of the mesh statistics, and we demonstrate that such meta-estimator, despite its simplicity, provides considerably more robust results than any existing approach.
Quaternion Julia Set Shape Optimization
(The Eurographics Association and John Wiley & Sons Ltd., 2015) Kim, Theodore; Mirela Ben-Chen and Ligang Liu
We present the first 3D algorithm capable of answering the question: what would a Mandelbrot-like set in the shape of a bunny look like? More concretely, can we find an iterated quaternion rational map whose potential field contains an isocontour with a desired shape? We show that it is possible to answer this question by casting it as a shape optimization that discovers novel, highly complex shapes. The problem can be written as an energy minimization, the optimization can be made practical by using an efficient method for gradient evaluation, and convergence can be accelerated by using a variety of multi-resolution strategies. The resulting shapes are not invariant under common operations such as translation, and instead undergo intricate, non-linear transformations.
Schrödinger Operator for Sparse Approximation of 3D Meshes
(The Eurographics Association, 2017) Choukroun, Yoni; Pai, Gautam; Kimmel, Ron; Jakob Andreas Bærentzen and Klaus Hildebrandt
We introduce a Schrödinger operator for spectral approximation of meshes representing surfaces in 3D. The operator is obtained by modifying the Laplacian with a potential function which defines the rate of oscillation of the harmonics on different regions of the surface. We design the potential using a vertex ordering scheme which modulates the Fourier basis of a 3D mesh to focus on crucial regions of the shape having high-frequency structures and employ a sparse approximation framework to maximize compression performance. The combination of the spectral geometry of the Hamiltonian in conjunction with a sparse approximation approach outperforms existing spectral compression schemes.
Stream Surface Parametrization by Flow-Orthogonal Front Lines
(The Eurographics Association and Blackwell Publishing Ltd., 2012) Schulze, Maik; Germer, Tobias; Rössl, Christian; Theisel, Holger; Eitan Grinspun and Niloy Mitra
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 surfaces depends on a number of parameters that can be controlled locally, such as time step or distance of adjacent vertices on the front line. In addition there is a parameter that cannot be controlled locally: stream surface meshes tend to show high quality, well-shaped elements only if the current front line is "globally" approximately perpendicular to the flow direction. We analyze the impact of this geometric property and present a novel solution a stream surface integrator that forces the front line to be perpendicular to the flow and that generates quaddominant meshes with well-shaped and well-aligned elements. It is based on the integration of a scaled version of the flow field, and requires repeated minimization of an error functional along the current front line. We show that this leads to computing the 1-dimensional kernel of a bidiagonal matrix: a linear problem that can be solved efficiently. We compare our method with existing stream surface integrators and apply it to a number of synthetic and real world data sets.
Surface Patches from Unorganized Space Curves
(The Eurographics Association and Blackwell Publishing Ltd., 2011) Abbasinejad, Fatemeh; Joshi, Pushkar; Amenta, Nina; Mario Botsch and Scott Schaefer
Recent 3D sketch tools produce networks of three-space curves that suggest the contours of shapes. The shapes may be non-manifold, closed three-dimensional, open two-dimensional, or mixed. We describe a system that automatically generates intuitively appealing piecewise-smooth surfaces from such a curve network, and an intelligent user interface for modifying the automatically chosen surface patches. Both the automatic and the semi-automatic parts of the system use a linear algebra representation of the set of surface patches to track the topology. On complicated inputs from ILoveSketch [BBS08], our system allows the user to build the desired surface with just a few mouse-clicks.

Browse

Browsing SGP: Eurographics Symposium on Geometry Processing by Subject "and object representations"

Results Per Page

Sort Options