SGP: Eurographics Symposium on Geometry Processing

Permanent URI for this community

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

Browse

Now showing 1 - 14 of 14

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.
Approximating Isosurfaces by Guaranteed-quality Triangular Meshes
(The Eurographics Association and John Wiley & Sons Ltd., 2020) Hass, Joel; Trnkova, Maria; Jacobson, Alec and Huang, Qixing
We describe a new method for approximating an implicit surface F by a piecewise-flat triangulated surface whose triangles are as close as possible to equilateral. The main advantage is improved mesh quality which is guaranteed for smooth surfaces. The GradNormal algorithm generates a triangular mesh that gives a piecewise-differentiable approximation of F, with angles between 35.2 and 101.5 degrees. As the mesh size approaches 0, the mesh converges to F through surfaces that are isotopic to F.
A Constrained Resampling Strategy for Mesh Improvement
(The Eurographics Association and John Wiley & Sons Ltd., 2017) Abdelkader, Ahmed; Mahmoud, Ahmed H.; Rushdi, Ahmad A.; Mitchell, Scott A.; Owens, John D.; Ebeida, Mohamed S.; Bærentzen, Jakob Andreas and Hildebrandt, Klaus
In many geometry processing applications, it is required to improve an initial mesh in terms of multiple quality objectives. Despite the availability of several mesh generation algorithms with provable guarantees, such generated meshes may only satisfy a subset of the objectives. The conflicting nature of such objectives makes it challenging to establish similar guarantees for each combination, e.g., angle bounds and vertex count. In this paper, we describe a versatile strategy for mesh improvement by interpreting quality objectives as spatial constraints on resampling and develop a toolbox of local operators to improve the mesh while preserving desirable properties. Our strategy judiciously combines smoothing and transformation techniques allowing increased flexibility to practically achieve multiple objectives simultaneously. We apply our strategy to both planar and surface meshes demonstrating how to simplify Delaunay meshes while preserving element quality, eliminate all obtuse angles in a complex mesh, and maximize the shortest edge length in a Voronoi tessellation far better than the state-of-the-art.
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.
Effective Characterization of Relief Patterns
(The Eurographics Association and John Wiley & Sons Ltd., 2018) Giachetti, Andrea; Ju, Tao and Vaxman, Amir
In this paper, we address the problem of characterizing relief patterns over surface meshes independently on the underlying shape. We propose to tackle the problem by estimating local invariant features and encoding them using the Improved Fisher Vector technique, testing both features estimated on 3D meshes and local descriptors estimated on raster images created by encoding local surface properties (e.g. mean curvature) over a surface parametrization. We compare the robustness of the obtained descriptors against noise and surface bending and evaluate retrieval performances on a specific benchmark proposed in a track of the Eurographics Shape REtrieval Contest 2017. Results show that, with the proposed framework, it is possible to obtain retrieval results largely improving the state of the art and that the image-based approach is still effective when the underlying surface is heavily deformed.
Fast and Memory-Efficient Voronoi Diagram Construction on Triangle Meshes
(The Eurographics Association and John Wiley & Sons Ltd., 2017) Qin, Yipeng; Yu, Hongchuan; Zhang, Jiangjun; Bærentzen, Jakob Andreas and Hildebrandt, Klaus
Geodesic based Voronoi diagrams play an important role in many applications of computer graphics. Constructing such Voronoi diagrams usually resorts to exact geodesics. However, exact geodesic computation always consumes lots of time and memory, which has become the bottleneck of constructing geodesic based Voronoi diagrams. In this paper, we propose the window-VTP algorithm, which can effectively reduce redundant computation and save memory. As a result, constructing Voronoi diagrams using the proposed window-VTP algorithm runs 3-8 times faster than Liu et al.'s method [LCT11], 1.2 times faster than its FWP-MMP variant and more importantly uses 10-70 times less memory than both of them.
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.
Ternary Sparse Matrix Representation for Volumetric Mesh Subdivision and Processing on GPUs
(The Eurographics Association and John Wiley & Sons Ltd., 2017) Mueller-Roemer, Johannes Sebastian; Altenhofen, Christian; Stork, André; Bærentzen, Jakob Andreas and Hildebrandt, Klaus
In this paper, we present a novel volumetric mesh representation suited for parallel computing on modern GPU architectures. The data structure is based on a compact, ternary sparse matrix storage of boundary operators. Boundary operators correspond to the first-order top-down relations of k-faces to their (k-1)-face facets. The compact, ternary matrix storage format is based on compressed sparse row matrices with signed indices and allows for efficient parallel computation of indirect and bottomup relations. This representation is then used in the implementation of several parallel volumetric mesh algorithms including Laplacian smoothing and volumetric Catmull-Clark subdivision. We compare these algorithms with their counterparts based on OpenVolumeMesh and achieve speedups from 3x to 531x, for sufficiently large meshes, while reducing memory consumption by up to 36%.

Browse

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

Results Per Page

Sort Options