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Polygonal Meshes (polygonal + mesh)

Distribution by Scientific Domains

Engineering	41%

Selected Abstracts

Exact and Robust (Self-)Intersections for Polygonal Meshes

COMPUTER GRAPHICS FORUM, Issue 2 2010
Marcel Campen
Abstract We present a new technique to implement operators that modify the topology of polygonal meshes at intersections and self-intersections. Depending on the modification strategy, this effectively results in operators for Boolean combinations or for the construction of outer hulls that are suited for mesh repair tasks and accurate mesh-based front tracking of deformable materials that split and merge. By combining an adaptive octree with nested binary space partitions (BSP), we can guarantee exactness (= correctness) and robustness (= completeness) of the algorithm while still achieving higher performance and less memory consumption than previous approaches. The efficiency and scalability in terms of runtime and memory is obtained by an operation localization scheme. We restrict the essential computations to those cells in the adaptive octree where intersections actually occur. Within those critical cells, we convert the input geometry into a plane-based BSP-representation which allows us to perform all computations exactly even with fixed precision arithmetics. We carefully analyze the precision requirements of the involved geometric data and predicates in order to guarantee correctness and show how minimal input mesh quantization can be used to safely rely on computations with standard floating point numbers. We properly evaluate our method with respect to precision, robustness, and efficiency. [source]

Resampling Feature and Blend Regions in Polygonal Meshes for Surface Anti-Aliasing

COMPUTER GRAPHICS FORUM, Issue 3 2001
Mario Botsch
Efficient surface reconstruction and reverse engineering techniques are usually based on a polygonal mesh representation of the geometry: the resulting models emerge from piecewise linear interpolation of a set of sample points. The quality of the reconstruction not only depends on the number and density of the sample points but also on their alignment to sharp and rounded features of the original geometry. Bad alignment can lead to severe alias artifacts. In this paper we present a sampling pattern for feature and blend regions which minimizes these alias errors. We show how to improve the quality of a given polygonal mesh model by resampling its feature and blend regions within an interactive framework. We further demonstrate sophisticated modeling operations that can be implemented based on this resampling technique. [source]

Embedded Implicit Stand-Ins for Animated Meshes: A Case of Hybrid Modelling

COMPUTER GRAPHICS FORUM, Issue 1 2010
D. Kravtsov
Abstract In this paper, we address shape modelling problems, encountered in computer animation and computer games development that are difficult to solve just using polygonal meshes. Our approach is based on a hybrid-modelling concept that combines polygonal meshes with implicit surfaces. A hybrid model consists of an animated polygonal mesh and an approximation of this mesh by a convolution surface stand-in that is embedded within it or is attached to it. The motions of both objects are synchronised using a rigging skeleton. We model the interaction between an animated mesh object and a viscoelastic substance, which is normally represented in an implicit form. Our approach is aimed at achieving verisimilitude rather than physically based simulation. The adhesive behaviour of the viscous object is modelled using geometric blending operations on the corresponding implicit surfaces. Another application of this approach is the creation of metamorphosing implicit surface parts that are attached to an animated mesh. A prototype implementation of the proposed approach and several examples of modelling and animation with near real-time preview times are presented. [source]

Exact and Robust (Self-)Intersections for Polygonal Meshes

Embedded Implicit Stand-Ins for Animated Meshes: A Case of Hybrid Modelling

A framework for quad/triangle subdivision surface fitting: Application to mechanical objects

COMPUTER GRAPHICS FORUM, Issue 1 2007
Guillaume Lavoué
Abstract In this paper we present a new framework for subdivision surface approximation of three-dimensional models represented by polygonal meshes. Our approach, particularly suited for mechanical or Computer Aided Design (CAD) parts, produces a mixed quadrangle-triangle control mesh, optimized in terms of face and vertex numbers while remaining independent of the connectivity of the input mesh. Our algorithm begins with a decomposition of the object into surface patches. The main idea is to approximate the region boundaries first and then the interior data. Thus, for each patch, a first step approximates the boundaries with subdivision curves (associated with control polygons) and creates an initial subdivision surface by linking the boundary control points with respect to the lines of curvature of the target surface. Then, a second step optimizes the initial subdivision surface by iteratively moving control points and enriching regions according to the error distribution. The final control mesh defining the whole model is then created assembling every local subdivision control meshes. This control polyhedron is much more compact than the original mesh and visually represents the same shape after several subdivision steps, hence it is particularly suitable for compression and visualization tasks. Experiments conducted on several mechanical models have proven the coherency and the efficiency of our algorithm, compared with existing methods. [source]

Differential Representations for Mesh Processing

COMPUTER GRAPHICS FORUM, Issue 4 2006
Olga Sorkine
Abstract Surface representation and processing is one of the key topics in computer graphics and geometric modeling, since it greatly affects the range of possible applications. In this paper we will present recent advances in geometry processing that are related to the Laplacian processing framework and differential representations. This framework is based on linear operators defined on polygonal meshes, and furnishes a variety of processing applications, such as shape approximation and compact representation, mesh editing, watermarking and morphing. The core of the framework is the definition of differential coordinates and new bases for efficient mesh geometry representation, based on the mesh Laplacian operator. [source]

Polygonal finite elements for topology optimization: A unifying paradigm

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2010
Cameron Talischi
Abstract In topology optimization literature, the parameterization of design is commonly carried out on uniform grids consisting of Lagrangian-type finite elements (e.g. linear quads). These formulations, however, suffer from numerical anomalies such as checkerboard patterns and one-node connections, which has prompted extensive research on these topics. A problem less often noted is that the constrained geometry of these discretizations can cause bias in the orientation of members, leading to mesh-dependent sub-optimal designs. Thus, to address the geometric features of the spatial discretization, we examine the use of unstructured meshes in reducing the influence of mesh geometry on topology optimization solutions. More specifically, we consider polygonal meshes constructed from Voronoi tessellations, which in addition to possessing higher degree of geometric isotropy, allow for greater flexibility in discretizing complex domains without suffering from numerical instabilities. Copyright © 2009 John Wiley & Sons, Ltd. [source]

A freeform shape optimization of complex structures represented by arbitrary polygonal or polyhedral meshes

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004
Jie Shen
Abstract In this paper we propose a new scheme for freeform shape optimization on arbitrary polygonal or polyhedral meshes. The approach consists of three main steps: (1) surface partitioning of polygonal meshes into different patches; (2) a new freeform perturbation scheme of using the Cox,de Boor basis function over arbitrary polygonal meshes, which supports multi-resolution shape optimization and does not require CAD information; (3) freeform shape optimization of arbitrary polygonal or polyhedral meshes. Numerical experiments indicate the effectiveness of the proposed approach. Copyright © 2004 John Wiley & Sons, Ltd. [source]

An implicit edge-based ALE method for the incompressible Navier,Stokes equations,

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2003
Richard W. Smith
Abstract A new finite volume method for the incompressible Navier,Stokes equations, expressed in arbitrary Lagrangian,Eulerian (ALE) form, is presented. The method uses a staggered storage arrangement for the pressure and velocity variables and adopts an edge-based data structure and assembly procedure which is valid for arbitrary n-sided polygonal meshes. Edge formulas are presented for assembling the ALE form of the momentum and pressure equations. An implicit multi-stage time integrator is constructed that is geometrically conservative to the precision of the arithmetic used in the computation. The method is shown to be second-order-accurate in time and space for general time-dependent polygonal meshes. The method is first evaluated using several well-known unsteady incompressible Navier,Stokes problems before being applied to a periodically forced aeroelastic problem and a transient free surface problem. Published in 2003 by John Wiley & Sons, Ltd. [source]

Generation and visualization of large-scale three-dimensional reconstructions from underwater robotic surveys

JOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 1 2010
Matthew Johnson-Roberson
Robust, scalable simultaneous localization and mapping (SLAM) algorithms support the successful deployment of robots in real-world applications. In many cases these platforms deliver vast amounts of sensor data from large-scale, unstructured environments. These data may be difficult to interpret by end users without further processing and suitable visualization tools. We present a robust, automated system for large-scale three-dimensional (3D) reconstruction and visualization that takes stereo imagery from an autonomous underwater vehicle (AUV) and SLAM-based vehicle poses to deliver detailed 3D models of the seafloor in the form of textured polygonal meshes. Our system must cope with thousands of images, lighting conditions that create visual seams when texturing, and possible inconsistencies between stereo meshes arising from errors in calibration, triangulation, and navigation. Our approach breaks down the problem into manageable stages by first estimating local structure and then combining these estimates to recover a composite georeferenced structure using SLAM-based vehicle pose estimates. A texture-mapped surface at multiple scales is then generated that is interactively presented to the user through a visualization engine. We adapt established solutions when possible, with an emphasis on quickly delivering approximate yet visually consistent reconstructions on standard computing hardware. This allows scientists on a research cruise to use our system to design follow-up deployments of the AUV and complementary instruments. To date, this system has been tested on several research cruises in Australian waters and has been used to reliably generate and visualize reconstructions for more than 60 dives covering diverse habitats and representing hundreds of linear kilometers of survey. © 2009 Wiley Periodicals, Inc. [source]