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A mapping-independent primitive for the triangulation of parametric surfaces

Marco Attene, Bianca Falcidieno, Michela Spagnuolo, Geoff Wyvill
2003 Graphical Models  
This paper describes a new technique for the triangulation of parametric surfaces.  ...  Conversely, we use a local tessellation primitive to sample and triangulate the surface. The sampling is almost uniform and the parameterization becomes irrelevant.  ...  The authors thank all the members of the Computer Graphics Group of the IMATI-GE/CNR and the ones of the Computer Graphics and Vision Lab of the University of Otago, for their encouragement in writing  ... 
doi:10.1016/s1524-0703(03)00048-1 fatcat:onzzudvj4va5rkz2mlnn2xllci

Radiative transfer sensitivity to the accuracy of canopy structure description. The case of a maize canopy

Marisa España, Frédéric Baret, Frank Aries, Bruno Andrieu, Michaël Chelle
1999 Agronomie  
We then finally degraded canopy architecture by dividing by a factor of 10 the number of triangles used in the previous representation.  ...  We showed that 24 plants allowed us to obtain an accurate representation of the gap fraction and the leaf angle distribution function with the finest triangulation level studied, i.e. with triangles smaller  ...  España and funds coming from the Programme National de Télédétection Spatiale in France. We thank also very much P. Clastre for his assistance in computation.  ... 
doi:10.1051/agro:19990305 fatcat:wd7vfg54sjdzbeqzolrffangfu

Animating images with drawings

Peter Litwinowicz, Lance Williams
1994 Proceedings of the 21st annual conference on Computer graphics and interactive techniques - SIGGRAPH '94  
The work described here extends the power of 2D animation with a form of texture mapping conveniently controlled by line drawings.  ...  By employing numerics developed in the computer vision community for rapid visual surface estimation, several important advantages are realized.  ...  Acknowledgments The authors would like to extend heartfelt thanks to Laurence Arcadias for the cartoon face animated in our illustrations, and to Subhana Ansari for layout.  ... 
doi:10.1145/192161.192270 dblp:conf/siggraph/LitwinowiczW94 fatcat:uqz5kwiyjja4xdy4sp45zo7rci

Deformations of Period Lattices of Flexible Polyhedral Surfaces

Alexander A. Gaifullin, Sergey A. Gaifullin
2014 Discrete & Computational Geometry  
The main result is that the period lattice of a flexible two-periodic surface homeomorphic to a plane cannot have two degrees of freedom.  ...  One of the most important results in this field is a theorem of Sabitov asserting that the volume of a flexible polyhedron is constant during the flexion.  ...  A mapping of a simplicial complex K 1 to a simplicial complex K 2 is called simplicial if it maps every simplex of K 1 linearly onto a simplex of K 2 .  ... 
doi:10.1007/s00454-014-9575-8 fatcat:3rwcpgwg4zda5mvrvbdifsyvgm

Para-Graph: Graph-Based Parameterization of Triangle Meshes with Arbitrary Genus

Giuseppe Patane, Michela Spagnuolo, Bianca Falcidieno
2004 Computer graphics forum (Print)  
A topology-based decomposition of the shape is computed and used to segment the shape into primitives, which define a chart decomposition of the mesh.  ...  The application of the parameterization approach to remeshing guarantees that extraordinary vertices are localized only where two patches share a boundary and they are not scattered on the whole surface  ...  Acknowledgments This work has been supported by the EC-IST FP6 Network of Excellence 'AIM@SHAPE'.  ... 
doi:10.1111/j.1467-8659.2004.00808.x fatcat:ovaulsdibnd6pb7unmmgikvi2u

Visualizing Minimal Surfaces

Michael Melko
2010 The Mathematica Journal  
In this article, we describe the mathematics of minimal surfaces in some detail, and then we present a Mathematica package for generating solid model data of such surfaces.  ...  In particular, we show how the package was used to generate a 3D model of Costa's surface.  ...  Loosely speaking, the Weierstrass representation provides a recipe for creating a parametrization of a minimal surface in  3 from two meromorphic functions defined on a Riemann surface.  ... 
doi:10.3888/tmj.12-6 fatcat:3rpnqzhf25cqhcvqahpstbt7ge

Surface distance maps

Avneesh Sud, Naga Govindaraju, Russell Gayle, Erik Andersen, Dinesh Manocha
2007 Graphics Interface  
We present an interactive algorithm for computing the surface distance map of triangulated meshes using graphics hardware.  ...  Given a set of orientable 2-manifold primitives, the surface distance map represents the (non-zero) signed distance-toclosest-primitive mapping at each point on a 2-manifold.  ...  We would like to acknowledge members of UNC GAMMA and the reviewers useful comments and feedback.  ... 
doi:10.1145/1268517.1268525 dblp:conf/graphicsinterface/SudGGAM07 fatcat:izuguxuqh5dwpeocvnexhprq3u

Using exact geometry information in finite element computations [article]

Luca Heltai, Wolfgang Bangerth, Martin Kronbichler, Andrea Mola
2019 arXiv   pre-print
The traditional workflow in continuum mechanics simulations is that a geometry description -- obtained using Constructive Solid Geometry or Computer Aided Design tools -- forms the input for a mesh generator  ...  We then show that it is possible to provide these primitives in all of the commonly used ways in which geometries are described in common industrial workflows.  ...  As a result, the final mesh is water-tight, and independent of the CAD surface parametrization and patch distribution.  ... 
arXiv:1910.09824v1 fatcat:fzo7sedvoba5tf7bdsmfjxzaqq

The virtual mesh: a geometric abstraction for efficiently computing radiosity

L. Alonso, F. Cuny, S. Petit Jean, J.-C. Paul, S. Lazard, E. Wies
2001 ACM Transactions on Graphics  
In this paper, we introduce a general-purpose method for computing radiosity on scenes made of parametric surfaces with arbitrary trimming curves.  ...  The virtual mesh is a collection of normalized square domains to which the input surfaces are mapped while preserving their energy properties.  ...  of classical push-pull coefficients (namely, their independence on the level of the hierarchy) to be transfered to general parametric surfaces.  ... 
doi:10.1145/501786.501789 fatcat:y4ujmqunqvcwrl2v2yqt5j77fi

Texture Atlas Generation for Inconsistent Meshes and Point Sets

Patrick Degener, Reinhard Klein
2007 IEEE International Conference on Shape Modeling and Applications 2007 (SMI '07)  
In the spirit of classical two-part mapping an intermediate proxy surface is created that can be processed by high quality texture mapping tools.  ...  The texture signal is transfered to the original geometry using a novel mapping technique.  ...  Although smoothing of the normal field can reduce such artifacts, the choice of a connectivity independent smoothing that guarantees a robust mapping is unclear. • Assuming that the surface S has a correct  ... 
doi:10.1109/smi.2007.35 dblp:conf/smi/DegenerK07 fatcat:7tcag27g3bgd7ert4t4wry7rx4

Corner-Sharing Tetrahedra for Modeling Micro-Structure [article]

Meera Sitharam, Jeremy Youngquist, Maxwell Nolan, Jörg Peters
2018 arXiv   pre-print
The paper develops a palette of simple geometry processing operations on CoSTs including graph manipulation, hierarchical refinement, randomization, and generating associated continuous representations  ...  We propose modeling micro-structure with a class of discrete Corner-Sharing Tetrahedra (CoSTs).  ...  A configuration of the joints given by a map p : V → R d and is a bar-joint D-rep realization of (G, δ) if the distance between p(u) and p(v) is δ(u, v) for all (u, v) ∈ E.  ... 
arXiv:1806.05528v1 fatcat:a5arrposebdilpoubdul3ju3te

Hex-dominant meshing: Mind the gap!

Nicolas Ray, Dmitry Sokolov, Maxence Reberol, Franck Ledoux, Bruno Lévy
2018 Computer-Aided Design  
Obviously, this surface must be a good approximation of the original object but, more importantly, it must be possible to remesh the volume bounded by this surface minus the extracted hexahedra (called  ...  We tested our method on a large collection of objects (200+) with different settings. In most cases, we obtained results of very good quality as compared to the state-of-the-art solutions.  ...  When our surface contains quad facets, both possible triangulations of the quad are tested.  ... 
doi:10.1016/j.cad.2018.04.012 fatcat:dtpoo2hoffgetgqvh27lux4jqi

Generic deformable implicit mesh models for automated reconstruction

S. Ilic, P. Fua
2003 First IEEE International Workshop on Higher-Level Knowledge in 3D Modeling and Motion Analysis, 2003. HLK 2003.  
To combine the strength of both approaches, we propose a method that can turn a completely arbitrary triangulated mesh, such as one taken from the web, into an implicit surface that closely approximates  ...  of the attractive properties of implicit surfaces.  ...  Here the FFDs ability to deform parametric surfaces has been exploited, but only to reshape a single primitive.  ... 
doi:10.1109/hlk.2003.1240856 dblp:conf/hlk/IlicF03 fatcat:iq22dcrmlnenbalyqtnxpu7ru4

Dynamics on the PSL(2,C)-character variety of a twisted I-bundle [article]

Michelle Lee
2011 arXiv   pre-print
Let M be a twisted interval bundle over a nonorientable hyperbolizable surface. Let X(M) be the PSL(2,C)-character variety of \pi_1(M).  ...  Further, we identify which discrete and faithful representations can lie in a domain of discontinuity for the action of Out(\pi_1(M)) on X(M).  ...  The maph i is a simplicial hyperbolic surface containing γ i andθ(γ i ) where the associated triangulation is the preimage of the triangulation on B.  ... 
arXiv:1103.3479v1 fatcat:4bagcxo6y5bqdpap4syadawsra

Reliable Implicit Surface Polygonization using Visibility Mapping [article]

Gokul Varadhan, Shankar Krishnan, Liangjun Zhang, Dinesh Manocha
2006 Symposium on geometry processing : [proceedings]. Symposium on Geometry Processing  
Based on these maps, we compute a homeomorphic and watertight triangulation as well as a parameterization of the implicit surface.  ...  We present a new algorithm to compute a topologically and geometrically accurate triangulation of an implicit surface.  ...  In this section, we present our algorithm to polygonize each patch independently and to generate a watertight triangulation of the implicit surface.  ... 
doi:10.2312/sgp/sgp06/211-221 fatcat:b2ytgvgsrzf4xfs56ok2hbsupa
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