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Voronoi diagrams on piecewise flat surfaces and an application to biological growth

C. Indermitte, Th.M. Liebling, M. Troyanov, H. Clémençon
2001 Theoretical Computer Science  
An application to biological membrane growth modeling is then given.  ...  This paper introduces the notion of Voronoi diagrams and Delaunay triangulations generated by the vertices of a piecewise at, triangulated surface.  ...  Thesis, [2] , where a more detailed account of the models and their biological validation can be found. Partial ÿnancial support from the Swiss National Science Foundation is gratefully acknowledged.  ... 
doi:10.1016/s0304-3975(00)00248-6 fatcat:ceykwwf4vvggpnkaxakilc6qta

Page 3399 of Mathematical Reviews Vol. , Issue 2002E [page]

2002 Mathematical Reviews  
(CH-LAUS-BSG; Lausanne) Voronoi diagrams on piecewise flat surfaces and an application to biological growth. (English summary) Combinatorics and computer science (Palaiseau, 1997). Theoret. Comput.  ...  An application to biological membrane growth modeling is then given.  ... 

Approximating the Pathway Axis and the Persistence Diagrams for a Collection of Balls in 3-Space

Eitan Yaffe, Dan Halperin
2010 Discrete & Computational Geometry  
We present an algorithm that constructs the pathway graph of ∪B, a piecewise-linear approximation of the pathway axis.  ...  We employ this bound and the approximation scheme to show how to approximate the persistence diagrams of ∪B, which can be used to extract major topological features such as the large voids and tunnels  ...  Note that the sample balls which constitute an ε-flower of a ball B = B(x, r) are tangent to the surface of B from the inside and are centered on the boundary surface of B(x, r − 1); see Figure 3 for  ... 
doi:10.1007/s00454-009-9240-9 fatcat:hsc636xjbndehlh2jvrjhviuee

A Toroidal Maxwell-Cremona-Delaunay Correspondence [article]

Jeff Erickson, Patrick Lin
2022 arXiv   pre-print
We establish a weaker correspondence: Every positive equilibrium embedding on any flat torus is affinely equivalent to a reciprocal/coherent embedding on some flat torus.  ...  On any flat torus, reciprocal and coherent embeddings are equivalent, and every reciprocal embedding is in positive equilibrium, but not every positive equilibrium embedding is reciprocal.  ...  Voronoi diagrams on piecewise flat surfaces and an application to biological growth. Theoret. Comput. Sci. [ ] Charles L. Lawson. Transforming triangulations.  ... 
arXiv:2003.10057v3 fatcat:lqxciqwhlnd3xfj4lzw72olbym

Stresses and Liftings of Cell-Complexes

K. Rybnikov
1999 Discrete & Computational Geometry  
As an application, two algorithms are given that determine whether a piecewise-linear realization of a d-manifold in R d admits a lifting to R d+1 which satisfies given constraints.  ...  We also demonstrate connections between stresses and Voronoi-Dirichlet diagrams and show that any weighted Voronoi-Dirichlet diagram without non-compact cells can be represented as a weighted Delaunay  ...  Ryshkov and W. Whiteley.  ... 
doi:10.1007/pl00009434 fatcat:p6lp5j56r5ehbp5qtqxmevwx5e

Segmenting Motifs in Protein-Protein Interface Surfaces [chapter]

Jeff M. Phillips, Johannes Rudolph, Pankaj K. Agarwal
2006 Lecture Notes in Computer Science  
Specifically, we define a method for identifying a set of structural motifs on protein-protein interface surfaces.  ...  These motifs are generated entirely from geometric properties and are easily annotated with additional biological data. We point to the use of these motifs in analyzing hotspot residues.  ...  Acknowledgments We thank Tammy Bailey and Herbert Edelsbrunner for observations and suggestions and Jeffrey Headd for help integrating the motifs into the MAPS software.  ... 
doi:10.1007/11851561_20 fatcat:ejgxxnocbza2vackq6vpkm65ai

Finite Element Decomposition of Human Neocortex [chapter]

David A. Batte, Travis S. Chow, Bruce H. McCormick
1998 Computational Neuroscience  
The finite elements provide the boundaries for numerical grid generators to establish boundary-conforming local coordinate systems for the systematic study and visualization of cortical neuron populations  ...  The decomposition method is implemented with a newly developed set of object-oriented software tools. iv To my parents v ACKNOWLEDGEMENTS  ...  The third type of tetrahedra T 12 , which are those with one edge in P 1 and another in P 2 , is constructed by finding the intersection of edges between the Voronoi diagram of P 1 with the Voronoi diagram  ... 
doi:10.1007/978-1-4615-4831-7_95 fatcat:rjafsifzmng2xb2mbv2mpyifdy

Analysis and applications of the Voronoi Implicit Interface Method

R.I. Saye, J.A. Sethian
2012 Journal of Computational Physics  
effects of varying density, viscosity and surface tension on a per-phase basis.  ...  In this paper, we present the method in detail, and demonstrate several new extensions of the method to different physical phenomena, including curvature flow with surface energy densities defined on a  ...  The Voronoi reconstruction Recall that the Voronoi diagram of a set of nodes in R n is a tessellation of R n into Voronoi cells, defined so that all the points in each cell are closer to one particular  ... 
doi:10.1016/ fatcat:4zmg42wnyjdwjlctpduualbhfu

The Geometry of Bubbles and Foams [chapter]

John M. Sullivan
1999 Foams and Emulsions  
The resulting surfaces have constant mean curvature and an invariant notion of equilibrium forces.  ...  We examine certain restrictions on the combinatorics of triangulations and some useful ways to construct triangulations.  ...  The author's vcs software for computing Voronoi diagrams [47] in three dimensions can send its output to Brakke's Surface Evolver [5] .  ... 
doi:10.1007/978-94-015-9157-7_23 fatcat:rrxr2ryyfzeq3amdqjeve7ifui

Shaping the Organ: A Biologist Guide to Quantitative Models of Plant Morphogenesis

Marco Marconi, Krzysztof Wabnik
2021 Frontiers in Plant Science  
We then provide an overview of the most common types of "digital plant" paradigms, and demonstrate how models benefit from diverse techniques used to describe cell growth mechanics.  ...  Because of the large body of data being produced by modern laboratories, solving this complexity requires the application of computational techniques and analyses.  ...  GFtbox, is a MATLAB application devised for flat organs commonly such as leaf and petal, but it is also compatible with other organ forms.  ... 
doi:10.3389/fpls.2021.746183 pmid:34675952 pmcid:PMC8523991 fatcat:ogsdtdbtgzelvoqu4lzibuk2aa

Phase-field modeling of crystal nucleation in undercooled liquids – A review

László Gránásy, Gyula I. Tóth, James A. Warren, Frigyes Podmaniczky, György Tegze, László Rátkai, Tamás Pusztai
2019 Progress in Materials Science  
We review how phase-field models contributed to the understanding of various aspects of crystal nucleation including homogeneous and heterogeneous processes, and their role in microstructure evolution.  ...  between the growth controlled cellular and the nucleation dominated equiaxial solidification morphologies.  ...  Sosso and A. Michaelides for the tabulated data on ice nucleation. This work was supported by the National Agency for Research, Development, and Innovation, Hungary (NKFIH) under Contract Nos.  ... 
doi:10.1016/j.pmatsci.2019.05.002 fatcat:hpgt477pojdxvny5oa45r27k5a

Interfaces and Free Boundaries: Analysis, Control and Simulation

Charles Elliott, Yoshikazu Giga, Michael Hinze, Vanessa Styles
2013 Oberwolfach Reports  
The aim of the workshop here was to focus on emerging new themes and developments in these fields and to establish and extend links between them.  ...  The governing equations for the dynamics of the interfaces in many of these applications involve surface tension expressed in terms of the mean curvature and a driving force.  ...  Interface development in biological tissue growth John R.  ... 
doi:10.4171/owr/2013/15 fatcat:fkpzvxt6a5bhdpswg6tyhuxusq

Advanced Algorithms of Collision Free Navigation and Flocking for Autonomous UAVs [article]

Taha Elmokadem
2021 arXiv   pre-print
This is a very challenging problem due to several factors such as the high complexity of UAV applications, operation in harsh environments, limited payload and onboard computing power and highly nonlinear  ...  General 3D kinematic models are considered in the design which makes these methods applicable to different UAV types in addition to underwater vehicles.  ...  .) • Geometric (ex. cell decomposition, generalized Voronoi diagrams, visibility graphs, etc.) • Sampling-based (ex.  ... 
arXiv:2111.00166v1 fatcat:5jnrdu24xrbhraqzucsfsadl4y

Fracture modeling in computer graphics

Lien Muguercia, Carles Bosch, Gustavo Patow
2014 Computers & graphics  
This process is one of the aging phenomena with an important amount of work done, due to its complexity and its extended application area.  ...  This master thesis focuses on the study of the state of the art on crack and fracture modeling.  ...  Acknowledgements I want to thank my advisor Carles Bosch for helping me and encouraging me.  ... 
doi:10.1016/j.cag.2014.08.006 fatcat:e2c7646tkbcozlmi22cvvcysim

A Multicellular Model of Intestinal Crypt Buckling and Fission

Axel A. Almet, Barry D. Hughes, Kerry A. Landman, Inke S. Näthke, James M. Osborne
2017 Bulletin of Mathematical Biology  
Crypt fission is an in vivo tissue deformation process that is involved in both intestinal homeostasis and colorectal tumourigenesis.  ...  Drawing inspiration from observations of organoid growth and fission in vivo, we develop a computational model of a deformable epithelial tissue layer.  ...  Cell birth and death In order to model continuous growth of the epithelial layer, epithelial cells are able to proliferate ad infinitum.  ... 
doi:10.1007/s11538-017-0377-z pmid:29234982 fatcat:kbmuah33ebahdn7hec5qqnzjba
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