From martin at farach-colton.com Wed Jul 3 10:18:21 2002
From: martin at farach-colton.com (Martin Farach-Colton)
Date: Mon Jan 9 13:41:06 2006
Subject: Reminder: SODA Deadline July 9th
Message-ID: <7E1220C5-8EA0-11D6-B3BD-00039388DD2E@farach-colton.com>
See CFP @ http://www.siam.org/meetings/da03/
See http://cmt.research.microsoft.com/SODA03/ for submission procedure.
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From aupetit at dase.bruyeres.cea.fr Mon Jul 1 12:41:35 2002
From: aupetit at dase.bruyeres.cea.fr (aupetit)
Date: Mon Jan 9 13:41:06 2006
Subject: Nearest Neighbor searching with Delaunay...
Message-ID: <200207010941.LAA26371@tupai.bruyeres.cea.fr>
Hello,
Locating the nearest neighbor (NN) of a
query point in a finite set of n reference points
is in O(n). But if we construct the Delaunay
triangulation of the reference points, then it
should be easier to find the NN of any query
point by marching along the graph structure from
a current reference point to its neighbor which is the
closest to the query, considering this as the new
current reference, and iterating until no neighbors are
closer to the query than the current reference
(i.e. steepest descent onto the graph considering the distance
between the current reference and the query).
Is there any paper using this approach or theorem
proving that using such steepest descent on the
Delaunay triangulation leads to a unique global optimum?
Thank you for your help.
Michael Aupetit
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From lhf at visgraf.impa.br Wed Jul 3 13:37:58 2002
From: lhf at visgraf.impa.br (Luiz Henrique de Figueiredo)
Date: Mon Jan 9 13:41:07 2006
Subject: IV Brazilian Symposium on GeoInformatics - Call for Papers
Message-ID: <200207031537.g63Fbwm05767@Newton.visgraf.impa.br>
------------------------------------------------------------------------
IV Brazilian Symposium on GeoInformatics - GeoInfo 2002
December 5-6 2002 - Hotel Gloria - Caxambu - Minas Gerais - Brazil
------------------------------------------------------------------------
(Apologies for cross-postings)
PRELIMINARY CALL FOR PAPERS
GeoInfo 2002 is an annual forum for exploring ongoing research,
development and innovative applications on geographic information
science and related areas, including, but not limited to, the
following fields:
* Spatial databases
* Spatial and spatio-temporal data modeling
* Interoperability and standards in GIS
* Ontologies for spatial data
* Spatial metadata
* Spatial, spatio-temporal, and multidimensional access methods
* Spatial queries processing and optimization
* Multiple representations in spatial databases
* Intrgrity constraints in spatio-temporal databases
* Geospatial versioning
* Graphical aspects of GIS and spatial databases
* Vector and raster data management issues
* Computational geometry
* Virtual reality and 3D GIS
* Large volume GIS servers and parallel GIS
* Visual query languages
* Similarity search
* GIS and Internet
* Location-based services
* Mobile and distributed geographic information services
* Real-time spatio-temporal GIS
* Spatial data warehouses and decision support systems
* Spatial and spatio-temporal data mining, knowledge discovery
* Spatial data quality
* Content-based image retrieval
* Geostatistics
* Spatial analysis and spatial statistics
* Innovative applications of geotechnologies
Papers should describe original research, ongoing (preferably) or
recently completed. Papers can be submitted in Portuguese, English
or Spanish, and are limited to 8 pages. Complete instructions and
further information are available at
http://www.pbh.gov.br/prodabel/cde/geoinfo2002.
IMPORTANT DATES
August 30, 2002 - Paper submission
September 30, 2002 - Notification of acceptance
October 15, 2002 - Camera-ready version
December 5-6, 2002 - GeoInfo 2002 at Caxambu, Minas Gerais, Brazil
PROGRAM COMMITTEE
Clodoveu Davis (PRODABEL) (coordinator)
Karla Albuquerque de Vasconcelos Borges (PRODABEL) (coordinator)
Alberto Laender (UFMG)
Ana Carolina Salgado (UFPE)
Antônio Miguel Monteiro (INPE)
Arnaldo de Albuquerque Araújo (UFMG)
Cirano Iochpe (UFRGS)
Cláudia Bauzer Medeiros (UNICAMP)
Frederico Fonseca (Penn State)
Gilberto Câmara (INPE)
Jansle Vieira Rocha (UNICAMP)
José Luiz de Souza Pio (FUA)
João Argemiro Paiva (INPE)
Jugurta Lisboa Filho (UFV)
Luiz Henrique de Figueiredo (IMPA)
Max Egenhofer (University of Maine)
Valeria Times (UFPE)
(other names to be confirmed)
EXECUTIVE COMMITTEE
Antonio Miguel Monteiro (INPE)
Clodoveu Davis (PRODABEL)
Gilberto Camara (INPE)
Maria da Piedade Oliveira (PRODABEL)
------------------------------------------------------------------------
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From mast at sbox.tugraz.at Tue Jul 9 11:05:23 2002
From: mast at sbox.tugraz.at (Martin Stettner)
Date: Mon Jan 9 13:41:07 2006
Subject: Nearest Neighbor searching with Delaunay...
In-Reply-To: <200207010941.LAA26371@tupai.bruyeres.cea.fr>
Message-ID: <000701c2271f$62cb1120$014ba8c0@martin>
Hi,
I'm not sure if I understand your intentions but I think that your
approach would not be useful: By building the Delaunay triangulation of
a point set you can easily obtain a point location structure which
allows to locate a new point in O(lg n) time.
cf.
Mark de Berg et al.
Computational Geometry - Algorithms an Applications
p. 194f
kind regards
Martin Stettner
Micahel Aupetit wrote
>
> Hello,
>
> Locating the nearest neighbor (NN) of a
> query point in a finite set of n reference points
> is in O(n). But if we construct the Delaunay
> triangulation of the reference points, then it
> should be easier to find the NN of any query
> point by marching along the graph structure from
> a current reference point to its neighbor which is the
> closest to the query, considering this as the new
> current reference, and iterating until no neighbors are
> closer to the query than the current reference
> (i.e. steepest descent onto the graph considering the
> distance between the current reference and the query).
>
> Is there any paper using this approach or theorem
> proving that using such steepest descent on the
> Delaunay triangulation leads to a unique global optimum?
>
> Thank you for your help.
>
> Michael Aupetit
>
>
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From jrs at buffy.EECS.Berkeley.EDU Sun Jul 7 22:42:17 2002
From: jrs at buffy.EECS.Berkeley.EDU (Jonathan Shewchuk)
Date: Mon Jan 9 13:41:07 2006
Subject: Nearest Neighbor searching with Delaunay...
In-Reply-To: Your message of "Mon, 01 Jul 2002 11:41:35 +0200."
<200207010941.LAA26371@tupai.bruyeres.cea.fr>
Message-ID: <200207080442.VAA16919@buffy.EECS.Berkeley.EDU>
Michael Aupetit asks:
> Locating the nearest neighbor (NN) of a
> query point in a finite set of n reference points
> is in O(n). But if we construct the Delaunay
> triangulation of the reference points, then it
> should be easier to find the NN of any query
> point by marching along the graph structure from
> a current reference point to its neighbor which is the
> closest to the query, considering this as the new
> current reference, and iterating until no neighbors are
> closer to the query than the current reference
> (i.e. steepest descent onto the graph considering the distance
> between the current reference and the query).
>
> Is there any paper using this approach or theorem
> proving that using such steepest descent on the
> Delaunay triangulation leads to a unique global optimum?
I am not aware of such a paper, but there must have been one (if not dozens).
Here's a "proof" that you will find a global optimum (though obviously it
might not be unique).
It's well known that the Delaunay triangulation is isomorphic to the lower
convex hull of the "lifted" point set. (Edelsbrunner and Seidel, Discrete &
Computational Geometry 1:25-44, 1986.) The "lifting map" maps each vertex
v of the d-dimensional DT to a vertex (v, |v|^2) in d+1 dimensions. The
downward-facing facets of the d+1 dimensional convex hull of the lifted
vertices correspond to the d-simplices of the DT. (I have a picture of a
lifting map at the bottom of http://www.cs.berkeley.edu/~jrs/stab.html if
you want to get a clearer idea.)
So the procedure you describe is the simplex algorithm for linear programming.
For instance, take your DT, translate it so the query point is at the origin,
and apply the lifting map to the translated vertices. Note that the height to
which each vertex is lifted, |v|^2, is its distance from the query point.
The goal is to find the lowest lifted vertex (i.e. the one lifted to the
least height) of the convex hull, which is a linear programming problem.
Jonathan Shewchuk
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From johnh at wv.mentorg.com Wed Jul 10 18:51:11 2002
From: johnh at wv.mentorg.com (John Hershberger)
Date: Mon Jan 9 13:41:07 2006
Subject: Nearest Neighbor searching with Delaunay...
In-Reply-To: <200207080442.VAA16919@buffy.EECS.Berkeley.EDU>
Message-ID:
Michael Aupetit asks:
> Locating the nearest neighbor (NN) of a
> query point in a finite set of n reference points
> is in O(n). But if we construct the Delaunay
> triangulation of the reference points, then it
> should be easier to find the NN of any query
> point by marching along the graph structure from
> a current reference point to its neighbor which is the
> closest to the query, considering this as the new
> current reference, and iterating until no neighbors are
> closer to the query than the current reference
> (i.e. steepest descent onto the graph considering the distance
> between the current reference and the query).
>
> Is there any paper using this approach or theorem
> proving that using such steepest descent on the
> Delaunay triangulation leads to a unique global optimum?
Jonathan Shewchuk replies:
> I am not aware of such a paper, but there must have been one (if not dozens).
> Here's a "proof" that you will find a global optimum (though obviously it
> might not be unique).
....and then goes on to give a nice argument that the search procedure
is really the simplex algorithm on the convex hull of lifted points.
The idea of searching for nearest neighbors using the Delaunay
triangulation was used by Dickerson and Drysdale. I've appended
relevant Geombib citations below.
--John Hershberger
@article{dd-frnns-90
, author = "M. T. Dickerson and R. S. Drysdale"
, title = "Fixed-radius near neighbor search algorithms for points and segments"
, journal = "Inform. Process. Lett."
, volume = 35
, year = 1990
, pages = "269--273"
, keywords = "near neighbor search, Delaunay triangulation"
, update = "93.09 drysdale"
}
@inproceedings{dd-ekdnp-91
, author = "M. T. Dickerson and R. L. Drysdale"
, title = "Enumerating $k$ distances for $n$ points in the plane"
, booktitle = "Proc. 7th Annu. ACM Sympos. Comput. Geom."
, year = 1991
, pages = "234--238"
, keywords = "Delaunay triangulation, proximity, enumeration"
, precedes = "dds-saeid-92"
, cites = "aass-sdp-90, bfprt-tbs-73, c-ntcos-85, dd-frnns-90, s-mmdpsl-90t, sh-cpp-75, y-cmstk-82, ZZZ"
, update = "97.11 bibrelex, 93.09 drysdale"
}
@article{dds-saeid-92
, author = "M. T. Dickerson and R. L. Drysdale and J. R. Sack"
, title = "Simple algorithms for enumerating interpoint distances and finding $k$ nearest neighbors"
, journal = "Internat. J. Comput. Geom. Appl."
, volume = 2
, number = 3
, year = 1992
, pages = "221--239"
, keywords = "enumeration, selection, Delaunay triangulation, nearest neighbors"
, succeeds = "dd-ekdnp-91"
, update = "94.01 smid"
}
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From lewis at bway.net Thu Jul 11 15:12:55 2002
From: lewis at bway.net (Robert H. Lewis)
Date: Mon Jan 9 13:41:07 2006
Subject: Fermat point in three-space
In-Reply-To:
Message-ID:
Hello,
The Fermat point of a triangle ABC is the point, say P, that
minimizes the sum of the distances d(z,A) + d(z,B) + d(z,C) where z is
any point in the plane. There was a good article on this in a recent
(May, I think) issue of the American Mathematical Monthly. If all the
angles in ABC are less than 120 degrees, P is inside ABC. Otherwise
it's one of the vertices.
I couldn't find there any reference to the generalization to
3-space. It seems there are two generalizations: Given a tetrahedron
ABCD,
(1) find the point that minimizes the sum d(z,A) + d(z,B) + d(z,C) +
d(z,D).
(2) find the point that minimizes the sum of the areas of the
triangles formed by z and the six edges of ABCD (assume z is inside ABCD).
Searching the web, I found only a comment (no proof) that soap films
assume the minimizing form on a wire frame tetrahedron. That would be
problem (2).
Any information on this problem would be of interest.
Robert H. Lewis
Mathematics
Fordham University
Bronx NY
rlewis@fordham.edu
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From shlomo.anglister at intel.com Sun Jul 14 09:34:23 2002
From: shlomo.anglister at intel.com (Anglister, Shlomo)
Date: Mon Jan 9 13:41:07 2006
Subject: Fermat point in three-space
Message-ID: <7C0E66E1B97BD5119B120002A50A63D202BFC345@hasmsx101.iil.intel.com>
Hi,
What you refer to as a Fermat point in space, can be called a "Steiner point
in space".
There is an abundance of data in this area.
Soap bubbles is an old one, Bell used it many years ago to connect US major
cities.
Shlomo
-----Original Message-----
From: Robert H. Lewis [mailto:lewis@bway.net]
Sent: Thursday, July 11, 2002 9:13 PM
To: compgeom-discuss@research.bell-labs.com
Subject: Fermat point in three-space
Hello,
The Fermat point of a triangle ABC is the point, say P, that
minimizes the sum of the distances d(z,A) + d(z,B) + d(z,C) where z is
any point in the plane. There was a good article on this in a recent
(May, I think) issue of the American Mathematical Monthly. If all the
angles in ABC are less than 120 degrees, P is inside ABC. Otherwise
it's one of the vertices.
I couldn't find there any reference to the generalization to
3-space. It seems there are two generalizations: Given a tetrahedron
ABCD,
(1) find the point that minimizes the sum d(z,A) + d(z,B) + d(z,C) +
d(z,D).
(2) find the point that minimizes the sum of the areas of the
triangles formed by z and the six edges of ABCD (assume z is inside ABCD).
Searching the web, I found only a comment (no proof) that soap films
assume the minimizing form on a wire frame tetrahedron. That would be
problem (2).
Any information on this problem would be of interest.
Robert H. Lewis
Mathematics
Fordham University
Bronx NY
rlewis@fordham.edu
-------------
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From pankaj at cs.duke.edu Wed Jul 17 09:51:32 2002
From: pankaj at cs.duke.edu (Pankaj Kumar Agarwal)
Date: Mon Jan 9 13:41:07 2006
Subject: DIMACS Workshop: Modeling Motion
Message-ID: <200207171251.IAA23213@kant.cs.duke.edu>
=============================================================================
********************************************************************
* DIMACS *
* Center for Discrete Mathematics and Theoretical Computer Science *
* Founded as a National Science and Technology Center *
********************************************************************
DIMACS Workshop on Algorithmic Issues in Modeling Motion
Date: November 18 - 20, 2002
Location: DIMACS Center, Rutgers University, Piscataway NJ, 08854-8018
Organizers:
Pankaj K. Agarwal, Duke University, pankaj@cs.duke.edu
Leonidas J. Guibas, Stanford University, guibas@cs.stanford.edu
Presented under the auspices of the DIMACS Special Focus on
Computational Geometry and Applications.
Rationale:
Motion, like shape, is one of the fundamental modalities to be modeled
in order to represent and manipulate the physical world in a
computer. As such, motion representations and the algorithms that
operate on them are central to all computational disciplines dealing
with physical objects: computer graphics, computer vision, robotics,
etc. Modeling motion is also crucial for other disciplines dealing
with temporally varying data, including mobile networks, temporal data
bases, etc. Motion algorithms require computational resources, and
frequently sensing and communication resources as well, in order to
accomplish their task. Despite the prominent position that motion
plays in so many computer disciplines, little has been done to date to
provide a clean conceptual framework for representing motion,
describing algorithms on moving objects, and analyzing their behavior
and performance.
Scope and Format:
This workshop aims to bring together people from the different
research communities interested in algorithmic issues related to
moving objects. The workshop will address core algorithmic issues as
well as aspects of modeling and analyzing motion. The goal is to
debate and discuss the issues in representing, processing, reasoning,
analyzing, searching, and visualizing moving objects; to identify key
research issues that need to be addressed, and to help establish
relationships which can be used to strengthen and foster collaboration
across the different areas.
Call for Participation:
Authors are invited to submit abstracts for talks to be given at the
workshop. Please send the organizers an abstract (up to 2 pages) and a
draft of a paper (if you have one). (Since there are no formal
proceedings for the workshop, submission of material that is to be
submitted to (or to appear in) a refereed conference is allowed and
encouraged.) Submissions will be due October 15, 2002.
Notification of acceptance: October 31, 2002.
Invited Speakers:
Mark de Berg, Utrecht University
David Mount, University of Maryland
Dinesh Pai, University of British Columbia
Ileana Streinu, Smith College
Carlo Tomasi, Duke University
Feng Zhao, Xerox Corporation
Registration: (Pre-registration date: November 11, 2002)
Regular rate
Preregister before deadline $120/day
After preregistration deadline $140/day
Reduced Rate*
Preregister before deadline $60/day
After preregistration deadline $70/day
Postdocs
Preregister before deadline $10/day
After preregistration deadline $15/day
DIMACS Postdocs $0
Non-Local Graduate & Undergraduate students
Preregister before deadline $5/day
After preregistration deadline $10/day
Local Graduate & Undergraduate students $0
(Rutgers & Princeton)
DIMACS partner institution employees** $0
DIMACS long-term visitors*** $0
Registration fee to be collected on site, cash, check, VISA/Mastercard
accepted.
Our funding agencies require that we charge a registration fee for the
workshop. Registration fees cover participation in the workshop, all
workshop materials, breakfast, lunch, breaks, and any scheduled social
events (if applicable).
* College/University faculty and employees of non-profit organizations
will automatically receive the reduced rate. Other participants may
apply for a reduction of fees. They should email their request for the
reduced fee to the Workshop Coordinator at
workshop@dimacs.rutgers.edu. Include your name, the Institution you
work for, your job title and a brief explanation of your
situation. All requests for reduced rates must be received before the
preregistration deadline. You will promptly be notified as to the
decision about it.
** Fees for employees of DIMACS partner institutions are
waived. DIMACS partner institutions are: Rutgers University, Princeton
University, AT&T Labs - Research, Avaya, Bell Labs, NEC Research
Institute and Telcordia Technologies.
***DIMACS long-term visitors who are in residence at DIMACS for two or
more weeks inclusive of dates of workshop.
Information on participation, registration, accommodations, and travel
can be found at:
http://dimacs.rutgers.edu/Workshops/Issues/index.html
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From goodrich at ics.uci.edu Mon Jul 22 14:14:33 2002
From: goodrich at ics.uci.edu (Michael T. Goodrich)
Date: Mon Jan 9 13:41:07 2006
Subject: Reminder: Graph Drawing 2002 -- Call for Participation
In-Reply-To: <200206281110.aa04451@gremlin-relay.ics.uci.edu>
Message-ID:
This is a brief reminder that the deadline for early registration for
Graph Drawing 2002 is July 31, 2002.
>
> 10th Annual Conference on Graph Drawing
> Graph Drawing 2002
>
> Irvine, California
> August 26-28, 2002
>
> http://www.ics.uci.edu/~gd2002/
>
> Call for Pariticipation: The Graph Drawing conference is the primary
> forum for papers devoted exclusively to techniques and systems for the
> visualization of relational and connectivity information represented
> in graphs.
>
> The deadline for early registration is July 31, 2002.
> Registration must be done online (by clicking the appropriate button)
> at the conference web site: http://www.ics.uci.edu/~gd2002/
>
> Accepted papers:
>
> A Hybrid Approach for Visualising Large Network Topologies
> Siew Cheong Au, Christopher Leckie, Ajeet Parhar and Gerard Wong
>
> Improving Walker's Algorithm to Run in Linear Time
> Christoph Buchheim, Michael Juenger and Sebastian Leipert
>
> Graph Layout for Workflow Applications with ILOG JViews (System Demonstration)
> Gilles Diguglielmo, Eric Durocher, Philippe Kaplan, Georg Sander
>
> Drawing outer-planar graphs in O(n log n) area
> Therese Biedl
>
> Separating Thickness from Geometric Thickness
> David Eppstein
>
> Book Embeddings and Point-Set Embeddings of Series-Parallel
> Emilio Di Giacomo, Walter Didimo and Giuseppe Liotta
>
> Computing Labeled Orthogonal Drawings
> Carla Binucci, Walter Didimo, Giuseppe Liotta and Maddalena
>
> Orthogonal 3D Shapes of Theta Graphs
> Emilio Di Giacomo, Giuseppe Liotta and Maurizio Patrignani
>
> Sketch-Driven Orthogonal Graph Drawing
> Ulrik Brandes, Markus Eiglsperger, Michael Kaufmann and Dorothea Wagner
>
> Some Applications of Orderly Spanning Trees in Graph Drawing
> Ho-Lin Chen, Chien-Chih Liao, Hsueh-I Lu and Hsu-Chun Yen
>
> Graphs, They are Changing -- Dynamic Graph Drawing for a Sequence of Graphs
> Stephan Diehl and Carsten Goerg
>
> Pathwidth and Three-Dimensional Straight Line Grid Drawings of Graphs
> Vida Dujmovi{\'c}, Pat Morin and David R. Wood
>
> InterViewer: Dynamic Visualization of Protein-Protein Interactions
> Kyungsook Han and Byong-Hyon Ju
>
> Compact Encodings of Planar Orthogonal Drawings
> Amrita Chanda and Ashim Garg
>
> Some Modifications of Sugiyama Approach
> Danil E. Baburin
>
> Semi-Dynamic Orthogonal Drawings of Planar Graphs
> Walter Bachl
>
> Rectangular Drawings of Planar Graphs
> Md. Saidur Rahman, Takao Nishizeki and Shubhashis Ghosh
>
> Extended Rectangular Drawings of Plane Graphs with Designated Corners
> Kazuyuki Miura, Ayako Miyazawa and Takao Nishizeki
>
> Graph Drawing by High-Dimensional Embedding
> Yehuda Koren and David Harel
>
> Layering of Nodes of Arbitrary Size
> Falk Schreiber
>
> HGV: A Library for Hierarchies, Graphs, and Views
> Marcus Raitner
>
> Applying Crossing Reduction Strategies to Layered Compound Graphs
> Michael Forster
>
> Computing and Drawing Isomorphic Subgraphs
> S. Bachl and F.J. Brandenburg
>
> A Framework for Complexity Management in Graph Visualization
> U. Dogrusoz and B. Genc
>
> Advances in C-Planarity Testing of Clustered Graphs
> Carsten Gutwenger, Michael J{\"u}nger, Sebastian Leipert, Petra Mutzel, Merijam Percan and Ren{\'e} Weiskircher
>
> A Branch-and-Cut Approach to the Directed Acyclic Graph Layering Problem
> Patrick Healy and Nikola S. Nikolov
>
> Simple and Efficient Bilayer Cross Counting
> W. Barth, M. Juenger and P. Mutzel
>
> Two New Heuristics for Two-Sided Bipartite Graph Drawings
> Matthew Newton, Ondrej Sykora and Imrich Vrto
>
> Crossing Reduction by Windows Optimization
> T. Eschbach, W. Guenther, B. Becker and R. Drechsler
>
> Drawing Graphs on Two and Three Lines
> Sabine Cornelsen, Thomas Schank and Dorothea Wagner
>
> Fractional Lengths and Crossing Numbers
> Ondrej Sykora, Laszlo A. Szekely and Imrich Vrto
>
> A Partitioned Approach to Protein Interaction Mapping
> Yanga Byun, Euna Jeong and Kyungsook Han
>
> Straight-line Drawings of Binary Trees with Linear Area and Good Aspect Ratio
> Ashim Garg and Adrian Rusu
>
> An Efficient Fixed Parameter Tractable Algorithm for 1-Sided
> Vida Dujmovic and Sue Whitesides
>
> Camera Position Reconstruction and Tight Decision Networks
> Ileana Streinu and Elif Tosun
>
> Geometric graphs with no self-intersecting path of
> Janos Pach, Rom Pinchasi and Gabor Tardos
>
> Drawing Directed Graphs Using One-Dimensional Optimization
> Liran Carmel and Yehuda Koren
>
> A Preprocessor and Two Approximations for the Spring Embedder
> P.J. Mutton and P.J. Rodgers
>
> Geometric Systems of Disjoint Representatives
> Jiri Fiala, Jan Kratochvil and Andrzej Proskurowski
>
> Maintaining the Mental Map for Circular Drawings
> Michael Kaufmann and Roland Wiese
>
> RINGS: A Technique for Visualizing Large Hierarchies
> Soon Tee Teoh and Kwan-Liu Ma
>
> A Group-Theoretic Method for Drawing Graphs Symmetrically
> D. Abelson and S.-H. Hong
>
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From John.Dickinson at nrc.ca Wed Jul 24 12:29:41 2002
From: John.Dickinson at nrc.ca (Dickinson, John)
Date: Mon Jan 9 13:41:07 2006
Subject: Analytic formulas for distance between geometric shapes.
Message-ID: <35C5DD9F60FED21192B00004ACA6E6C70245C706@nrclonex1.imti.nrc.ca>
I am looking for analytic formulas for distance between basic geometric
shapes arbitrarily located and orientated in space. Any references (papers,
books) would be greatly appreciated.
The Sphere is the easy example as the distance between two spheres in the
distance between their centers minus the sum of their radii. On the other
hand orientated boxes can't be done analytically but must be done face by
face.
How about other shapes formed by implicit quadratic equations (eggs,
ovaloids, ...) that form not purely symmetric shapes which can be orientated
inspace. Do any of these shapes have analytic formulae for distance?
John
--
-((Insert standard disclaimer here))-|--- Ray's Rule for Precision ----
John Kenneth Dickinson, Ph.D. | "Measure with micrometer;
Research Council Officer IMTI-NRC | Mark with chalk;
email: john.dickinson@nrc.ca | Cut with axe."
-------------
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From zach at cs.uni-bonn.de Thu Jul 25 23:01:05 2002
From: zach at cs.uni-bonn.de (Gabriel Zachmann)
Date: Mon Jan 9 13:41:07 2006
Subject: estimate of the volume of a convex body?
Message-ID: <20020725220105.A17159@cs.uni-bonn.de>
As the subject says, I am looking for an estimate of the volume of a
convex body given by
A * x <= b
where A is an mx3 matrix and b is in R^m.
The goal is a *simple* to compute estimation (but not too bad estimate).
I am looking for something simpler and more efficient than converting
to vertex enumeration.
I was thinking of an approximate maximal inscribed ellipsoid,
but it seems this is even more complicated ;-)
Any ideas, hints, or suggestions will be highly appreciated.
Gabriel.
--
/---------------------------------------------------------------------\
| Unix is user-friendly -- |
| it is just a bit selective about who it makes friends with. |
| |
| zach@cs.uni-bonn.de __@/' Gabriel.Zachmann@gmx.net |
| web.informatik.uni-bonn.de/~zach __@/' www.gabrielzachmann.org |
\---------------------------------------------------------------------/
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From ph+ at cs.cmu.edu Wed Jul 31 01:11:59 2002
From: ph+ at cs.cmu.edu (Paul Heckbert)
Date: Mon Jan 9 13:41:07 2006
Subject: Analytic formulas for distance between geometric shapes.
References: <35C5DD9F60FED21192B00004ACA6E6C70245C706@nrclonex1.imti.nrc.ca>
Message-ID: <020d01c23848$79925870$41e110ac@PHECKBERTDT2>
Reference regarding distance from a point to an ellipsoid (requires roots of
6th degree polynomial):
@INCOLLECTION{Hart94,
AUTHOR={John C. Hart},
TITLE={Distance to an Ellipsoid},
BOOKTITLE={Graphics Gems IV},
EDITOR={Paul Heckbert},
PAGES={113-119},
PUBLISHER={Academic Press},
YEAR={1994},
ADDRESS={Boston},
KEYWORDS={ray tracing, ellipse},
SUMMARY={
Gives the formulas necessary to find the distance from a point to an
ellipsoid, or from a point to an ellipse. These formulas can be useful
for geometric modeling or for ray tracing.
},
}
----- Original Message -----
From: "Dickinson, John"
To: "compgeom-discuss@research. bell-labs. com (E-mail)"
Sent: Wednesday, July 24, 2002 11:29 AM
Subject: Analytic formulas for distance between geometric shapes.
> I am looking for analytic formulas for distance between basic geometric
> shapes arbitrarily located and orientated in space. Any references
(papers,
> books) would be greatly appreciated.
>
> The Sphere is the easy example as the distance between two spheres in the
> distance between their centers minus the sum of their radii. On the other
> hand orientated boxes can't be done analytically but must be done face by
> face.
>
> How about other shapes formed by implicit quadratic equations (eggs,
> ovaloids, ...) that form not purely symmetric shapes which can be
orientated
> inspace. Do any of these shapes have analytic formulae for distance?
>
> John
>
> --
> -((Insert standard disclaimer here))-|--- Ray's Rule for Precision ----
> John Kenneth Dickinson, Ph.D. | "Measure with micrometer;
> Research Council Officer IMTI-NRC | Mark with chalk;
> email: john.dickinson@nrc.ca | Cut with axe."
>
>
>
> -------------
> The compgeom mailing lists: see
> http://netlib.bell-labs.com/netlib/compgeom/readme.html
> or send mail to compgeom-request@research.bell-labs.com with the line:
> send readme
> Now archived at http://www.uiuc.edu/~sariel/CG/compgeom/maillist.html.
>
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From youngkim at cs.unc.edu Wed Jul 31 14:25:47 2002
From: youngkim at cs.unc.edu (Young J. Kim)
Date: Mon Jan 9 13:41:07 2006
Subject: Incremental Penetration Depth Algorithm/Implementation Release
Message-ID:
Hello folks,
We announce the release of an incremental penetration depth algorithm, DEEP
(Dual-space Expansion for Estimating Penetration depth). It is now available
at:
http://gamma.cs.unc.edu/DEEP/
You can also find more info about DEEP from the above web site.
Regards,
__________________________________________________________________
Young J. Kim http://www.cs.unc.edu/~youngkim
GAMMA group, Computer Science TEL: +1-919-962-1761
UNC-Chapel Hill FAX: +1-919-962-1799
__________________________________________________________________
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From jch at ad.uiuc.edu Wed Jul 31 11:11:30 2002
From: jch at ad.uiuc.edu (John C Hart)
Date: Mon Jan 9 13:41:07 2006
Subject: Analytic formulas for distance between geometric shapes.
Message-ID:
Here's some more references:
This paper has a bunch of distance algorithms for a variety of
primitives in its appendix:
J.C. Hart. Sphere tracing: A geometric method for the antialiased ray
tracing of implicit surfaces. The Visual Computer 12 (10), Dec. 1996,
pp. 527-545. Available online at:
http://graphics.cs.uiuc.edu/~jch/papers/zeno.ps.gz
Some optimizations are also available in:
S. Worley, J.C. Hart. Hyper-rendering of hyper-textured surfaces. Proc.
of Implicit Surfaces '96 , Oct. 1996, pp. 99-104.
http://graphics.cs.uiuc.edu/~jch/papers/hyper.pdf
There's also a really nice book I just bought at SIGGRAPH that has a
chapter devoted to computing distance functions and finding their
stationary points (to find the closest distance from a point to all of
the points on a surface).
Nicholas M. Patrikalakis & Takashi Maekawa. Shape Interrogation
for Computer Aided Design and Manufacturing. Springer, 2002.
ISBN: 3540424547.
Good luck,
-John
> -----Original Message-----
> From: Paul Heckbert [mailto:ph+@cs.cmu.edu]
> Sent: Tuesday, July 30, 2002 11:12 PM
> To: Dickinson, John; compgeom-discuss@research. bell-labs.
> com (E-mail)
> Cc: Hart, John
> Subject: Re: Analytic formulas for distance between geometric shapes.
>
>
> Reference regarding distance from a point to an ellipsoid
> (requires roots of 6th degree polynomial):
>
> @INCOLLECTION{Hart94,
> AUTHOR={John C. Hart},
> TITLE={Distance to an Ellipsoid},
> BOOKTITLE={Graphics Gems IV},
> EDITOR={Paul Heckbert},
> PAGES={113-119},
> PUBLISHER={Academic Press},
> YEAR={1994},
> ADDRESS={Boston},
> KEYWORDS={ray tracing, ellipse},
> SUMMARY={
> Gives the formulas necessary to find the distance from a
> point to an ellipsoid, or from a point to an ellipse. These
> formulas can be useful for geometric modeling or for ray tracing. }, }
>
> ----- Original Message -----
> From: "Dickinson, John"
> To: "compgeom-discuss@research. bell-labs. com (E-mail)"
>
> Sent: Wednesday, July 24, 2002 11:29 AM
> Subject: Analytic formulas for distance between geometric shapes.
>
>
> > I am looking for analytic formulas for distance between basic
> > geometric shapes arbitrarily located and orientated in space. Any
> > references
> (papers,
> > books) would be greatly appreciated.
> >
> > The Sphere is the easy example as the distance between two
> spheres in
> > the distance between their centers minus the sum of their
> radii. On
> > the other hand orientated boxes can't be done analytically
> but must be
> > done face by face.
> >
> > How about other shapes formed by implicit quadratic
> equations (eggs,
> > ovaloids, ...) that form not purely symmetric shapes which can be
> orientated
> > inspace. Do any of these shapes have analytic formulae for distance?
> >
> > John
> >
> > --
> > -((Insert standard disclaimer here))-|--- Ray's Rule for
> Precision ----
> > John Kenneth Dickinson, Ph.D. | "Measure with micrometer;
> > Research Council Officer IMTI-NRC | Mark with chalk;
> > email: john.dickinson@nrc.ca | Cut with axe."
> >
> >
> >
> > -------------
> > The compgeom mailing lists: see
> > http://netlib.bell-labs.com/netlib/compgeom/readme.html
> > or send mail to compgeom-request@research.bell-labs.com
> with the line:
> > send readme Now archived at
> > http://www.uiuc.edu/~sariel/CG/compgeom/maillist.html.
> >
>
-------------
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