%%%%%%%%%%% Bertinirealref.bib %%%%%%%%%%%%%%%%%%%

@Inbook{Brake2014,
author="Brake, Daniel A.
and Bates, Daniel J.
and Hao, Wenrui
and Hauenstein, Jonathan D.
and Sommese, Andrew J.
and Wampler, Charles W.",
editor="Hong, Hoon and Yap, Chee",
chapter="Bertini\_real: Software for One- and Two-Dimensional Real Algebraic Sets",
title="Mathematical Software -- ICMS 2014: 4th International Congress, Seoul, South Korea, August 5-9, 2014. Proceedings",
year="2014",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="175--182",
isbn="978-3-662-44199-2",
doi="10.1007/978-3-662-44199-2_29",
url="http://dx.doi.org/10.1007/978-3-662-44199-2_29"
}


@article{BrN15,
  Author   = {Daniel Brake and Daniel Bates and Wenrui Hao and Jonathan Hauenstein and Andrew Sommese and Charles Wampler},
  Title  = {Algorithm xxx: Bertini\_real: Numerical Decomposition of Real Algebraic Curves and Surfaces},
  Abstract   = {Bertini real is a compiled command line program for numerically decomposing the real portion of a positive-dimensional complex component of an algebraic set. The software uses homotopy continuation to solve a series of systems via regeneration from a witness set to compute a cell decomposition. This decomposition captures the topological information and permits further computation on the real sets, such as sampling, visualization, and 3D printing.},
  Year      = {2015},
  Month    = {February}
}

@article{On14,
Author = {Daniel Brake and Daniel Bates and Wenrui Hao and Jonathan Hauenstein and Andrew Sommese and Charles Wampler},
Title = {On computing a cell decomposition of a real surface containing infinitely many singularities},
Abstract ={Numerical algorithms for decomposing the real points of a complex curve or surface in any number of variables have been developed and implemented in the new software package Bertini real. These algorithms use homotopy continuation to produce a cell decomposition with the currently employed algorithm for surfaces assuming that it is almost smooth, i.e., most nitely many singular points. The following summarizes using isosingular deflation to remove the almost smooth condition along describing the use of Bertini with MATLAB to perform the deflation.},
year = {2014}
}

@manual{BM13,
Title = {Bertini Manual},
Year = {2013},
Author = {Dan Bates and  Jon Hauenstein} 
}

@manual{Br15,
Title = {Bertini\_real Manual},
Author = {Daniel Brake and Pierce Cunneen},
Year = {2015}
}

@misc{RM15,
Title = {README.md},
Author = {Daniel Brake}
}

@misc{installnewerGCC,
      author = "MartyMacGyver.",
      title = "How to install a newer version of GCC",
      month = "July",
      year = "2011",
      url = {\url{http://cygwin.wikia.com/wiki/How_to_install_GCC_4.3.0}}
}

@misc{CygwinMATLAB,
      author = "Matthew Zahr",
      title = "How to install a newer version of GCC",
      month = "April",
      year = "2015",
      url = {\url{http://stanford.edu/~mzahr/extras/cme292/spring2014/AccessToMatlabAndAlternatives.pdf}}
}

@misc{Bertinisite,
      author = "Andrew Sommese",
      title = "Bertini Home Page",
      month = "August",
      year = "2015",
      url = {\url{http://bertini.nd.edu/index.htm}}
}

@misc{Bertinirealsite,
      author = "Daniel Brake",
      title = "Bertini\_real",
      month = "April",
      year = "2015",
      url = {\url{http://bertinireal.com/index.htm}}
}

@misc{BertinirealGitHub,
      author = "Daniel Brake",
      title = "bertini\_real",
      month = "April",
      year = "2015",
      url = {\url{https://github.com/ofloveandhate/bertini_real/tree/master/matlab_codes/%40bertini_real_plotter}}
}

@misc{Homebrewsite,
      author = "Remi Prevost",
      title = "Homebrew",
      month = "November",
      year = "2015",
      url = {\url{https://github.com/ofloveandhate/bertini_real/tree/master/matlab_codes/%40bertini_real_plotter}}
}

@misc{GMPLib,
      author = "Torbjorn Granlund",
      title = "Homebrew",
      month = "July",
      year = "2015",
      howpublished = {\url{https://gmplib.org/}}
}

@misc{MPFRLib,
      author = "Guillaume Hanrot",
      title = "The GNU MPFR Library",
      month = "June",
      year = "2015",
     url = {\url{http://www.mpfr.org/index.htm}}
}

@misc{MPCLib,
      author = "Andreas Enge",
      title = "multiprecision.org",
      month = "February",
      year = "2015",
      url = {\url{http://www.multiprecision.org/}}
}

@misc{CygRef,
      author = "Kevin Squire",
      title = "Cygwin Reference Sheet",
      year = "2007",
      url = {\url{http://faculty.nps.edu/kmsquire/cs2900/cygwin/fwcygwinref.pdf}}
}
















%%%%%%%%%%%%%%%%%
%
%  PAPERS
%
%%%%%%%%%%%%%%%%%



http://www.afhalifax.ca/magazine/wp-content/sciences/EmpilementDeDisques/delaunaycourbe/chew93.pdf
http://link.springer.com/article/10.1007/s00366-009-0162-1#page-1
http://www.mathemagix.org/www/mmdoc/doc/html/language/man-history.en.html
meshing implicit algebraic surfaces: the smooth case  (this paper contains some dead links)

https://sites.google.com/a/varlog.com/www/admesh-htm
http://www.robertschneiders.de/meshgeneration//software.html



@string{jmd = "ASME J. Mech. Design"}



@misc{goodhomotopy,
title = "Homotopies for connected components applied to computing critical sets",
author = "D.J. Bates and D.A. Brake and J.D. Hauenstein and A.J. Sommese and C.W. Wampler",
url = "www.nd.edu/~jhauenst/preprints/bbhswCritical.pdf",
journal = "Preprint",
year = 2014
}




@inproceedings{chew1993guaranteed,
  title={Guaranteed-quality mesh generation for curved surfaces},
  author={Chew, L.P.},
  booktitle={Proceedings of the ninth annual symposium on Computational geometry},
  pages={274--280},
  year={1993},
  organization={ACM}
}



@article{dey2010polygonal,
  title={Polygonal surface remeshing with Delaunay refinement},
  author={Dey, T. K. and Ray, T.},
  journal={Engineering with Computers},
  volume={26},
  number={3},
  pages={289--301},
  year={2010},
  publisher={Springer}
}



@inproceedings{Appel:1968:TSM:1468075.1468082,
 author = {Appel, A.},
 title = {Some Techniques for Shading Machine Renderings of Solids},
 booktitle = {Proceedings of the April 30--May 2, 1968, Spring Joint Computer Conference},
 series = {AFIPS '68 (Spring)},
 year = {1968},
 location = {Atlantic City, New Jersey},
 pages = {37--45},
 numpages = {9},
 acmid = {1468082},
 publisher = {ACM},
 address = {New York, NY, USA},
}




@book{glassner1989introduction,
  title={An introduction to ray tracing},
  author={Glassner, A.S.},
  year={1989},
  publisher={Morgan Kaufmann}
}



@book{ cgal:eb-14a
, title        = "{CGAL} User and Reference Manual"
, author      = "{The CGAL Project}"
, publisher     = "{CGAL Editorial Board}"
, edition     = "{4.4}"
, year         = 2014
, url =    "doc.cgal.org/4.4/Manual/packages.html"
}




@article{alberti2004meshing,
  title={Meshing implicit algebraic surfaces: the smooth case},
  author={Alberti, L. and Comte, G. and Mourrain, B.},
  journal={Mathematical Methods for Curves and Surfaces: Tromso},
  volume={4},
  pages={11--26},
  year={2004}
}



@incollection{gatellier2005computing,
  title={Computing the topology of three-dimensional algebraic curves},
  author={Gatellier, G. and Labrouzy, A. and Mourrain, B. and T{\'e}court, J.-P.},
  booktitle={Computational methods for algebraic spline surfaces},
  pages={27--43},
  year={2005},
  publisher={Springer}
}

@incollection {BHPS09,
    AUTHOR = {Bates, D.J. and Hauenstein, J.D. and Peterson,
              C. and Sommese, A.J.},
     TITLE = {Numerical decomposition of the rank-deficiency set of a matrix
              of multivariate polynomials},
 BOOKTITLE = {Approximate commutative algebra},
    SERIES = {Texts Monogr. Symbol. Comput.},
     PAGES = {55--77},
 PUBLISHER = {SpringerWienNewYork, Vienna},
      YEAR = {2009},
}

@article{bates2011efficient,
  title={Efficient path tracking methods},
  author={Bates, D.J. and Hauenstein, J.D. and Sommese, A.J.},
  journal={Numerical Algorithms},
  volume={58},
  number={4},
  pages={451--459},
  year={2011},
  publisher={Springer}
}



%Weisstein, Eric W. "Barth Sextic." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/BarthSextic.html


@misc{barth,
	author = "E.W. Weisstein",
	title = "Barth Sextic",
	journal="From MathWorld--A Wolfram Web Resource",
	url = "mathworld.wolfram.com/BarthSextic.html",
	year = "2014"
}


@misc{blender,
	author = "The Blender Foundation",
	title = "Blender",
	url = "www.blender.org",
	year = "2014"
}



@misc{bertini,
	author = "D.J. Bates and J. D. Hauenstein and A.J. Sommese and C.W. Wampler",
	title = "Bertini: Software for numerical algebraic geometry",
	url = "bertini.nd.edu",
	year = "2006",
}




@misc{algebraicsurfacegallery,
	author="H. Hauser and J. Schicho",
	title="Algebraic Surfaces",
	url="homepage.univie.ac.at/herwig.hauser/bildergalerie/gallery.html",
	year=2014
}



@book{SW05,
	author = "A.J. Sommese and C.W. Wampler",
	title = "The numerical solution to systems of polynomials arising in engineering and science",
	publisher = "World Scientific",
	address = "Singapore",
	year = "2005",
	}
	
	
@incollection{removing_almost_smooth,
year={2014},
author={Bates, D.J. and Brake, D.A. and Hauenstein, J.D. and Sommese, A.J. and Wampler, C.W.},
booktitle={Mathematical Software – ICMS 2014},
volume={8592},
series={Lecture Notes in Computer Science},
editor={Hong, Hoon and Yap, Chee},
title={On Computing a Cell Decomposition of a Real Surface Containing Infinitely Many Singularities},
publisher={Springer},
pages={246--252},
}



@incollection{br_extended_abstract,
year={2014},
booktitle={Mathematical Software – ICMS 2014},
volume={8592},
series={Lecture Notes in Computer Science},
editor={Hong, Hoon and Yap, Chee},
title={Bertini\_real: Software for One- and Two-Dimensional Real Algebraic Sets},
publisher={Springer},
keywords={Numerical algebraic geometry; cell decomposition; algebraic surface; algebraic curve; homotopy continuation; deflation},
author={Brake, D.A. and Bates, D.J. and Hao, W. and Hauenstein, J.D. and Sommese, A.J. and Wampler, C.W.},
pages={175--182},
}




@inproceedings{adaptive_implicit_sibgrapi,
    author = {A. Paiva and H. Lopes and T. Lewiner and L.H. de Figueiredo},
    title = {Robust adaptive meshes for implicit surfaces},
    year = {2006},
    month = {october},
    booktitle = {Sibgrapi 2006 (XIX Brazilian Symposium on Computer Graphics and Image Processing)},
    pages = {205--212},
    publisher = {IEEE},
    address = {Manaus, AM},
}





@article{sommese2001numerical,
  title={Numerical decomposition of the solution sets of polynomial systems into irreducible components},
  author={Sommese, A.J. and Verschelde, J. and Wampler, C.W.},
  journal={SIAM Journal on Numerical Analysis},
  volume={38},
  number={6},
  pages={2022--2046},
  year={2001},
  publisher={SIAM}
}

@article{lu2007finding,
  title={Finding all real points of a complex curve},
  author={Lu, Y. and Bates, D.J. and Sommese, A.J. and Wampler, C.W.},
  journal={Contemporary Mathematics},
  volume={448},
  pages={183--205},
  year={2007},
  publisher={Providence, RI; American Mathematical Society; 1999}
}

@article{hauenstein2013isosingular,
  title={Isosingular sets and deflation},
  author={Hauenstein, J.D. and Wampler, C.W.},
  journal={Foundations of Computational Mathematics},
  volume={13},
  number={3},
  pages={371--403},
  year={2013},
  publisher={Springer}
}


@article{besana2013cell,
  title={Cell decomposition of almost smooth real algebraic surfaces},
  author={Besana, G.M. and Di Rocco, S. and Hauenstein, J.D. and Sommese, A.J. and Wampler, C.W.},
  journal={Numerical Algorithms},
  volume={63},
  number={4},
  pages={645--678},
  year={2013},
  publisher={Springer}
}


@masterthesis{tong2013four,
  title={Four-bar Linkage Synthesis for a Combination of Motion and Path-point Generation},
  author={Tong, Y.},
  year={2013},
  school={University of Dayton}
}

@book{bates2013numerically,
  title={Numerically solving polynomial systems with Bertini},
  author={Bates, D.J. and Hauenstein, J.D. and Sommese, A.J. and Wampler, C.W.},
  volume={25},
  year={2013},
  publisher={SIAM}
}



@article{hauenstein2011regeneration,
  title={Regeneration homotopies for solving systems of polynomials},
  author={Hauenstein, J.D. and Sommese, A.J. and Wampler, C.W.},
  journal={Mathematics of Computation},
  volume={80},
  number={273},
  pages={345--377},
  year={2011}
}


@article{arnon1984cylindrical,
  title={Cylindrical algebraic decomposition {I}: The basic algorithm},
  author={Arnon, D.S. and Collins, G.E. and McCallum, S.},
  journal={SIAM Journal on Computing},
  volume={13},
  number={4},
  pages={865--877},
  year={1984},
  publisher={SIAM}
}

@article{collins75,
 author = {Collins, G.E.},
 title = {Quantifier elimination for real closed fields by cylindrical algebraic decomposition},
 publisher = {Springer},
 journal = {Lec. Notes Comp. Sci},
 volume = {33},
 year = {1975},
 pages =  {134--183}
}

@misc{CGAL,
author = {{C}{G}{A}{L}},
title = {{C}omputational {G}eometry {A}lgorithms {L}ibrary},
url = {www.cgal.org}
}

@INPROCEEDINGS {HK00 ,
AUTHOR = "Husty, M.L. and  Karger, A." ,
TITLE = "Self-motions of {G}riffis-{D}uffy type parallel manipulators" ,
BOOKTITLE = "Proceedings of the 2000 IEEE Int. Conf. Robotics and Automation,
CDROM, San Francisco, CA, April 24--28, 2000" ,
PUBLISHER = "IEEE",
YEAR = "2000" ,
}


@ARTICLE {SVW7 ,
    AUTHOR = {Sommese, A.J. and Verschelde, J. and Wampler, C.W.},
TITLE = "Advances in polynomial continuation for solving problems
         in kinematics" ,
JOURNAL = jmd,
VOLUME = "126" ,
NUMBER = {2},
PAGES = "262--268" ,
YEAR = "2004" ,
}

@book {Burmester,
    AUTHOR = {Burmester, L.E.H.} ,
     TITLE = {Lehrbuch der {K}inematik},
 PUBLISHER = {Leipzig A. Felix},
      YEAR = {1888},
}

@book {BR79,
    AUTHOR = {Bottema, O. and Roth, B.},
     TITLE = {Theoretical Kinematics},
    SERIES = {North-Holland Series in Applied Mathematics and Mechanics},
    VOLUME = {24},
 PUBLISHER = {North-Holland Publishing Co.},
   ADDRESS = {Amsterdam},
      YEAR = {1979},
      NOTE = {Reprinted by Dover Publications, New York, 1990},
     PAGES = {xiv+558},
      ISBN = {0-444-85124-0},
   MRCLASS = {70-02 (51Nxx 53A17 70B99)},
  MRNUMBER = {81c:70001},
MRREVIEWER = {Robert Connelly},
}

@article {Alt23,
    AUTHOR = {Alt, H.},
     TITLE = {{\"U}ber die {E}rzeugung gegebener ebener
                           {K}urven mit {H}ilfe des {G}elenkvierecks},
   JOURNAL = {Zeitschrift f\"ur Angewandte Mathematik und Mechanik},
    VOLUME = {3},
    NUMBER = {1},
      YEAR = {1923},
     PAGES = {13--19},
}

@ARTICLE {WMS92 ,
AUTHOR = "Wampler, C.W. and Morgan, A.P. and Sommese, A.J." ,
TITLE = "Complete solution of the nine-point path synthesis problem
         for four-bar linkages" ,
   JOURNAL = jmd,
   FJOURNAL= {ASME Journal of Mechanical Design},
VOLUME = "114" ,
PAGES = "153--159" ,
YEAR = "1992" ,
}

@article {SVW2004:Intersection,
    author={A.J. Sommese and J. Verschelde and C.W. Wampler},
     TITLE = {Homotopies for intersecting solution components of polynomial
              systems},
   JOURNAL = {SIAM J. Numer. Anal.},
  FJOURNAL = {SIAM Journal on Numerical Analysis},
    VOLUME = {42},
      YEAR = {2004},
    NUMBER = {4},
     PAGES = {1552--1571},
      ISSN = {0036-1429},
}

@article{HW12,
  author = {J.D. Hauenstein and C.W. Wampler},
  title = {Numerically intersecting algebraic varieties via witness sets},
  journal = {Appl. Math. Comput.},
 year = {2012},
 note = {{\tt DOI:10.1016/j.amc.2012.06.034}},
}

@Misc{HW:IntersectRegen,
  author = {J.D. Hauenstein and C.W. Wampler},
  title = {Numerical algebraic intersection using regeneration},
  note = {Under review.  Available at www.nd.edu/~jdhauens/preprints/hwGeneralIntersection.pdf},
  year = {2014}
}

@book{Basu06,
 author = {Basu, S. and Pollack, R. and Roy, M.-F.},
 title = {Algorithms in Real Algebraic Geometry (Algorithms and Computation in Mathematics)},
 year = {2006},
 isbn = {3540330984},
 publisher = {Springer-Verlag New York, Inc.},
 address = {Secaucus, NJ, USA},
}

@article{BHPS:LocalDimension:2009,
    AUTHOR = {Bates, D.J. and Hauenstein, J.D. and Peterson, C. and Sommese, A.J.},
     TITLE = {A numerical local dimensions test for points on the solution set of a system of polynomial equations},
   JOURNAL = {SIAM J. Numer. Anal.},
  FJOURNAL = {SIAM Journal on Numerical Analysis},
    VOLUME = {47},
      YEAR = {2009},
    NUMBER = {5},
     PAGES = {3608--3623},
      ISSN = {0036-1429},
     CODEN = {SJNAAM},
   MRCLASS = {65H10 (13P15 65H20 68W30)},
  MRNUMBER = {2576513 (2011k:65072)},
MRREVIEWER = {Guillermo Matera},
}


