@article{nas-pai-fig-sto-14-aa-imptri-cg,
  author = {Filipe de {Carvalho Nascimento} and Afonso Paiva and Luiz Henrique {de Figueiredo} and Jorge Stolfi}
  title = {Approximating Implicit Curves on Plane and Surface Triangulations with Affine Arithmetic}
  fullhash = {68cc950186ecba48de6b5d95817d5301}
  journal = {Computers {\&} Graphics}
  volume = {40}
  year = {2014}
  pages = {36-48}
  numpages = {13}
  doi = {10.1016/j.cag.2014.01.005}
  abstract = {We present a spatially and geometrically adaptive method for computing a robust polygonal approximation of an implicit curve defined on a planar region or on a triangulated surface. Our method uses affine arithmetic to identify regions where the curve lies inside a thin strip. Unlike other interval methods, even those based on affine arithmetic, our method works on both rectangular and triangular decompositions and can use any refinement scheme that the decomposition offers.}
}

@inproceedings{pai-nas-fig-sto-12-aa-tri-sigb,
  author = {Afonso Paiva and Filipe de {Carvalho Nascimento} and Luiz Henrique {de Figueiredo} and Jorge Stolfi}
  title = {Approximating Implicit Curves on Triangulations with Affine Arithmetic}
  fullhash = {fa65056881f7a70bf2705e26c3227df7}
  booktitle = {Proc.~25th Conference on Graphics, Patterns and Images - SIBGRAPI}
  location = {Ouro Preto, Brazil}
  isbn = {978-1-4673-2802-9}
  month = {8}
  year = {2012}
  pages = {94-101}
  numpages = {8}
  abstract = {We present an adaptive method for computing a robust polygonal approximation of an implicit curve in the plane that uses affine arithmetic to identify regions where the curve lies inside a thin strip. Unlike other interval methods, even those based on affine arithmetic, our method works on triangulations, not only on rectangular quad trees.}
}

@article{pai-fig-sto-06-aa-stratt,
  author = {Afonso Paiva and Luiz Henrique {de Figueiredo} and Jorge Stolfi}
  title = {Robust Visualization of Strange Attractors using Affine Arithmetic}
  fullhash = {50d30eb209965b416665390b034a2219}
  journal = {Computers {\&} Graphics}
  publisher = {Elsevier}
  month = {12}
  number = {6}
  volume = {30}
  year = {2006}
  pages = {1020-1026}
  numpages = {7}
  doi = {10.1016/j.cag.2006.08.016}
  abstract = {We propose the use of affine arithmetic in cell-mapping methods for the robust visualization of strange attractors and show that the resulting cellular approximations converge faster than those produced by cell-mapping methods based on classical interval arithmetic.}
}

@article{fig-sto-04-aa-capl,
  author = {Luiz Henrique {de Figueiredo} and Jorge Stolfi}
  title = {Affine Arithmetic: {Concepts} and Applications}
  fullhash = {ea839e83da4bdb03da621670870918dd}
  journal = {Numerical Algorithms}
  month = {12}
  number = {1-4}
  volume = {37}
  year = {2004}
  pages = {147-158}
  numpages = {12}
  doi = {10.1023/B:NUMA.0000049462.70970.b6}
}

@article{sto-fig-03-aa-intro,
  author = {Jorge Stolfi and Luiz Henrique {de Figueiredo}}
  title = {An Introduction to Affine Arithmetic}
  fullhash = {c2a4ea7f6627451ed90569ec9c10bf52}
  journal = {TEMA - Tend{\^{e}}ncias em Matem{\'{a}}tical Aplicada e Computacional}
  number = {3}
  volume = {4}
  year = {2003}
  pages = {297-312}
  numpages = {16}
}

@article{fig-sto-vel-03-aa-parcur-cgf,
  author = {Luiz Henrique {de Figueiredo} and Jorge Stolfi and Luiz Velho}
  title = {Approximating Parametric Curves with Strip Trees using Affine Arithmetic}
  fullhash = {be0b87156f5d08f88dc66659947fbecf}
  journal = {Computer Graphics Forum}
  month = {6}
  number = {2}
  volume = {22}
  year = {2003}
  pages = {171-179}
  numpages = {9}
  doi = {10.1111/1467-8659.00658}
  abstract = {Abstract We show how to use affine arithmetic to represent a parametric curve with a strip tree. The required bounding rectangles for pieces of the curve are computed by exploiting the linear correlation information given by affine arithmetic. As an application, we show how to compute approximate distance fields for parametric curves.}
}

@inproceedings{fig-sto-vel-02-aa-parcur,
  author = {Luiz Henrique {de Figueiredo} and Jorge Stolfi and Luiz Velho}
  title = {Approximating Parametric Curves with Strip Trees using Affine Arithmetic}
  fullhash = {04501f85dd363b968515089f7bc7ce3f}
  booktitle = {XV Brazilian Symposium on Computer Graphics and Image Processing (SIBGRAPI'02)}
  month = {10}
  year = {2002}
  pages = {163-170}
  numpages = {8}
  doi = {10.1109/SIBGRA.2002.1167139}
  abstract = {We show how to use affine arithmetic to represent a parametric curve with a strip tree. The required bounding rectangles for pieces of the curve are computed by exploiting the linear correlation information given by affine arithmetic. As an application, we show how to compute approximate distance fields for parametric curves.}
}

@techreport{fig-iwa-sto-97-aa-glopt-tr,
  author = {Luiz Henrique {de Figueiredo} and Ronald {Van Iwaarden} and Jorge Stolfi}
  title = {Fast Interval Branch-and-Bound Methods for Unconstrained Global Optimization with Affine Arithmetic}
  institution = {Institute of Computing, Univ. of Campinas}
  fullhash = {dbb3b1ff42db1325163dbac0e592766e}
  month = {6}
  number = {IC-97-08}
  year = {1997}
  abstract = {We show that faster solutions to unconstrained global optimization problems can be obtained by combining previous accelerations techniques for interval branch-and-bound methods with affine arithmetic, a recent alternative to interval arithmetic that often provides tighter estimates. We support this claim by solving a few well-known optimization problems.}
}

@article{fig-sto-96-aa-impl,
  author = {Luiz Henrique {de Figueiredo} and Jorge Stolfi}
  title = {Adaptive Enumeration of Implicit Surfaces with Affine Arithmetic}
  fullhash = {332f2be3b6773a16c239c5101ffd44bc}
  journal = {Computer Graphics Forum}
  month = {12}
  number = {5}
  volume = {15}
  year = {1996}
  pages = {287-296}
  numpages = {10}
  doi = {10.1111/1467-8659.00658}
  abstract = {We discuss adaptive enumeration and rendering methods for implicit surfaces, using octrees computed with affine arithmetic, a new tool for range analysis. Affine arithmetic is similar to standard interval arithmetic, but takes into account correlations between operands and sub-formulas, generally providing much tighter bounds for the computed quantities. The resulting octrees are accordingly much smaller, and the rendering faster.}
}

@inproceedings{fig-sto-95-aa-impl-conf,
  author = {Luiz Henrique {de Figueiredo} and Jorge Stolfi}
  title = {Adaptive Enumeration of Implicit Surfaces with Affine Arithmetic}
  fullhash = {332f2be3b6773a16c239c5101ffd44bc}
  booktitle = {Proceedings of the Eurographics Workshop on Implicit Surfaces '95}
  location = {Grenoble, France}
  month = {4}
  year = {1995}
  pages = {161-170}
  numpages = {10}
}

@techreport{fig-sto-95-aa-impl-tr,
  author = {Luiz Henrique {de Figueiredo} and Jorge Stolfi}
  title = {Adaptive Enumeration of Implicit Surfaces with Affine Arithmetic}
  institution = {Departamento de Ci\^{e}ncia da Computa{\c{c}}{\~{a}}o, Univ. of Campinas}
  fullhash = {332f2be3b6773a16c239c5101ffd44bc}
  month = {3}
  number = {DCC-95-02}
  year = {1995}
  pages = {16}
  numpages = {1}
  abstract = {We discuss adaptive enumeration and rendering methods for implicit surfaces, using octrees computed with affine arithmetic, a new tool for range analysis. Affine arithmetic is similar to standard interval arithmetic, but takes into account correlations between operands and sub-formulas, generally providing much tighter bounds for the computed quantities. The resulting octrees are accordingly much smaller, and the rendering faster. We also describe applications of affine arithmetic to intersection and ray tracing of implicit surfaces.}
}

@inproceedings{and-com-sto-94-aa-rus,
  author = {Marcus V. A. Andrade and Jo{\~{a}}o L. D. Comba and Jorge Stolfi}
  title = {Affine Arithmetic}
  fullhash = {68b070b6be8248424c96e1847e49affa}
  booktitle = {Abstracts of the International Conference on Interval and Computer-Algebraic Methods in Science and Engineering (INTERVAL/94)}
  location = {St. Petersburg, Russia}
  month = {3}
  year = {1994}
  pages = {36-40}
  numpages = {5}
}

@misc{and-com-sto-94-aa-x,
  author = {Marcus V. A. Andrade and Jo{\~{a}}o L. D. Comba and Jorge Stolfi}
  title = {Affine Arithmetic}
  fullhash = {68b070b6be8248424c96e1847e49affa}
  howpublished = {Unpublished manuscript}
  month = {3}
  note = {Full version of~\cite{and-com-sto-94-aa}.}
  year = {1994}
  pages = {10}
  numpages = {1}
}

@inproceedings{com-sto-93-aa-sib,
  author = {Jo{\~{a}}o L. D. Comba and Jorge Stolfi}
  title = {Affine Arithmetic and its Applications to Computer Graphics}
  fullhash = {618912c2f8cefd0d00401f3f7dd260df}
  booktitle = {Anais do VI Simp{\'{o}}sio Brasileiro de Computa{\c{c}}{\~{a}}o Gr{\'{a}}fica e Processamento de Imagens (SIBGRAPI'93)}
  location = {Recife, PE, Brazil}
  month = {10}
  year = {1993}
  pages = {9-18}
  numpages = {10}
}

@misc{sto-93-aa-lib,
  author = {Jorge Stolfi}
  title = {{\tt LIBAA}: An Affine Arithmetic Library in {C}}
  fullhash = {189e3d5f115903fe3f60fffc7d751b98}
  howpublished = {Software package}
  year = {1993}
  url = {http://www.ic.unicamp.br/~stolfi/}
}