Research
My research focuses on robust and adaptive methods for
the solution of problems in computer graphics and geometric modeling.
Robustness means that
I am interested in using computers to prove properties of curves and surfaces.
This usually takes the form of solving equations in several variables.
The main tools for achieving robustness are
interval computation methods using interval arithmetic and
affine arithmetic.
Interval methods provide guaranteed numerical results
that are not affected by rounding errors in floatingpoint computations.
More importantly,
interval methods allows us to analyse the global behaviour of functions over
whole regions of the space without sampling it.
Adaptiveness means that
I want to concentrate the computational effort near interesting regions of the space,
such as near a solution curve or in regions where the surface curvature is high.
Global analysis with interval methods leads naturally to adaptive methods.
I am also interested in using computers to prove properties of nonlinear
dynamical systems. Again, interval methods are the main tools. One result of
this research is a computeraided proof that the Jouanolou foliation of low
degree admits no nontrivial minimal sets. Recently, I have been working on
adaptive algorithms for generating
guaranteed images of Julia sets and fractal basins for Newton's method.
I am also interested in programming languages and I am one of the designers of
the
Lua language.
Selected publications

Oliveira, J. B., Figueiredo, L. H.,
Robust approximation of offsets, bisectors, and medial axes of plane curves,
Reliable Computing 9 #2 (2003) 161175.

Lopes, H., Oliveira, J. B., Figueiredo, L. H.,
Robust adaptive polygonal approximation of implicit curves,
Computers & Graphics 26 #6 (2002) 841852.

Camacho, C., Figueiredo, L. H.,
The dynamics of the Jouanolou foliation on the complex projective 2space,
Ergodic Theory and Dynamical Systems 21 #3 (2001) 757766.

Coelho, L. C. G., Gattass, M., Figueiredo, L. H.,
Intersecting and trimming parametric meshes on finiteelement shells,
International Journal for Numerical Methods in Engineering
47 #4 (2000) 777800.

Velho, L., Figueiredo, L. H., Gomes, J.,
A unified approach for hierarchical adaptive tesselation of surfaces,
ACM Transactions on Graphics 18 #4 (1999) 329360.

Velho, L., Figueiredo, L. H., Gomes, J.,
A methodology for piecewise linear approximation of surfaces,
Journal of the Brazilian Computer Society 3 #3 (1997) 3042.

Figueiredo, L. H., Stolfi, J.,
Adaptive enumeration of implicit surfaces with affine arithmetic,
Computer Graphics Forum 15 #5 (1996) 287296.

Ierusalimschy, R., Figueiredo, L. H., Celes, W.,
Lua: an extensible extension language,
Software: Practice & Experience 26 #6 (1996) 635652.
First prize (technological category)
in the
II Compaq Award for Research and Development in Computer Science.

Figueiredo, L. H., Gomes, J.,
Sampling implicit objects with physicallybased particle systems,
Computers & Graphics 20 #3 (1996) 365375.

Figueiredo, L. H., Gomes, J.,
Computational morphology of curves,
The Visual Computer 11 #2 (1995) 105112.

Figueiredo, L. H.,
Adaptive sampling of parametric curves,
in A. Paeth (ed.),
Graphics Gems V, Academic Press, 1995, 173178.
Last update:
Fri May 15 08:11:46 BRST 2009
by lhf.