I've come to graphics
relatively recently (in the year 2000), and up to now I've been
working on the following projects:
Voxel Global Illumination
I've proposed a Voxel method
for radiosity which was published as a poster at DGCI'2002. This is a
completely
new approach to global illumination. Basically,
when we want to render a 3D scene, we approximate the surfaces of
all the objects by a voxel surface (see the topological part
of my research for a theoretical study of such discrete surfaces).
Once we have a discrete scene composed of voxels, encoded
in an octree data structure, we discretize both surfaces
and directions in the space in the continuous diffuse illumination
equation
(a classical equation used in radiosity), thus obtaining
a discrete equation. As in classical radiosity, this
discrete equation fullfils the requirements for applying
(say) the Gauss-Seidel method, so we can numerically compute
a solution of the equation.
This method has been much improved and made practical by my PhD student
Pierre Chatelier, who
made substantial optimization (providing optimal complexity for the
visibility problem) and generalized the method for general
BRDF.
Lukasz Piwowar
is
currently improving the method a lot, by providing unaliased display
which enables to
reduce the number of voxels dramatically, and including all source code
in a comprehensive software.
The method is being developped with a parallel algorithm for cluster by
my student
Rita Zrour,
under the joint supervision of
Fabien Feschet.



Here are the two first images, (with only
lambertian reflexion and
aliased display) ever obtained by our method
(at that time, the method was
very slow and nobody took it seriously. It was published as a poster):

Result of radiosity, display by
z-buffer
same scene as above, other
viewpoint, display by z-buffer.
My research on geometric
modeling up to now consists in the joint supervision with
Yan Gerard of
the PhD student
Thibault
Marzais, Who designed a linear programming
approach to (piecewise) polynomial surfaces fitting experimental
data (clouds of points). The advantage of this method compared to least
square methods is that we optimize the uniform error instead of a
statistical
error.