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MPI-INF D4 Publications :: Thesis :: Langer, Torsten

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Thesis - Doctoral dissertation | @PhdThesis | Doktorarbeit

Author(s)*:Langer, Torsten
BibTeX citekey*:Langer08

Title, School
Title*:On Generalized Barycentric Coordinates and Their Applications in Geometric Modeling
School:Universität des Saarlandes
Type of Thesis*:Doctoral dissertation

Note, Abstract, Copyright
LaTeX Abstract:Generalized barycentric coordinate systems allow us to express the

position of a point in space with respect to a given polygon or higher
dimensional polytope. In such a system, a coordinate exists for each
vertex of the polytope such that its vertices are represented by unit
vectors $\vect{e}_i$ (where the coordinate associated with the respective
vertex is 1, and all other coordinates are 0). Coordinates thus have a
geometric meaning, which allows for the simplification of a number of tasks in geometry processing.

Coordinate systems with respect to triangles have been around since
the 19\textsuperscript{th} century, and have since been generalized; however, all of
them have certain drawbacks, and are often restricted to
special types of polytopes. We eliminate most of these restrictions
and introduce a definition for 3D mean value coordinates that is
valid for arbitrary polyhedra in $\realspace{3}$, with a straightforward generalization
to higher dimensions.

Furthermore, we extend the notion of barycentric coordinates in such a
way as to allow Hermite interpolation and investigate the
capabilities of generalized barycentric coordinates for constructing
generalized B\'ezier surfaces. Finally, we show that barycentric
coordinates can be used to obtain a novel formula for curvature
computation on surfaces.

Keywords:Barycentric Coordinates, Bezier Theory, Surface Curvature
Download Access Level:Public
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Referees, Status, Dates
1. Referee:Seidel, Hans-Peter
2. Referee:Belyaev, Alexander
Supervisor:Belyaev, Alexander
Date Kolloquium:18 December 2008
Chair Kolloquium:Weickert, Joachim

MPG Unit:Max-Planck-Institut für Informatik
MPG Subunit:Computer Graphics Group
Audience:experts only
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BibTeX Entry:
AUTHOR = {Langer, Torsten},
TITLE = {On Generalized Barycentric Coordinates and Their Applications in Geometric Modeling},
SCHOOL = {Universit{\"a}t des Saarlandes},
YEAR = {2008},
TYPE = {Doctoral dissertation}
MONTH = {December},

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Entry last modified by Torsten Langer, 03/03/2009
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Torsten Langer
12/19/2008 02:06:31 PM

Torsten Langer

Edit Date
12/19/2008 02:06:31 PM