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Michael Floater answers a
few questions about this month's fast breaking paper in the field of
Computer Science.
From
>>December 2004
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[late entry]
Field:
Computer Science
Article Title: Mean value coordinates
Authors: Floater, MS
Journal: COMPUT AIDED GEOM DESIGN
Volume: 20
Page: 19-27
Year: MAR 2003
* SINTEF, Postbox 124, Blindern, N-0314 Oslo, Norway.
* SINTEF, N-0314 Oslo, Norway.
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 Why
do you think your paper is highly cited?
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The paper is significant because it offers a fast and
safe method of generating such a representation.
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Mainly because it offers a simple and robust method for
computing a parametric representation of a surface initially
given as a mesh of triangles. The method has been used by other
researchers either directly or as the start point for more
sophisticated methods.
Does
it describe a new discovery or a new methodology that's useful to
others?
Yes, the discovery is a simple, but apparently new, system of
coordinates which generalize barycentric coordinates. While
barycentric coordinates are used to locate a point in a
triangle, these generalized coordinates locate a point in an
n-sided polygon.
Could
you summarize the significance of your paper in layman's terms?
Nowadays most 3D objects, such as an aircraft wing, a
mechanical part, or a character in a computer-animated film, are
modelled and designed with the help of a computer. Almost all
computer modelling systems are based on surfaces that have a
parametric representation, such as splines. Surfaces that don't
are very difficult to work with.
The paper is significant because it offers a fast and safe
method of generating such a representation. This is a crucial
step in, for example, reverse engineering (converting a cloud of
measured sample points to a CAD model) and in texture mapping
for visualization in computer graphics.
How
did you become involved in this research?
In the mid-nineties I worked in a research team at SINTEF on
a project to build a software system for reverse engineering. We
needed a method for fitting parametric surfaces to
scattered data and I came up with the idea of a "convex
combination mapping." This current paper offers a
simplification of the "coordinates" part of the
original method.
Michael Floater
Professor, Department of Informatics
Centre of Mathematics for Applications
University of Oslo
Oslo, Norway
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ESI Special Topics,
December 2004
Citing URL - http://www.esi-topics.com/fbp/2004/december04-MichaelFloater.html
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