🚀 go-pugleaf

US SANTA CRUZ:		Computer & Information Sciences and
			Computer Engineering


Faculty Recruitment Seminar: 	Friday, February 21, 11-12:00 Noon
				Room 330 Applied Sciences Bldg.
				Refreshments at 10:45 am


Dinesh Manocha from UC Berkeley will speak on:

"NON-LINEAR GEOMETRY AND  LINEAR ALGEBRA"

Many problems in computer graphics, geometric and solid modeling, robotics,
vision, symbolic  and scientific computation are reduced to manipulating
system of polynomial equations.  In particular, sets of equations are used
for object representation and constraints formulation.  Typical applications
include curve and surface intersections, robot motion planning, ray tracing,
cusps and loops detection, inverse kinematics, symbolic elimination and
solving systems of non--linear equations.  Earlier approaches to deal with 
these problems can be classified into symbolic and numeric methods.
Symbolic techniques, like Groebner bases, are too slow and suffer from
numerical accuracy problems in the context of floating point computation.
At the same time numerical methods based on subdivision, iterative techniques
and continuation are far from being robust and slow in practice as well.

In this talk we present multipolynomial resultants and show their
effectiveness for manipulating system of polynomial equations.  The resultant 
is represented in terms of matrices and determinants.  As a result, we 
use algorithms from linear algebra for their application.  These include 
multivariate interpolation and modular computation for symbolic applications 
and Gauss elimination, singular value decomposition and eigendecomposition 
for numeric methods.  Based on multipolynomial resultants we present 
efficient algorithms for implicitizing rational parametric surfaces and 
eliminating a set of variables from a system of equations to obtain a 
symbolically smaller system. We also apply the results to the problem 
of curve and surface intersections and present efficient and robust 
representations and algorithms for geometric and solid modeling systems. 
The technique can also be specialized for ray tracing and detecting cusps 
and loops.  Finally we present a real time algorithm for the inverse 
kinematics of general six revolute and serial manipulators.  Inverse 
kinematics of general six revolute manipulators had been an open problem 
in industrial robotics for more than three decades and had significant 
impact on the design of robot manipulators.  Other applications of inverse 
kinematics algorithm include goal directed computer animation and physical 
based modeling.