From: utzoo!utcsrgv!phyllis
Newsgroups: ont.events
Title: UofT DCS Seminar Schedule
Article-I.D.: utcsrgv.1330
Posted: Mon Apr 25 13:22:17 1983
Received: Mon Apr 25 13:49:05 1983



	UofT Department of Computer Science Seminar Schedule for
		     the week of May 2nd, 1983


Monday, May 2nd, 4:00 P.M., SF1105:  Dr. Theo Pavlidis, Bell Laboratories,
  Murray Hill, New Jersey:  "Curve fitting with conic splines".

     ABSTRACT:  Conic splines are formed by arcs of conics, each
     defined by its endpoints and the tangents at them plus an
     intermediate point.  Instead of the common general equation
     that depends on five parameters, an equation with a single
     parameter is used, thus simplifying significantly the curve
     fitting problem.  The resulting guided conics resemble Bezier
     polynomials and for parabolas are identical to them.  Such
     splines can be used conveniently both for interactive design
     and for automatic curve fitting.  They allow circular,
     elliptical and hyperbolic arcs to be included in the spline
     family, while the common forms using a B-spline basis include
     only parabolic arcs.  Conic splines are described either in a
     rational parametric or algebraic form f(x y) = 0.  A simple
     estimate for the distance of a point from such a curve is
     given and is used to test the quality of approximations.
     The data to be fitted are first approximated by a polygon, and
     then simple heuristics are used to decide which sequences of
     vertices should be approximated by conics.  The conics found by
     the applications of the heuristics are usually close approximations
     of the data and need no further adjustments.  When adjustments
     are needed the interval is split and a conic is fitted on each
     part.  It is shown theoretically, that exact knot placement at
     the optimal locations is less important for higher order splines
     than for polygons.  Examples of application of the method to
     the fitting of font and other contours are given.  Comparisons
     with other methods suggest that conic splines require no more
     than knots than cubic splines for similar quality of approximation.


Tuesday, May 3rd, 4:00 P.M., SF1105:  Professor A.K. Lenstra, Mathematisch
  Centrum, Amsterdam, Holland:  "Recent developments in primality testing".


     ABSTRACT:  Until recently it could have taken a very long time
     to give a rigorous proof of the primality of an arbitrary
     200-digit prime number.  This situation changed in 1980 when a
     new primality-test was invented by L. Adleman and R. Rumely.
     A simplified version of their algorithm, due to H.W. Lenstra, Jr.
     and H. Cohen, was implemented on a CDC Cyber 170-750 computer in
     Amsterdam; 200-digit numbers can now be handled within approximately
     ten minutes.  In this talk this algorithm and its implementation
     will be discussed.