ylfink@water.UUCP (10/28/87)
DEPARTMENT OF COMPUTER SCIENCE
UNIVERSITY OF WATERLOO
SEMINAR ACTIVITIES
COMPUTER GRAPHICS SEMINAR
- Monday, November 2, 1987
Dr. Charles A. Micchelli, of IBM, will speak on
``Geometric Continuity and Corner Cutting Algorithms
For Piecewise Polynomial Curves''.
TIME: 2:00 PM
ROOM: MC 6082
ABSTRACT
This talk deals with two problems related to modeling
curves by piecewise polynomials. The main problem
discussed is that of various interpretations of the
notion of ``visual'' continuity of curves. This leads
us into methods for curve representation that have
``shape parameters'' which can be used to model a curve
while still preserving its visual smoothness. The
resulting piecewise polynomial spaces determined by
connection matrices are analyzed and shown to share
familiar properties of spline functions.
The second issues we address concerns algorithms which
successively compute convex combinations of adjacent
control points to pass from some preferred piecewise
polynomial representation of a curve to its Bezier
representation. We discuss circumstances when there
are such corner cutting algorithms and show, in
particular, that this is available for curves modeled
piecewise polynomials determined by certain connection
matrices.