Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

Spline Knots and Their Control Polygons With Differing Knottedness

Carlo H. Séquin

EECS Department
University of California, Berkeley
Technical Report No. UCB/EECS-2009-152
November 1, 2009

http://www.eecs.berkeley.edu/Pubs/TechRpts/2009/EECS-2009-152.pdf

Spline knots based on Bézier curves or B-splines can exhibit a knot type that is different from that exhibited by its control polygon, i.e., the spline and its control polygon are not ambient isotopic. By forming composite knots from suitably designed building blocks the difference in knottedness of the two 1-manifolds can be made arbitrarily large.


BibTeX citation:

@techreport{Séquin:EECS-2009-152,
    Author = {Séquin, Carlo H.},
    Title = {Spline Knots and Their Control Polygons With Differing Knottedness},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {2009},
    Month = {Nov},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2009/EECS-2009-152.html},
    Number = {UCB/EECS-2009-152},
    Abstract = {Spline knots based on Bézier curves or B-splines can exhibit a knot type that is different from that exhibited by its control polygon, i.e., the spline and its control polygon are not ambient isotopic. By forming composite knots from suitably designed building blocks the difference in knottedness of the two 1-manifolds can be made arbitrarily large.}
}

EndNote citation:

%0 Report
%A Séquin, Carlo H.
%T Spline Knots and Their Control Polygons With Differing Knottedness
%I EECS Department, University of California, Berkeley
%D 2009
%8 November 1
%@ UCB/EECS-2009-152
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/2009/EECS-2009-152.html
%F Séquin:EECS-2009-152