Bezier Spline Sigmac Project
For your final project, you will generate a "sigmac" (signature machine) from
your signature (or other word at least 6 distinct letters long), as well
as carry out a few preliminary analyses.
Essentially you have to determine the so-called "control points" for a Bezier
spline that will cause some piece of software (your choice) to draw your
signature.
A Bezier spline is made up of cubics of the form
=(1-t)^3\bf{P}_0+3(1-t)^2t\bf{P}_1+3(1-t)t^2\bf{P}_2+t^3\bf{P}_3{}})
The following problems should be written up, most sensibly perhaps in a
Mathematica notebook (but you may use Word, for example).
- Given points
})
,
})
})
, investigate graphically
the range of motion of the Bezier cubic possible depending on the choice of
control point 
.
Describe the kinds of qualitatively different curves you can generate.
- Under what conditions will a Bezier cubic actually pass through
one or both of the control points
and ?
- Since many letters contain a circle, create a Bezier cubic spline
that does a nice job of approximating the unit circle. Describe your
criterion for "nice".
- Sample your signature for the interpolating points (best to do
this on a piece of graph paper), and then choose your control points so
as to generate your sigmac. Print out a copy of your signature, as well
as the output of your sigmac.
Discuss the success you had, and the problems you encountered.
Website maintained by Andy Long.
Comments appreciated.