# [Maxima] Cornu spiral

Edwin Woollett woollett at charter.net
Wed Dec 10 15:04:35 CST 2008

```On Dec. 9, Richard Hennessy wrote:
------------------------------------
Try
assume(t>0)\$
x (t) := ''(integrate (cos (s^2 * %pi/2), s, 0, t))\$
y (t) := ''(integrate (sin (s^2 * %pi/2), s, 0, t))\$
showtime:true\$
L:makelist([realpart(float(x(t/100))),realpart(float(y(t/100)))],t,0,300)\$
draw2d(points_joined=true, point_type=dot, points(L))\$

This smooths out the curve very well.
--------------------------------------------

Hi Richard,
Thanks for the suggestions, and the list plot approach
does excellent smoothing of draw2d's parametric plot.

I have looked at the smoothing switches in draw2d
which are ip_grid (first pass grid), and ip_grid_in.
( second pass grid ),
the first has the default value [50,50] according to
the manual, and the second has the default value
[5,5] according to the manual.

Using my qdraw defaults with draw2d directly
( ip_grid_in = [10,10] , nticks = 100 ,
and line_width = 3 ) , draw2d produces
a nice smooth (and thicker) cornu spiral.

Equivalent nice smooth curves:

draw2d( nticks = 100, line_width = 3,
ip_grid_in = [10,10],
parametric( x(t), y(t), t, 0, 3) )\$

qdraw( para (x(t), y(t), t,0,3 ) )\$

So thanks to Robert Dodier for the double quote
construct for a much simpler approach that works.

But, until Dieter Kaiser crafts a new erf(z) evaluation, we are
restricted in the range of t to about 4.8.

Ted Woollett
http://www.csulb.edu/~woollett/

```