Drawing curved lines - which app?

I am trying to find the best application for drawing curved lines (over
a background photo).  I am trying Photoshop and Illustrator, and I have
used mspaint for sometime.

The main feature I need is to be able to pick a series of points that
will represent points on a CURVED line, and then when I terminate the
open line, I need the application to smooth out the jaggies for me
according to the following rule:  the curvature at each of the non-end
point lines should be parallel to the line drawn from the two points on
either side of the given point.  The curvature at the end points should
complete a circular arc from the nearest inner point.

If that rule seems complicated, it really isn't.  It just makes sense
for curved lines to always be heading through any given point parallel
to a line drawn from the two surrounding points.

Illustrator and photoshop allow me to manually control the slope by
dragging, but, it is very cumbersome and course, and I find it not easy
to make the correct slopes this way.  If either of these two apps have
an automatic "curve smoothing" option that follows the rule above, I
need to learn about that.

Another option I would like would be for the app to be able to adjust
both the color, the width, and the anti-aliasing, according to values
that are set for the two points.  So, if I pick a point and make it
small and red, then I pick the next point and make it large and blue,
then the app should vary both the color and thickness evenly from on
point to the next (ditto with the degree of anti-aliasing applied).
Does that make sense?

Anyway, I am seeking an application that all this curvesmooting worked
out.  Any ideas?

littlberry