Getting coordinates on curve.

Hello everybody and special one for Dan.

Today I thought about interesting mathematical thing...
It's even more spooky as for me then arrow functions...

Let's imagine if we have curve with 2 points.
[like this](http://savepic.net/10282822.htm)

And...What if we'll want to get all points of this CURVE ? (between point2 and point3 from image)...
And what if they're moving? (point 2 and point 3 coordinates belongs to objects with their own life).
Here should exist some kind of formula I guess...
what if...we'll have special lesson for it ? :D
(and maybe if it realy will be lesson someday - how about curve with more then 2 points...)