Envelope of family of 2D graphs?

[juliangilbey]

I want to demonstrate the accessible region of a projectile to a further maths group.  I have parametric equations x=ut cos a, y=ut sin a - 1/2gt^2, with an appropriate range of t, and those plot fine.  I can change the value of a using the constant controller, and can animate it too.

But what I\'d really like to be able to do is to get Autograph to draw the curves for a=0, 5, 10, ..., 90 with them all being simultaneously visible, so that the envelope of the family of curves becomes clear.  This facility would also be useful when demonstrating the effect of adjusting parameters in definitions of conics and so on, as well as for demonstrating envelopes of other families.

Is there a way to do this other than entering all of the equations explicitly?

Thanks!

Julian

[Simon]

Dear Julian,

Autograph can do exactly this, we call it the "family plot" function.  Select the parametric curve you entered and then the Constant Controller icon on the top toolbar.  Select Options, then family plot and enter the parameters you want (Start: 0, Finish: 90, Step:10).  Click OK.

Hope this helps!  Remember to check out Version 3.2 which is just about to be released!

Best regards,

Simon

[juliangilbey]

Thanks - that\'s perfect!

Julian