# Choppy graphs in mathematica

1. Nov 20, 2007

### robert spicuzza

I have recently been working in Mathematica 6.0 trying to graph various curves using ParametricPlot3D. I have specifically defined:
a1[p_]={(sqrt(25-p^2))*Sin[10*p],(Sqrt(25-p^2))*Cos[10*p],(p)^2};

Graphing this is no problem.

The problem is I am trying to turn this into a Fernet type curve using the standard INT normalized basis vectors one studies in Cal3. ( take the tangent vector, then the normal vector, then the cross product). When I finally end up using the PramametricPlot3D the result although looking correct is pretty rough (very choppy, not clean at all) .

Any thoughts on how to improving the appearance and hopefully calculation speed as I want to ultimately use this in a much larger Mathematica programming context.

I have tried other simplifier Fernet curves and they look ok, examples like a standard doughnut or corkscrew, {Sin, Cos, u }

I assume I probably need to carry greater immediate precision in the various calculations and also need to somehow speed up the calculations. I’ve tried some increased precision commands, but they did not help the graph.

Thanks

2. Nov 20, 2007

### robert spicuzza

made the graph a little better

After calculating the normal and bi normal vector I adjusted the final parameters:
I used 0.1v with v from 0 to 500

This made the curve look a little crisper, but it still has its problems.

The final fernet equation using the normal and bi-normal vectors
w[p_, v_] := a1[p] + 1.0 Sin[.10 v]*an[p] + 1.0 Cos[.10 v]*ab[p];
pp = ParametricPlot3D[w[p, v], {p, 0, 10}, {v, 0, 500*Pi},
PlotRange -> {{-8, 8}, {-8, 8}, {0, 30}}]

Again I think the precision issue is really the problem.
Again any thoughts!

Bob