I frequently have this rendering problem when I plot a complicated curve with ParametricPlot3D, found by solving a differential equation with NDSolve :
The curve should be more "regular" (it is showing the motion of a charged particle around some magnetic field lines). I've indicated in red the typical artifacts I'm getting. And yet, in ParametricPlot3D, I'm using options like these :
PlotPoints -> 1000, MaxRecursion -> 7, PerformanceGoal -> "Quality"
In NDSolve, I'm using these options :
Method -> ExplicitRungeKutta, PrecisionGoal -> 7, MaxSteps -> 1000000,
So what may be wrong ? How can I get a better graphical output of the curve, without the glitches and straight line artifacts shown on the picture above ?
EDIT : You can see some of the artifacts I'm describing if you play a bit with the code from this demonstration (you need to lower the "velocity" and "distance", using the Manipulate sliders.) : http://demonstrations.wolfram.com/DipoleFieldsAreComplicated/
My own code is more complicated than this demo (this is why I don't provide a MWE example here), but the artifacts are the same.