MaplePrimes - answers and comments on Question, How to extract all points from an implicitplot3d structure

Interpolation

Preben Alsholm — Fri, 08 Mar 2013 22:10:25 Z

From the help page for implicitplot3d:

"It uses an numerical algorithm based on triangulation into tetrahedrons combined with simple interpolation."

I guess the plotting interface is doing the interpolation and the resulting points are not available. That may be the reason that isosurface structures are not handled by plottools:-getdata.

Without implicitplot3d (in any case, for the connected sets)…

one_man — Fri, 08 Mar 2013 22:12:44 Z

The Draghilev method for F(x,y,z)=0. Many points with good precision (variants with h and h1).

diffanimationAA.mw

2.5e-2 is too restrictive

Carl Love — Fri, 08 Mar 2013 22:45:15 Z

Try raising your cutoff value of 2.5e-2 to 0.3 or 0.4. Then you can really see the points from which it is interpolating the surface. You can see a collection of points on each side of the surface such that the surface lies neatly between them. It might also be instructive to vary the symbolsize of your plotted points, with points closer to the surface plotted larger. This might give more of a clue as to how the algorithm works.

Thank you

Adri van der Meer — Tue, 12 Mar 2013 19:06:00 Z

Now I understand that it is not possible (at least not efficient) to try to extract points on the surface from the plot structure. Draghilev method (one-man) is a good suggestion.