6-Contributor

Question

implicit surface

Forum|Forum|12 years ago
November 23, 2013
6 replies
8633 views

Is it possible to plot an implicit surface

like the Ortho Circles Surface

f(x,y,z)=((x^2 + y^2 - 1)^2 + z^2)*((y^2 + z^2 - 1)^2 + x^2)*((z^2 + x^2 - 1)^2 + y^2) - ff^2*(1 + bb*(x^2 + y^2 + z^2))

thank you!

Other

W

Werner_E

25-Diamond I

You mean to plot f(x,y,z)=0, right? Otherwise you would demand to plot a 3-dimensional structure in 4-dimensional space.

Mathcad unfortunately does not support plotting of implicit functions, neither 2D nor 3D. Its a long voiced but still unfulfilled wish of the Mathcad community to be able to do so.

That does not mean that its impossible, but Mathcad would need a little (to be honest, much) help to be capable to plot your function. You would have to specify ff and bb, of course.

V

ValeryOchkov

24-Ruby IV

See pease pictures in this article

http://twt.mpei.ac.ru/ochkov/Ellipsoid/index.htm

W

Werner_E

25-Diamond I

This is what it looks like (ff=0.075, bb=3) if you follow Valery's suggestion and use that kind of Monte Carlo procedure.

And this is what is should look like (done with PovRay by P. Burke (http://paulbourke.net/geometry/orthocircle/)

What I had in mind was the approach of Viacheslav Mezentsev: http://communities.ptc.com/message/23461#23461

W

Werner_E

25-Diamond I

This is the result of Viacheslav's fine method for implicit plots.

Its not raytracig quality but quite good. Drawback is the calculation time. The picture was made with an 80x80x80 grid and took "endless".

If the goal is just implicit plotting you may use other software packages like Maple or Mathcad. But for even better results you may use software like PovRay (see above) or Surfer (http://www.imaginary-exhibition.com/surfer?lang=en).

W

Werner_E

25-Diamond I

Forgot to attach the Mathcad sheet in the last post - here it is.

The following pic and the attached animation was done with the free software Surfer (link in post above):

1_implicit3D_OrthoCircles-xmcdz.zip

2_Implicit3D_01surfer.avi

V

ValeryOchkov

24-Ruby IV

Thanks, Werner - a fine animation!

I see it and think about this 3D surfase - see bellow.

What is its implicit formulа f(x, y, z):=???

Can we create it for next Halloween day?

PS

Mathcad 15 has 8 outside points for the lighting 3D surfaces

Mathcad MM and Prime Minister has an add one inside points for the lighting 3D surfaces

PPS

Werner, sorry, I see You have a lot of time for Mathcad and PlanetPTC..

Can You help me to translate this text into English?

http://twt.mpei.ac.ru/ochkov/Ellipsoid/index.htm

I hope it will be interesting for Mathcad users.

M

mj2

Author

6-Contributor

Thank you Valery and Werner for the answers.

Thank you very much for the worksheet. It is amazing your job.

I know the the imaginay exhibition web and the surfer software but I wanted to reproduce those surfaces in mathcad. I would like my students to create funny or interesting surfaces (like the Halloween pumpkin) with mathcad and print 3D models of the results.

I hope that mathcad developers add your implicitplot3d() function in the future versions of mathcad