Numerical parameterization implicit surfaces of the form f (x, y, z) = 0

#1 Pubblicato: 29/05/2015 20:25:23

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The grid lines are found by Draghilev Method
Method 1.
Building a line of intersection of the required surface
with the plane x = 0. This line is rotated in steps of 2 * Pi / s
about a vertical axis by an angle 2 * Pi, where s is the number of steps (the grid lines)

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Davide Carpi 31/05/2015 07:19:00

#2 Pubblicato: 29/05/2015 20:39:51

Fridel Selitsky

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Method 2.
The rectangular grid

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Davide Carpi 31/05/2015 07:19:00

#3 Pubblicato: 17/12/2016 18:17:47

Fridel Selitsky

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The graph an implicit surface depicted by lines
Examples of the idea of the algorithm taken from the publication of Alexey Ivanov
http://www.mapleprimes.com/questions/219995-Finding-A-Convinient-Parametrization-Of-Surfaces#answer233804

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Вячеслав Мезенцев 19/12/2016 01:43:00, Davide Carpi 18/12/2016 19:04:00, frapuano 18/12/2016 05:42:00

#4 Pubblicato: 29/01/2017 16:56:41

Fridel Selitsky

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Two surfaces are taken from the site
http://xrt.wikidot.com/gallery:implicit
The calculation algorithm:
1.Find the line of intersection of the given surface with the plane Z=0
2.Through each point hold the plane x1 = C and find the line of intersection of that plane with a given surface.These lines represent a given surface.

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Davide Carpi 30/01/2017 09:18:00

#5 Pubblicato: 29/01/2017 23:28:16

Jean Giraud

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Thanks for these two animations. In each one, the last three plots
stay red, though the animated plot works fine. A small detail:
each work sheet has three definitions left over at page 17.

Jean

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Davide Carpi 30/01/2017 09:18:00

#6 Pubblicato: 30/01/2017 03:51:39

Fridel Selitsky

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Thank you Jean,
Worksheets corrected. In addition, in the algorithm for calculating along with x1 = C can be used x2 = C:

double torus x2.sm (73,26 KiB) scaricato 1321 volta(e).

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Davide Carpi 30/01/2017 09:18:00, NDTM Amarasekera 30/01/2017 11:30:00

#7 Pubblicato: 31/01/2017 17:50:55

Fridel Selitsky

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The tube in the form of a line of intersection of the cylinder and the torus (See post 7)
http://en.smath.info/forum/yaf_postst2307_Method-A-B--Draghilev-and-animation-spatial-mechanisms.aspx

Time calculation, 9 min.
Villarceau 9.sm (39,38 KiB) scaricato 1302 volta(e).

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Davide Carpi 01/02/2017 05:58:00

#8 Pubblicato: 01/03/2017 04:25:37

Fridel Selitsky

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Helical Tube

NonCirc.sm (53,28 KiB) scaricato 1289 volta(e).
TubeCir.sm (53,28 KiB) scaricato 1345 volta(e).

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Davide Carpi 01/03/2017 06:42:00

#9 Pubblicato: 01/03/2017 04:44:07

Fridel Selitsky

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The surface of the Wikipedia
https://en.wikipedia.org/wiki/File:Tri-brezel.svg

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Davide Carpi 01/03/2017 06:42:00

#10 Pubblicato: 14/06/2017 13:27:49

Fridel Selitsky

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Non-circular cylindrical vessels with quasi-ellipsoidal ends
Krivoshapko S.N. Ivanov V.N,Encyclopedia of Analytical Surfaces ,Springer,2015

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Non-circular cylindrical vessels.sm (209,71 KiB) scaricato 1341 volta(e).
Shell1.sm (255,15 KiB) scaricato 1379 volta(e).
Shell2.sm (33,38 KiB) scaricato 1359 volta(e).
Shell3.sm (34,18 KiB) scaricato 1304 volta(e).

#11 Pubblicato: 15/06/2017 09:43:57

Jean Giraud

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Thanks Ber7 for the work sheets [Not finished downloading].
If you visit this document, I'm wondering:
"How to add red points in this plot".

Thanks in advance ... Jean

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#12 Pubblicato: 15/06/2017 12:23:51

Fridel Selitsky

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Hello Jean,
Unfortunately, the 3d chart does not allow you to draw points.
Exit (hopefully temporary) -make a 3d chart on a 2d chart.
Maths sph2xyz2d.sm (21,1 KiB) scaricato 1335 volta(e).

#13 Pubblicato: 06/02/2018 03:56:52

Fridel Selitsky

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Implicit surfaces in Maxima

ImplicitMaxima.sm (363,82 KiB) scaricato 1365 volta(e).

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frapuano 06/02/2018 04:34:00, Martin Kraska 06/02/2018 04:59:00, Radovan Omorjan 06/02/2018 06:22:00

#14 Pubblicato: 06/02/2018 05:06:49

Martin Kraska

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Nice examples!

Just some remarks for those who want to play around with Maxima Draw.

Instead of Image region with Draw() command you can use Maxima Draw3D region with interactive zoom, rotation and resize and a settings dialog.
Insert-> Maxima-> Draw3D
The performance isn't overwhelming, as the image is recalculated for each interaction.
The snippet "draw" provides help texts for the available draw commands and options.
Follow the link in my signature to see how to configure SMath with Maxima.

ImplicitMaxima_Kr.sm (492,51 KiB) scaricato 1404 volta(e).

2018-02-06 08_55_49-SMath Studio - [ImplicitMaxima.sm_].png

Technische Mechanik mit SMath Studio: https://link.springer.com/book/10.1007/978-3-658-50592-9

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Вячеслав Мезенцев 06/02/2018 06:15:00, Radovan Omorjan 06/02/2018 06:22:00, frapuano 06/02/2018 10:28:00, Fridel Selitsky 06/02/2018 05:08:00

#15 Pubblicato: 21/02/2018 16:41:18

Fridel Selitsky

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Continuation:

MaximPlus1.sm (237,91 KiB) scaricato 1335 volta(e).

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frapuano 21/02/2018 18:56:00

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Numerical parameterization implicit surfaces of the form f (x, y, z) = 0 - Messaggi