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Numerical parameterization implicit surfaces of the form f (x, y, z) = 0
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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) Edited by user 21 October 2018 20:26:30(UTC)
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on 18/12/2016(UTC), on 19/12/2016(UTC), on 19/12/2016(UTC)
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Two surfaces are taken from the site http://xrt.wikidot.com/gallery:implicitThe 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. double torus x2.sm (74kb) downloaded 44 time(s). Bretzel (4 holes).sm (215kb) downloaded 35 time(s).Edited by user 30 January 2017 09:27:33(UTC)
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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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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 (74kb) downloaded 40 time(s).
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on 30/01/2017(UTC), on 30/01/2017(UTC)
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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 Maths sph2xyz.sm (14kb) downloaded 34 time(s).
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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 (22kb) downloaded 41 time(s).
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on 06/02/2018(UTC), on 06/02/2018(UTC), on 06/02/2018(UTC)
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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 (493kb) downloaded 37 time(s).Edited by user 06 February 2018 11:09:11(UTC)
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on 06/02/2018(UTC), on 06/02/2018(UTC), on 06/02/2018(UTC), on 06/02/2018(UTC)
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Numerical parameterization implicit surfaces of the form f (x, y, z) = 0
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