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Cubic_surface.gif (400 × 400 pixels, file size: 3.36 MB, MIME type: image/gif, looped, 50 frames, 17 s)

Summary

Description
English: Cubic surface. Section with plane x=0 (as well as y=0) - parabola, eccentricity e=1, sections with planes z=k, k=0..0.5 - ellipses with e from 0 to 1, k=0.5..1 - hyperbolas with e from 1 to infinity. Painted in Maple. Author of this animation calls this surface Marsik's Surface.
Русский: Поверхность 3-го порядка. В сечении плоскостью x=0 (а также y=0) — парабола, эксцентриситет e=1, в сечении плоскостями z=k, k=0..0.5 — эллипсы с e от 0 до 1, при k=0.5..1 — гиперболы с e от 1 до бесконечности. Нарисована в Maple. Чтобы увидеть все эти сечения в реальности, можно попробовать отпечатать эту поверхность на 3d-принтере, поместить в ёмкость и наполнять её водой. Автор этой анимации называет эту поверхность поверхностью Марсика.
Date
Source Own work
Author Anpe0681

Source code:

restart; with(plots):
A := implicitplot3d(x^2*(1-2*z)+y^2*(1-z)-(1-2*z)*(1-z) = 0, x = -1 .. 1, y = -1 .. 1, z = 0 .. 1, axes = boxed, numpoints = 9000, view = [-1 .. 1, -1 .. 1, 0 .. 1]):
F := proc(t) 
global pl,eks;
pl := implicitplot3d(z = t, x = -1 .. 1, y = -1 .. 1, z = 0 .. 1, color = blue);
eks := evalf(sqrt(t/(1-t)));
if t<0.5 then 
pr1 := spacecurve([sqrt(1-t)*cos(s), sqrt(1-2*t)*sin(s), t+0.005], s = 0 .. 2*Pi, color = red, thickness = 5);
display(pr1, pl, caption = typeset(cat("z= ", sprintf("%2.3f", t)), cat(",   e= ", sprintf("%2.3f", eks))),captionfont=[HELVETICA, NORMAL, 20]);
else
pr1 := spacecurve([sqrt(1-t)*cosh(s)+0.01, sqrt(2*t-1)*sinh(s), t], s = -2 .. 2, color = red, thickness = 5);
pr2 := spacecurve([-sqrt(1-t)*cosh(s)+0.05, sqrt(2*t-1)*sinh(s), t], s = -2 .. 2, color = red, thickness = 5);
display(pr1, pr2, pl, caption = typeset(cat("z= ", sprintf("%2.3f", t)), cat(",   e= ", sprintf("%2.3f", eks))), captionfont=[HELVETICA, NORMAL, 20]);
end if;
end proc:
animate(F, [theta], theta = 0..0.999, background = A, axes = boxed, frames = 50, title = typeset(x^2*(1-2*z)+y^2*(1-z)-(1-2*z)*(1-z) = 0), titlefont = [HELVETICA, BOLD, 12]);

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
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You are free:
  • to share – to copy, distribute and transmit the work
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Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

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depicts

2 December 2012

image/gif

b97131389dfb2088037fd6804b407c071ec8be07

3,521,861 byte

16.5 second

400 pixel

400 pixel

File history

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Date/TimeThumbnailDimensionsUserComment
current10:34, 5 November 2018Thumbnail for version as of 10:34, 5 November 2018400 × 400 (3.36 MB)Anpe0681bottom caption: make font normal, reduce font size
15:50, 4 November 2018Thumbnail for version as of 15:50, 4 November 2018400 × 400 (3.34 MB)Anpe0681caption splitted into top and bottom part, font size increased
07:45, 4 November 2018Thumbnail for version as of 07:45, 4 November 2018446 × 400 (3.31 MB)Anpe0681number of frames reduced for fasterload, render them slowly, bold font
18:10, 3 November 2018Thumbnail for version as of 18:10, 3 November 2018412 × 400 (9.68 MB)Anpe0681increased sizes of the plot and the image
17:37, 3 November 2018Thumbnail for version as of 17:37, 3 November 2018406 × 400 (6.62 MB)Anpe0681more frames, sections highlighted
13:23, 11 October 2016Thumbnail for version as of 13:23, 11 October 2016436 × 400 (2.09 MB)Anpe0681error fixed
18:37, 2 December 2012Thumbnail for version as of 18:37, 2 December 2012400 × 400 (2.05 MB)Anpe0681User created page with UploadWizard

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