File:Cubic surface.gif
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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:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- 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.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 12:34, 5 November 2018 | | 400 × 400 (3.36 MB) | wikimediacommons>Anpe0681 | bottom caption: make font normal, reduce font size |
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