File:Cubic surface.gif
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Cubic_surface.gif (400 × 400 pixels, file size: 3.36 MB, MIME type: image/gif, luip't, 50 frames, 17 s)
Ootline
| Descreeption |
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 | |
| Soorce | Ain wirk |
| 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]);
Licensin
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed unner the Creative Commons Attribution-Share Alike 3.0 Unported license.
- Ye are free:
- tae share – tae copy, distribute an transmit the wirk
- tae remix – tae adapt the wirk
- Unner the follaein condeetions:
- attribution – Ye must attribute the wirk in the manner specified bi the author or licensor (but nae in ony way that suggests that thay endorse ye or yer uise o the wirk).
- share alik – If ye alter, transform, or big upon this wirk, ye mey distribute the resultin wirk anly unner the same or seemilar license tae this ane.
File history
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| Date/Time | Thummnail | Dimensions | Uiser | Comment | |
|---|---|---|---|---|---|
| current | 11:34, 5 November 2018 | | 400 × 400 (3.36 MB) | wikimediacommons>Anpe0681 | bottom caption: make font normal, reduce font size |
File uisage
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