File:Cubic surface.gif

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Summary

DescriptionCubic surface.gif	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	2 December 2012, 20:35:51
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

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File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Dimensions	User	Comment
current	10:34, 5 November 2018	400 × 400 (3.36 MB)	Anpe0681	bottom caption: make font normal, reduce font size
	15:50, 4 November 2018	400 × 400 (3.34 MB)	Anpe0681	caption splitted into top and bottom part, font size increased
	07:45, 4 November 2018	446 × 400 (3.31 MB)	Anpe0681	number of frames reduced for fasterload, render them slowly, bold font
	18:10, 3 November 2018	412 × 400 (9.68 MB)	Anpe0681	increased sizes of the plot and the image
	17:37, 3 November 2018	406 × 400 (6.62 MB)	Anpe0681	more frames, sections highlighted
	13:23, 11 October 2016	436 × 400 (2.09 MB)	Anpe0681	error fixed
	18:37, 2 December 2012	400 × 400 (2.05 MB)	Anpe0681	User created page with UploadWizard