Draw a truncated pyramid with a square base
9
I want to draw a truncated pyramid that is suspended on a rope, and submersed inside water in a cylinder.
documentclass{standalone}
usepackage{tikz}
usetikzlibrary{patterns}
begin{document}
begin{tikzpicture}
draw[gray!66](0,1) ellipse (2cm and 1cm);
draw(0,2) ellipse (2cm and 1cm);
draw(0,-3) ellipse (2cm and 1cm);
draw(2,-3)--(2,2);
draw(-2,-3)--(-2,2);
fill[pattern=north west lines](-1,4.4) rectangle (1,4.75);
draw(-1,4.4)--(1,4.4);
draw(0,4.4)--(0,-1);
end{tikzpicture}
end{document}
tikz-pgf
edited Feb 4 at 14:46
Peter Mortensen
55037
asked Feb 4 at 5:41
ThumboltThumbolt
1,509821
add a comment |
9
I want to draw a truncated pyramid that is suspended on a rope, and submersed inside water in a cylinder.
documentclass{standalone}
usepackage{tikz}
usetikzlibrary{patterns}
begin{document}
begin{tikzpicture}
draw[gray!66](0,1) ellipse (2cm and 1cm);
draw(0,2) ellipse (2cm and 1cm);
draw(0,-3) ellipse (2cm and 1cm);
draw(2,-3)--(2,2);
draw(-2,-3)--(-2,2);
fill[pattern=north west lines](-1,4.4) rectangle (1,4.75);
draw(-1,4.4)--(1,4.4);
draw(0,4.4)--(0,-1);
end{tikzpicture}
end{document}
tikz-pgf
edited Feb 4 at 14:46
Peter Mortensen
55037
asked Feb 4 at 5:41
ThumboltThumbolt
1,509821
add a comment |
9
9
9
I want to draw a truncated pyramid that is suspended on a rope, and submersed inside water in a cylinder.
documentclass{standalone}
usepackage{tikz}
usetikzlibrary{patterns}
begin{document}
begin{tikzpicture}
draw[gray!66](0,1) ellipse (2cm and 1cm);
draw(0,2) ellipse (2cm and 1cm);
draw(0,-3) ellipse (2cm and 1cm);
draw(2,-3)--(2,2);
draw(-2,-3)--(-2,2);
fill[pattern=north west lines](-1,4.4) rectangle (1,4.75);
draw(-1,4.4)--(1,4.4);
draw(0,4.4)--(0,-1);
end{tikzpicture}
end{document}
tikz-pgf
edited Feb 4 at 14:46
Peter Mortensen
55037
asked Feb 4 at 5:41
ThumboltThumbolt
1,509821
I want to draw a truncated pyramid that is suspended on a rope, and submersed inside water in a cylinder.
documentclass{standalone}
usepackage{tikz}
usetikzlibrary{patterns}
begin{document}
begin{tikzpicture}
draw[gray!66](0,1) ellipse (2cm and 1cm);
draw(0,2) ellipse (2cm and 1cm);
draw(0,-3) ellipse (2cm and 1cm);
draw(2,-3)--(2,2);
draw(-2,-3)--(-2,2);
fill[pattern=north west lines](-1,4.4) rectangle (1,4.75);
draw(-1,4.4)--(1,4.4);
draw(0,4.4)--(0,-1);
end{tikzpicture}
end{document}
tikz-pgf
tikz-pgf
edited Feb 4 at 14:46
Peter Mortensen
55037
asked Feb 4 at 5:41
ThumboltThumbolt
1,509821
edited Feb 4 at 14:46
Peter Mortensen
55037
asked Feb 4 at 5:41
ThumboltThumbolt
1,509821
edited Feb 4 at 14:46
Peter Mortensen
55037
edited Feb 4 at 14:46
Peter Mortensen
55037
edited Feb 4 at 14:46
Peter Mortensen
55037
55037
asked Feb 4 at 5:41
ThumboltThumbolt
1,509821
asked Feb 4 at 5:41
ThumboltThumbolt
1,509821
asked Feb 4 at 5:41
ThumboltThumbolt
1,509821
1,509821
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
15
I'd use 3d coordinates for that.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{tikz-3dplot}
usetikzlibrary{patterns}
% https://tex.stackexchange.com/a/12033/121799
tikzset{reverseclip/.style={insert path={(current bounding box.north
east) rectangle (current bounding box.south west)}}}
begin{document}
tdplotsetmaincoords{70}{30}
begin{tikzpicture}[tdplot_main_coords,font=sffamily,line join=bevel]
pgfmathsetmacro{rcyl}{2}
pgfmathsetmacro{hcyl}{5}
pgfmathsetmacro{hpyr}{2.5}
pgfmathsetmacro{hremoved}{0.5}
pgfmathsetmacro{zpyr}{3.5}
pgfmathsetmacro{wpyr}{1.5}
pgfmathsetmacro{wtop}{hremoved*wpyr/hpyr}
pgfmathsetmacro{hwater}{4}
pgfmathsetmacro{whpyr}{wpyr-(hwater-zpyr)*wpyr/hpyr} % width of pyramid at water level
fill[tdplot_screen_coords,pattern=north west lines] (-1,7.4) rectangle (1,7.75);
draw[tdplot_screen_coords] (-1,7.4) -- (1,7.4) coordinate[midway] (hang);
%
draw[dashed] plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi+180] ({rcyl*cos(t)},{rcyl*sin(t)},0);
draw[dashed] (wpyr/2,wpyr/2,zpyr)
-- (-wpyr/2,wpyr/2,zpyr) -- (-wpyr/2,-wpyr/2,zpyr)
(-wpyr/2,wpyr/2,zpyr) -- (-wtop/2,wtop/2,zpyr+hpyr-hremoved);
draw[fill=gray!30,fill opacity=0.5]
(-wpyr/2,-wpyr/2,zpyr) -- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- (wpyr/2,-wpyr/2,zpyr)
-- cycle;
draw[fill=gray!50,fill opacity=0.5] (wpyr/2,-wpyr/2,zpyr)
-- (wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (wpyr/2,wpyr/2,zpyr)
-- cycle;
draw[fill=gray!20,fill opacity=0.5]
(wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- cycle;
begin{scope}
clip (-whpyr/2,-whpyr/2,hwater)
-- (whpyr/2,-whpyr/2,hwater) -- (whpyr/2,whpyr/2,hwater)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- (-whpyr/2,-whpyr/2,hwater)
[reverseclip];
fill[blue,opacity=0.2]
plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi+360] ({rcyl*cos(t)},{rcyl*sin(t)},hwater);
end{scope}
fill[blue,opacity=0.4]
plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi-180]
({rcyl*cos(t)},{rcyl*sin(t)},hwater)
--
plot[smooth,variable=t,domain=tdplotmainphi-180:tdplotmainphi]
({rcyl*cos(t)},{rcyl*sin(t)},0);
draw plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi-180]
({rcyl*cos(t)},{rcyl*sin(t)},0)
-- plot[smooth,variable=t,domain=tdplotmainphi-180:tdplotmainphi+180] ({rcyl*cos(t)},{rcyl*sin(t)},hcyl)
({rcyl*cos(tdplotmainphi)},{rcyl*sin(tdplotmainphi)},0) --
({rcyl*cos(tdplotmainphi)},{rcyl*sin(tdplotmainphi)},hcyl);
draw (hang) -- (0,0,zpyr+hpyr-hremoved);
end{tikzpicture}
end{document}
And this is an animation for Christian Hupfer with corrections due to @circumscribe.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{tikz-3dplot}
usetikzlibrary{patterns}
% https://tex.stackexchange.com/a/12033/121799
tikzset{reverseclip/.style={insert path={(current bounding box.north
east) rectangle (current bounding box.south west)}}}
begin{document}
foreach Z in {0,10,...,350}
{tdplotsetmaincoords{70}{30}
begin{tikzpicture}[tdplot_main_coords,font=sffamily,line join=bevel]
pgfmathsetmacro{rcyl}{2}
pgfmathsetmacro{hcyl}{5}
pgfmathsetmacro{hpyr}{2.5}
pgfmathsetmacro{hremoved}{1.2}
pgfmathsetmacro{zpyr}{2.8+0.8*cos(Z)}
pgfmathsetmacro{wpyr}{1.5}
pgfmathsetmacro{wtop}{hremoved*wpyr/hpyr}
pgfmathsetmacro{hwater}{4}
pgfmathsetmacro{deltahmax}{(wpyr^2/(pi*rcyl^2))*(hpyr-hremoved^3/hpyr^2)/3}
pgfmathsetmacro{waterlevel}{hwater+ifthenelse(zpyr<hwater,1,0)*deltahmax*
ifthenelse(zpyr>hwater-hpyr+hremoved,
1-((zpyr-hwater+hpyr-hremoved)/(hpyr-hremoved))^3,1)}
%typeout{deltahmax=deltahmax,waterlevel=waterlevel,zpyr=zpyr,hwater=hwater}
fill[tdplot_screen_coords,pattern=north west lines] (-1,7.4) rectangle (1,7.75);
draw[tdplot_screen_coords] (-1,7.4) -- (1,7.4) coordinate[midway] (hang);
%
draw[dashed] plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi+180] ({rcyl*cos(t)},{rcyl*sin(t)},0);
draw[dashed] (wpyr/2,wpyr/2,zpyr)
-- (-wpyr/2,wpyr/2,zpyr) -- (-wpyr/2,-wpyr/2,zpyr)
(-wpyr/2,wpyr/2,zpyr) -- (-wtop/2,wtop/2,zpyr+hpyr-hremoved);
draw[fill=gray!30,fill opacity=0.5]
(-wpyr/2,-wpyr/2,zpyr) -- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- (wpyr/2,-wpyr/2,zpyr)
-- cycle;
draw[fill=gray!50,fill opacity=0.5] (wpyr/2,-wpyr/2,zpyr)
-- (wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (wpyr/2,wpyr/2,zpyr)
-- cycle;
draw[fill=gray!20,fill opacity=0.5]
(wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- cycle;
pgfmathsetmacro{whpyr}{wpyr-(waterlevel-zpyr)*wpyr/hpyr} % width of pyramid at water level
begin{scope}
pgfmathtruncatemacro{itest}{sign(-(waterlevel-zpyr)+(hpyr-hremoved))}
ifnumitest=1
clip (-whpyr/2,-whpyr/2,waterlevel)
-- (whpyr/2,-whpyr/2,waterlevel) -- (whpyr/2,whpyr/2,waterlevel)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- (-whpyr/2,-whpyr/2,waterlevel)
[reverseclip];
fi
fill[blue,opacity=0.2]
plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi+360] ({rcyl*cos(t)},{rcyl*sin(t)},waterlevel);
end{scope}
fill[blue,opacity=0.4]
plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi-180]
({rcyl*cos(t)},{rcyl*sin(t)},waterlevel)
--
plot[smooth,variable=t,domain=tdplotmainphi-180:tdplotmainphi]
({rcyl*cos(t)},{rcyl*sin(t)},0);
draw plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi-180]
({rcyl*cos(t)},{rcyl*sin(t)},0)
-- plot[smooth,variable=t,domain=tdplotmainphi-180:tdplotmainphi+180] ({rcyl*cos(t)},{rcyl*sin(t)},hcyl)
({rcyl*cos(tdplotmainphi)},{rcyl*sin(tdplotmainphi)},0) --
({rcyl*cos(tdplotmainphi)},{rcyl*sin(tdplotmainphi)},hcyl);
draw (hang) -- (0,0,zpyr+hpyr-hremoved);
% node[anchor=north west,tdplot_screen_coords,align=right]
% at (1,7.75){waterlevel\ zpyr};
end{tikzpicture}}
end{document}
answered Feb 4 at 6:22
marmotmarmot
118k6151284
The top of the pyramid should be removed so that the resulting cross-section is a square. The rope is attached to the center of that square.
– Thumbolt
Feb 4 at 6:28
3
Well, the pyramid is apparently full of holes -- the water level does not rise during the lowering of the pyramid. ;-)
– user31729
Feb 4 at 9:28
1
@ChristianHupfer Perhaps the dotted line at the bottom suggests an infinitely long cilinder?
– Servaes
Feb 4 at 12:09
2
@ChristianHupfer That's a so-called well-tempered pyramid, which changes the water temperature in such a way that the water level remains constant. ;-)
– marmot
Feb 4 at 15:31
1
@marmot: Yeah, that's probably wise, since it'd be hard to notice the difference. The change in water level looks more realistic now, but also less impressive somehow :).
– Circumscribe
Feb 6 at 15:31
|
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1 Answer
1
active
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1 Answer
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active
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votes
active
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active
oldest
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15
I'd use 3d coordinates for that.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{tikz-3dplot}
usetikzlibrary{patterns}
% https://tex.stackexchange.com/a/12033/121799
tikzset{reverseclip/.style={insert path={(current bounding box.north
east) rectangle (current bounding box.south west)}}}
begin{document}
tdplotsetmaincoords{70}{30}
begin{tikzpicture}[tdplot_main_coords,font=sffamily,line join=bevel]
pgfmathsetmacro{rcyl}{2}
pgfmathsetmacro{hcyl}{5}
pgfmathsetmacro{hpyr}{2.5}
pgfmathsetmacro{hremoved}{0.5}
pgfmathsetmacro{zpyr}{3.5}
pgfmathsetmacro{wpyr}{1.5}
pgfmathsetmacro{wtop}{hremoved*wpyr/hpyr}
pgfmathsetmacro{hwater}{4}
pgfmathsetmacro{whpyr}{wpyr-(hwater-zpyr)*wpyr/hpyr} % width of pyramid at water level
fill[tdplot_screen_coords,pattern=north west lines] (-1,7.4) rectangle (1,7.75);
draw[tdplot_screen_coords] (-1,7.4) -- (1,7.4) coordinate[midway] (hang);
%
draw[dashed] plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi+180] ({rcyl*cos(t)},{rcyl*sin(t)},0);
draw[dashed] (wpyr/2,wpyr/2,zpyr)
-- (-wpyr/2,wpyr/2,zpyr) -- (-wpyr/2,-wpyr/2,zpyr)
(-wpyr/2,wpyr/2,zpyr) -- (-wtop/2,wtop/2,zpyr+hpyr-hremoved);
draw[fill=gray!30,fill opacity=0.5]
(-wpyr/2,-wpyr/2,zpyr) -- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- (wpyr/2,-wpyr/2,zpyr)
-- cycle;
draw[fill=gray!50,fill opacity=0.5] (wpyr/2,-wpyr/2,zpyr)
-- (wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (wpyr/2,wpyr/2,zpyr)
-- cycle;
draw[fill=gray!20,fill opacity=0.5]
(wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- cycle;
begin{scope}
clip (-whpyr/2,-whpyr/2,hwater)
-- (whpyr/2,-whpyr/2,hwater) -- (whpyr/2,whpyr/2,hwater)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- (-whpyr/2,-whpyr/2,hwater)
[reverseclip];
fill[blue,opacity=0.2]
plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi+360] ({rcyl*cos(t)},{rcyl*sin(t)},hwater);
end{scope}
fill[blue,opacity=0.4]
plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi-180]
({rcyl*cos(t)},{rcyl*sin(t)},hwater)
--
plot[smooth,variable=t,domain=tdplotmainphi-180:tdplotmainphi]
({rcyl*cos(t)},{rcyl*sin(t)},0);
draw plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi-180]
({rcyl*cos(t)},{rcyl*sin(t)},0)
-- plot[smooth,variable=t,domain=tdplotmainphi-180:tdplotmainphi+180] ({rcyl*cos(t)},{rcyl*sin(t)},hcyl)
({rcyl*cos(tdplotmainphi)},{rcyl*sin(tdplotmainphi)},0) --
({rcyl*cos(tdplotmainphi)},{rcyl*sin(tdplotmainphi)},hcyl);
draw (hang) -- (0,0,zpyr+hpyr-hremoved);
end{tikzpicture}
end{document}
And this is an animation for Christian Hupfer with corrections due to @circumscribe.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{tikz-3dplot}
usetikzlibrary{patterns}
% https://tex.stackexchange.com/a/12033/121799
tikzset{reverseclip/.style={insert path={(current bounding box.north
east) rectangle (current bounding box.south west)}}}
begin{document}
foreach Z in {0,10,...,350}
{tdplotsetmaincoords{70}{30}
begin{tikzpicture}[tdplot_main_coords,font=sffamily,line join=bevel]
pgfmathsetmacro{rcyl}{2}
pgfmathsetmacro{hcyl}{5}
pgfmathsetmacro{hpyr}{2.5}
pgfmathsetmacro{hremoved}{1.2}
pgfmathsetmacro{zpyr}{2.8+0.8*cos(Z)}
pgfmathsetmacro{wpyr}{1.5}
pgfmathsetmacro{wtop}{hremoved*wpyr/hpyr}
pgfmathsetmacro{hwater}{4}
pgfmathsetmacro{deltahmax}{(wpyr^2/(pi*rcyl^2))*(hpyr-hremoved^3/hpyr^2)/3}
pgfmathsetmacro{waterlevel}{hwater+ifthenelse(zpyr<hwater,1,0)*deltahmax*
ifthenelse(zpyr>hwater-hpyr+hremoved,
1-((zpyr-hwater+hpyr-hremoved)/(hpyr-hremoved))^3,1)}
%typeout{deltahmax=deltahmax,waterlevel=waterlevel,zpyr=zpyr,hwater=hwater}
fill[tdplot_screen_coords,pattern=north west lines] (-1,7.4) rectangle (1,7.75);
draw[tdplot_screen_coords] (-1,7.4) -- (1,7.4) coordinate[midway] (hang);
%
draw[dashed] plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi+180] ({rcyl*cos(t)},{rcyl*sin(t)},0);
draw[dashed] (wpyr/2,wpyr/2,zpyr)
-- (-wpyr/2,wpyr/2,zpyr) -- (-wpyr/2,-wpyr/2,zpyr)
(-wpyr/2,wpyr/2,zpyr) -- (-wtop/2,wtop/2,zpyr+hpyr-hremoved);
draw[fill=gray!30,fill opacity=0.5]
(-wpyr/2,-wpyr/2,zpyr) -- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- (wpyr/2,-wpyr/2,zpyr)
-- cycle;
draw[fill=gray!50,fill opacity=0.5] (wpyr/2,-wpyr/2,zpyr)
-- (wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (wpyr/2,wpyr/2,zpyr)
-- cycle;
draw[fill=gray!20,fill opacity=0.5]
(wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- cycle;
pgfmathsetmacro{whpyr}{wpyr-(waterlevel-zpyr)*wpyr/hpyr} % width of pyramid at water level
begin{scope}
pgfmathtruncatemacro{itest}{sign(-(waterlevel-zpyr)+(hpyr-hremoved))}
ifnumitest=1
clip (-whpyr/2,-whpyr/2,waterlevel)
-- (whpyr/2,-whpyr/2,waterlevel) -- (whpyr/2,whpyr/2,waterlevel)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- (-whpyr/2,-whpyr/2,waterlevel)
[reverseclip];
fi
fill[blue,opacity=0.2]
plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi+360] ({rcyl*cos(t)},{rcyl*sin(t)},waterlevel);
end{scope}
fill[blue,opacity=0.4]
plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi-180]
({rcyl*cos(t)},{rcyl*sin(t)},waterlevel)
--
plot[smooth,variable=t,domain=tdplotmainphi-180:tdplotmainphi]
({rcyl*cos(t)},{rcyl*sin(t)},0);
draw plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi-180]
({rcyl*cos(t)},{rcyl*sin(t)},0)
-- plot[smooth,variable=t,domain=tdplotmainphi-180:tdplotmainphi+180] ({rcyl*cos(t)},{rcyl*sin(t)},hcyl)
({rcyl*cos(tdplotmainphi)},{rcyl*sin(tdplotmainphi)},0) --
({rcyl*cos(tdplotmainphi)},{rcyl*sin(tdplotmainphi)},hcyl);
draw (hang) -- (0,0,zpyr+hpyr-hremoved);
% node[anchor=north west,tdplot_screen_coords,align=right]
% at (1,7.75){waterlevel\ zpyr};
end{tikzpicture}}
end{document}
answered Feb 4 at 6:22
marmotmarmot
118k6151284
The top of the pyramid should be removed so that the resulting cross-section is a square. The rope is attached to the center of that square.
– Thumbolt
Feb 4 at 6:28
3
Well, the pyramid is apparently full of holes -- the water level does not rise during the lowering of the pyramid. ;-)
– user31729
Feb 4 at 9:28
1
@ChristianHupfer Perhaps the dotted line at the bottom suggests an infinitely long cilinder?
– Servaes
Feb 4 at 12:09
2
@ChristianHupfer That's a so-called well-tempered pyramid, which changes the water temperature in such a way that the water level remains constant. ;-)
– marmot
Feb 4 at 15:31
1
@marmot: Yeah, that's probably wise, since it'd be hard to notice the difference. The change in water level looks more realistic now, but also less impressive somehow :).
– Circumscribe
Feb 6 at 15:31
|
show 5 more comments
15
I'd use 3d coordinates for that.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{tikz-3dplot}
usetikzlibrary{patterns}
% https://tex.stackexchange.com/a/12033/121799
tikzset{reverseclip/.style={insert path={(current bounding box.north
east) rectangle (current bounding box.south west)}}}
begin{document}
tdplotsetmaincoords{70}{30}
begin{tikzpicture}[tdplot_main_coords,font=sffamily,line join=bevel]
pgfmathsetmacro{rcyl}{2}
pgfmathsetmacro{hcyl}{5}
pgfmathsetmacro{hpyr}{2.5}
pgfmathsetmacro{hremoved}{0.5}
pgfmathsetmacro{zpyr}{3.5}
pgfmathsetmacro{wpyr}{1.5}
pgfmathsetmacro{wtop}{hremoved*wpyr/hpyr}
pgfmathsetmacro{hwater}{4}
pgfmathsetmacro{whpyr}{wpyr-(hwater-zpyr)*wpyr/hpyr} % width of pyramid at water level
fill[tdplot_screen_coords,pattern=north west lines] (-1,7.4) rectangle (1,7.75);
draw[tdplot_screen_coords] (-1,7.4) -- (1,7.4) coordinate[midway] (hang);
%
draw[dashed] plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi+180] ({rcyl*cos(t)},{rcyl*sin(t)},0);
draw[dashed] (wpyr/2,wpyr/2,zpyr)
-- (-wpyr/2,wpyr/2,zpyr) -- (-wpyr/2,-wpyr/2,zpyr)
(-wpyr/2,wpyr/2,zpyr) -- (-wtop/2,wtop/2,zpyr+hpyr-hremoved);
draw[fill=gray!30,fill opacity=0.5]
(-wpyr/2,-wpyr/2,zpyr) -- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- (wpyr/2,-wpyr/2,zpyr)
-- cycle;
draw[fill=gray!50,fill opacity=0.5] (wpyr/2,-wpyr/2,zpyr)
-- (wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (wpyr/2,wpyr/2,zpyr)
-- cycle;
draw[fill=gray!20,fill opacity=0.5]
(wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- cycle;
begin{scope}
clip (-whpyr/2,-whpyr/2,hwater)
-- (whpyr/2,-whpyr/2,hwater) -- (whpyr/2,whpyr/2,hwater)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- (-whpyr/2,-whpyr/2,hwater)
[reverseclip];
fill[blue,opacity=0.2]
plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi+360] ({rcyl*cos(t)},{rcyl*sin(t)},hwater);
end{scope}
fill[blue,opacity=0.4]
plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi-180]
({rcyl*cos(t)},{rcyl*sin(t)},hwater)
--
plot[smooth,variable=t,domain=tdplotmainphi-180:tdplotmainphi]
({rcyl*cos(t)},{rcyl*sin(t)},0);
draw plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi-180]
({rcyl*cos(t)},{rcyl*sin(t)},0)
-- plot[smooth,variable=t,domain=tdplotmainphi-180:tdplotmainphi+180] ({rcyl*cos(t)},{rcyl*sin(t)},hcyl)
({rcyl*cos(tdplotmainphi)},{rcyl*sin(tdplotmainphi)},0) --
({rcyl*cos(tdplotmainphi)},{rcyl*sin(tdplotmainphi)},hcyl);
draw (hang) -- (0,0,zpyr+hpyr-hremoved);
end{tikzpicture}
end{document}
And this is an animation for Christian Hupfer with corrections due to @circumscribe.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{tikz-3dplot}
usetikzlibrary{patterns}
% https://tex.stackexchange.com/a/12033/121799
tikzset{reverseclip/.style={insert path={(current bounding box.north
east) rectangle (current bounding box.south west)}}}
begin{document}
foreach Z in {0,10,...,350}
{tdplotsetmaincoords{70}{30}
begin{tikzpicture}[tdplot_main_coords,font=sffamily,line join=bevel]
pgfmathsetmacro{rcyl}{2}
pgfmathsetmacro{hcyl}{5}
pgfmathsetmacro{hpyr}{2.5}
pgfmathsetmacro{hremoved}{1.2}
pgfmathsetmacro{zpyr}{2.8+0.8*cos(Z)}
pgfmathsetmacro{wpyr}{1.5}
pgfmathsetmacro{wtop}{hremoved*wpyr/hpyr}
pgfmathsetmacro{hwater}{4}
pgfmathsetmacro{deltahmax}{(wpyr^2/(pi*rcyl^2))*(hpyr-hremoved^3/hpyr^2)/3}
pgfmathsetmacro{waterlevel}{hwater+ifthenelse(zpyr<hwater,1,0)*deltahmax*
ifthenelse(zpyr>hwater-hpyr+hremoved,
1-((zpyr-hwater+hpyr-hremoved)/(hpyr-hremoved))^3,1)}
%typeout{deltahmax=deltahmax,waterlevel=waterlevel,zpyr=zpyr,hwater=hwater}
fill[tdplot_screen_coords,pattern=north west lines] (-1,7.4) rectangle (1,7.75);
draw[tdplot_screen_coords] (-1,7.4) -- (1,7.4) coordinate[midway] (hang);
%
draw[dashed] plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi+180] ({rcyl*cos(t)},{rcyl*sin(t)},0);
draw[dashed] (wpyr/2,wpyr/2,zpyr)
-- (-wpyr/2,wpyr/2,zpyr) -- (-wpyr/2,-wpyr/2,zpyr)
(-wpyr/2,wpyr/2,zpyr) -- (-wtop/2,wtop/2,zpyr+hpyr-hremoved);
draw[fill=gray!30,fill opacity=0.5]
(-wpyr/2,-wpyr/2,zpyr) -- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- (wpyr/2,-wpyr/2,zpyr)
-- cycle;
draw[fill=gray!50,fill opacity=0.5] (wpyr/2,-wpyr/2,zpyr)
-- (wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (wpyr/2,wpyr/2,zpyr)
-- cycle;
draw[fill=gray!20,fill opacity=0.5]
(wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- cycle;
pgfmathsetmacro{whpyr}{wpyr-(waterlevel-zpyr)*wpyr/hpyr} % width of pyramid at water level
begin{scope}
pgfmathtruncatemacro{itest}{sign(-(waterlevel-zpyr)+(hpyr-hremoved))}
ifnumitest=1
clip (-whpyr/2,-whpyr/2,waterlevel)
-- (whpyr/2,-whpyr/2,waterlevel) -- (whpyr/2,whpyr/2,waterlevel)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- (-whpyr/2,-whpyr/2,waterlevel)
[reverseclip];
fi
fill[blue,opacity=0.2]
plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi+360] ({rcyl*cos(t)},{rcyl*sin(t)},waterlevel);
end{scope}
fill[blue,opacity=0.4]
plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi-180]
({rcyl*cos(t)},{rcyl*sin(t)},waterlevel)
--
plot[smooth,variable=t,domain=tdplotmainphi-180:tdplotmainphi]
({rcyl*cos(t)},{rcyl*sin(t)},0);
draw plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi-180]
({rcyl*cos(t)},{rcyl*sin(t)},0)
-- plot[smooth,variable=t,domain=tdplotmainphi-180:tdplotmainphi+180] ({rcyl*cos(t)},{rcyl*sin(t)},hcyl)
({rcyl*cos(tdplotmainphi)},{rcyl*sin(tdplotmainphi)},0) --
({rcyl*cos(tdplotmainphi)},{rcyl*sin(tdplotmainphi)},hcyl);
draw (hang) -- (0,0,zpyr+hpyr-hremoved);
% node[anchor=north west,tdplot_screen_coords,align=right]
% at (1,7.75){waterlevel\ zpyr};
end{tikzpicture}}
end{document}
answered Feb 4 at 6:22
marmotmarmot
118k6151284
The top of the pyramid should be removed so that the resulting cross-section is a square. The rope is attached to the center of that square.
– Thumbolt
Feb 4 at 6:28
3
Well, the pyramid is apparently full of holes -- the water level does not rise during the lowering of the pyramid. ;-)
– user31729
Feb 4 at 9:28
1
@ChristianHupfer Perhaps the dotted line at the bottom suggests an infinitely long cilinder?
– Servaes
Feb 4 at 12:09
2
@ChristianHupfer That's a so-called well-tempered pyramid, which changes the water temperature in such a way that the water level remains constant. ;-)
– marmot
Feb 4 at 15:31
1
@marmot: Yeah, that's probably wise, since it'd be hard to notice the difference. The change in water level looks more realistic now, but also less impressive somehow :).
– Circumscribe
Feb 6 at 15:31
|
show 5 more comments
15
15
15
I'd use 3d coordinates for that.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{tikz-3dplot}
usetikzlibrary{patterns}
% https://tex.stackexchange.com/a/12033/121799
tikzset{reverseclip/.style={insert path={(current bounding box.north
east) rectangle (current bounding box.south west)}}}
begin{document}
tdplotsetmaincoords{70}{30}
begin{tikzpicture}[tdplot_main_coords,font=sffamily,line join=bevel]
pgfmathsetmacro{rcyl}{2}
pgfmathsetmacro{hcyl}{5}
pgfmathsetmacro{hpyr}{2.5}
pgfmathsetmacro{hremoved}{0.5}
pgfmathsetmacro{zpyr}{3.5}
pgfmathsetmacro{wpyr}{1.5}
pgfmathsetmacro{wtop}{hremoved*wpyr/hpyr}
pgfmathsetmacro{hwater}{4}
pgfmathsetmacro{whpyr}{wpyr-(hwater-zpyr)*wpyr/hpyr} % width of pyramid at water level
fill[tdplot_screen_coords,pattern=north west lines] (-1,7.4) rectangle (1,7.75);
draw[tdplot_screen_coords] (-1,7.4) -- (1,7.4) coordinate[midway] (hang);
%
draw[dashed] plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi+180] ({rcyl*cos(t)},{rcyl*sin(t)},0);
draw[dashed] (wpyr/2,wpyr/2,zpyr)
-- (-wpyr/2,wpyr/2,zpyr) -- (-wpyr/2,-wpyr/2,zpyr)
(-wpyr/2,wpyr/2,zpyr) -- (-wtop/2,wtop/2,zpyr+hpyr-hremoved);
draw[fill=gray!30,fill opacity=0.5]
(-wpyr/2,-wpyr/2,zpyr) -- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- (wpyr/2,-wpyr/2,zpyr)
-- cycle;
draw[fill=gray!50,fill opacity=0.5] (wpyr/2,-wpyr/2,zpyr)
-- (wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (wpyr/2,wpyr/2,zpyr)
-- cycle;
draw[fill=gray!20,fill opacity=0.5]
(wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- cycle;
begin{scope}
clip (-whpyr/2,-whpyr/2,hwater)
-- (whpyr/2,-whpyr/2,hwater) -- (whpyr/2,whpyr/2,hwater)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- (-whpyr/2,-whpyr/2,hwater)
[reverseclip];
fill[blue,opacity=0.2]
plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi+360] ({rcyl*cos(t)},{rcyl*sin(t)},hwater);
end{scope}
fill[blue,opacity=0.4]
plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi-180]
({rcyl*cos(t)},{rcyl*sin(t)},hwater)
--
plot[smooth,variable=t,domain=tdplotmainphi-180:tdplotmainphi]
({rcyl*cos(t)},{rcyl*sin(t)},0);
draw plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi-180]
({rcyl*cos(t)},{rcyl*sin(t)},0)
-- plot[smooth,variable=t,domain=tdplotmainphi-180:tdplotmainphi+180] ({rcyl*cos(t)},{rcyl*sin(t)},hcyl)
({rcyl*cos(tdplotmainphi)},{rcyl*sin(tdplotmainphi)},0) --
({rcyl*cos(tdplotmainphi)},{rcyl*sin(tdplotmainphi)},hcyl);
draw (hang) -- (0,0,zpyr+hpyr-hremoved);
end{tikzpicture}
end{document}
And this is an animation for Christian Hupfer with corrections due to @circumscribe.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{tikz-3dplot}
usetikzlibrary{patterns}
% https://tex.stackexchange.com/a/12033/121799
tikzset{reverseclip/.style={insert path={(current bounding box.north
east) rectangle (current bounding box.south west)}}}
begin{document}
foreach Z in {0,10,...,350}
{tdplotsetmaincoords{70}{30}
begin{tikzpicture}[tdplot_main_coords,font=sffamily,line join=bevel]
pgfmathsetmacro{rcyl}{2}
pgfmathsetmacro{hcyl}{5}
pgfmathsetmacro{hpyr}{2.5}
pgfmathsetmacro{hremoved}{1.2}
pgfmathsetmacro{zpyr}{2.8+0.8*cos(Z)}
pgfmathsetmacro{wpyr}{1.5}
pgfmathsetmacro{wtop}{hremoved*wpyr/hpyr}
pgfmathsetmacro{hwater}{4}
pgfmathsetmacro{deltahmax}{(wpyr^2/(pi*rcyl^2))*(hpyr-hremoved^3/hpyr^2)/3}
pgfmathsetmacro{waterlevel}{hwater+ifthenelse(zpyr<hwater,1,0)*deltahmax*
ifthenelse(zpyr>hwater-hpyr+hremoved,
1-((zpyr-hwater+hpyr-hremoved)/(hpyr-hremoved))^3,1)}
%typeout{deltahmax=deltahmax,waterlevel=waterlevel,zpyr=zpyr,hwater=hwater}
fill[tdplot_screen_coords,pattern=north west lines] (-1,7.4) rectangle (1,7.75);
draw[tdplot_screen_coords] (-1,7.4) -- (1,7.4) coordinate[midway] (hang);
%
draw[dashed] plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi+180] ({rcyl*cos(t)},{rcyl*sin(t)},0);
draw[dashed] (wpyr/2,wpyr/2,zpyr)
-- (-wpyr/2,wpyr/2,zpyr) -- (-wpyr/2,-wpyr/2,zpyr)
(-wpyr/2,wpyr/2,zpyr) -- (-wtop/2,wtop/2,zpyr+hpyr-hremoved);
draw[fill=gray!30,fill opacity=0.5]
(-wpyr/2,-wpyr/2,zpyr) -- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- (wpyr/2,-wpyr/2,zpyr)
-- cycle;
draw[fill=gray!50,fill opacity=0.5] (wpyr/2,-wpyr/2,zpyr)
-- (wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (wpyr/2,wpyr/2,zpyr)
-- cycle;
draw[fill=gray!20,fill opacity=0.5]
(wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- cycle;
pgfmathsetmacro{whpyr}{wpyr-(waterlevel-zpyr)*wpyr/hpyr} % width of pyramid at water level
begin{scope}
pgfmathtruncatemacro{itest}{sign(-(waterlevel-zpyr)+(hpyr-hremoved))}
ifnumitest=1
clip (-whpyr/2,-whpyr/2,waterlevel)
-- (whpyr/2,-whpyr/2,waterlevel) -- (whpyr/2,whpyr/2,waterlevel)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- (-whpyr/2,-whpyr/2,waterlevel)
[reverseclip];
fi
fill[blue,opacity=0.2]
plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi+360] ({rcyl*cos(t)},{rcyl*sin(t)},waterlevel);
end{scope}
fill[blue,opacity=0.4]
plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi-180]
({rcyl*cos(t)},{rcyl*sin(t)},waterlevel)
--
plot[smooth,variable=t,domain=tdplotmainphi-180:tdplotmainphi]
({rcyl*cos(t)},{rcyl*sin(t)},0);
draw plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi-180]
({rcyl*cos(t)},{rcyl*sin(t)},0)
-- plot[smooth,variable=t,domain=tdplotmainphi-180:tdplotmainphi+180] ({rcyl*cos(t)},{rcyl*sin(t)},hcyl)
({rcyl*cos(tdplotmainphi)},{rcyl*sin(tdplotmainphi)},0) --
({rcyl*cos(tdplotmainphi)},{rcyl*sin(tdplotmainphi)},hcyl);
draw (hang) -- (0,0,zpyr+hpyr-hremoved);
% node[anchor=north west,tdplot_screen_coords,align=right]
% at (1,7.75){waterlevel\ zpyr};
end{tikzpicture}}
end{document}
answered Feb 4 at 6:22
marmotmarmot
118k6151284
I'd use 3d coordinates for that.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{tikz-3dplot}
usetikzlibrary{patterns}
% https://tex.stackexchange.com/a/12033/121799
tikzset{reverseclip/.style={insert path={(current bounding box.north
east) rectangle (current bounding box.south west)}}}
begin{document}
tdplotsetmaincoords{70}{30}
begin{tikzpicture}[tdplot_main_coords,font=sffamily,line join=bevel]
pgfmathsetmacro{rcyl}{2}
pgfmathsetmacro{hcyl}{5}
pgfmathsetmacro{hpyr}{2.5}
pgfmathsetmacro{hremoved}{0.5}
pgfmathsetmacro{zpyr}{3.5}
pgfmathsetmacro{wpyr}{1.5}
pgfmathsetmacro{wtop}{hremoved*wpyr/hpyr}
pgfmathsetmacro{hwater}{4}
pgfmathsetmacro{whpyr}{wpyr-(hwater-zpyr)*wpyr/hpyr} % width of pyramid at water level
fill[tdplot_screen_coords,pattern=north west lines] (-1,7.4) rectangle (1,7.75);
draw[tdplot_screen_coords] (-1,7.4) -- (1,7.4) coordinate[midway] (hang);
%
draw[dashed] plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi+180] ({rcyl*cos(t)},{rcyl*sin(t)},0);
draw[dashed] (wpyr/2,wpyr/2,zpyr)
-- (-wpyr/2,wpyr/2,zpyr) -- (-wpyr/2,-wpyr/2,zpyr)
(-wpyr/2,wpyr/2,zpyr) -- (-wtop/2,wtop/2,zpyr+hpyr-hremoved);
draw[fill=gray!30,fill opacity=0.5]
(-wpyr/2,-wpyr/2,zpyr) -- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- (wpyr/2,-wpyr/2,zpyr)
-- cycle;
draw[fill=gray!50,fill opacity=0.5] (wpyr/2,-wpyr/2,zpyr)
-- (wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (wpyr/2,wpyr/2,zpyr)
-- cycle;
draw[fill=gray!20,fill opacity=0.5]
(wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- cycle;
begin{scope}
clip (-whpyr/2,-whpyr/2,hwater)
-- (whpyr/2,-whpyr/2,hwater) -- (whpyr/2,whpyr/2,hwater)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- (-whpyr/2,-whpyr/2,hwater)
[reverseclip];
fill[blue,opacity=0.2]
plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi+360] ({rcyl*cos(t)},{rcyl*sin(t)},hwater);
end{scope}
fill[blue,opacity=0.4]
plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi-180]
({rcyl*cos(t)},{rcyl*sin(t)},hwater)
--
plot[smooth,variable=t,domain=tdplotmainphi-180:tdplotmainphi]
({rcyl*cos(t)},{rcyl*sin(t)},0);
draw plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi-180]
({rcyl*cos(t)},{rcyl*sin(t)},0)
-- plot[smooth,variable=t,domain=tdplotmainphi-180:tdplotmainphi+180] ({rcyl*cos(t)},{rcyl*sin(t)},hcyl)
({rcyl*cos(tdplotmainphi)},{rcyl*sin(tdplotmainphi)},0) --
({rcyl*cos(tdplotmainphi)},{rcyl*sin(tdplotmainphi)},hcyl);
draw (hang) -- (0,0,zpyr+hpyr-hremoved);
end{tikzpicture}
end{document}
And this is an animation for Christian Hupfer with corrections due to @circumscribe.
documentclass[tikz,border=3.14mm]{standalone}
usepackage{tikz-3dplot}
usetikzlibrary{patterns}
% https://tex.stackexchange.com/a/12033/121799
tikzset{reverseclip/.style={insert path={(current bounding box.north
east) rectangle (current bounding box.south west)}}}
begin{document}
foreach Z in {0,10,...,350}
{tdplotsetmaincoords{70}{30}
begin{tikzpicture}[tdplot_main_coords,font=sffamily,line join=bevel]
pgfmathsetmacro{rcyl}{2}
pgfmathsetmacro{hcyl}{5}
pgfmathsetmacro{hpyr}{2.5}
pgfmathsetmacro{hremoved}{1.2}
pgfmathsetmacro{zpyr}{2.8+0.8*cos(Z)}
pgfmathsetmacro{wpyr}{1.5}
pgfmathsetmacro{wtop}{hremoved*wpyr/hpyr}
pgfmathsetmacro{hwater}{4}
pgfmathsetmacro{deltahmax}{(wpyr^2/(pi*rcyl^2))*(hpyr-hremoved^3/hpyr^2)/3}
pgfmathsetmacro{waterlevel}{hwater+ifthenelse(zpyr<hwater,1,0)*deltahmax*
ifthenelse(zpyr>hwater-hpyr+hremoved,
1-((zpyr-hwater+hpyr-hremoved)/(hpyr-hremoved))^3,1)}
%typeout{deltahmax=deltahmax,waterlevel=waterlevel,zpyr=zpyr,hwater=hwater}
fill[tdplot_screen_coords,pattern=north west lines] (-1,7.4) rectangle (1,7.75);
draw[tdplot_screen_coords] (-1,7.4) -- (1,7.4) coordinate[midway] (hang);
%
draw[dashed] plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi+180] ({rcyl*cos(t)},{rcyl*sin(t)},0);
draw[dashed] (wpyr/2,wpyr/2,zpyr)
-- (-wpyr/2,wpyr/2,zpyr) -- (-wpyr/2,-wpyr/2,zpyr)
(-wpyr/2,wpyr/2,zpyr) -- (-wtop/2,wtop/2,zpyr+hpyr-hremoved);
draw[fill=gray!30,fill opacity=0.5]
(-wpyr/2,-wpyr/2,zpyr) -- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- (wpyr/2,-wpyr/2,zpyr)
-- cycle;
draw[fill=gray!50,fill opacity=0.5] (wpyr/2,-wpyr/2,zpyr)
-- (wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (wpyr/2,wpyr/2,zpyr)
-- cycle;
draw[fill=gray!20,fill opacity=0.5]
(wtop/2,-wtop/2,zpyr+hpyr-hremoved)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- cycle;
pgfmathsetmacro{whpyr}{wpyr-(waterlevel-zpyr)*wpyr/hpyr} % width of pyramid at water level
begin{scope}
pgfmathtruncatemacro{itest}{sign(-(waterlevel-zpyr)+(hpyr-hremoved))}
ifnumitest=1
clip (-whpyr/2,-whpyr/2,waterlevel)
-- (whpyr/2,-whpyr/2,waterlevel) -- (whpyr/2,whpyr/2,waterlevel)
-- (wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,wtop/2,zpyr+hpyr-hremoved)
-- (-wtop/2,-wtop/2,zpyr+hpyr-hremoved) -- (-whpyr/2,-whpyr/2,waterlevel)
[reverseclip];
fi
fill[blue,opacity=0.2]
plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi+360] ({rcyl*cos(t)},{rcyl*sin(t)},waterlevel);
end{scope}
fill[blue,opacity=0.4]
plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi-180]
({rcyl*cos(t)},{rcyl*sin(t)},waterlevel)
--
plot[smooth,variable=t,domain=tdplotmainphi-180:tdplotmainphi]
({rcyl*cos(t)},{rcyl*sin(t)},0);
draw plot[smooth,variable=t,domain=tdplotmainphi:tdplotmainphi-180]
({rcyl*cos(t)},{rcyl*sin(t)},0)
-- plot[smooth,variable=t,domain=tdplotmainphi-180:tdplotmainphi+180] ({rcyl*cos(t)},{rcyl*sin(t)},hcyl)
({rcyl*cos(tdplotmainphi)},{rcyl*sin(tdplotmainphi)},0) --
({rcyl*cos(tdplotmainphi)},{rcyl*sin(tdplotmainphi)},hcyl);
draw (hang) -- (0,0,zpyr+hpyr-hremoved);
% node[anchor=north west,tdplot_screen_coords,align=right]
% at (1,7.75){waterlevel\ zpyr};
end{tikzpicture}}
end{document}
answered Feb 4 at 6:22
marmotmarmot
118k6151284
edited Feb 6 at 15:22
answered Feb 4 at 6:22
marmotmarmot
118k6151284
answered Feb 4 at 6:22
marmotmarmot
118k6151284
answered Feb 4 at 6:22
marmotmarmot
118k6151284
118k6151284
The top of the pyramid should be removed so that the resulting cross-section is a square. The rope is attached to the center of that square.
– Thumbolt
Feb 4 at 6:28
3
Well, the pyramid is apparently full of holes -- the water level does not rise during the lowering of the pyramid. ;-)
– user31729
Feb 4 at 9:28
1
@ChristianHupfer Perhaps the dotted line at the bottom suggests an infinitely long cilinder?
– Servaes
Feb 4 at 12:09
2
@ChristianHupfer That's a so-called well-tempered pyramid, which changes the water temperature in such a way that the water level remains constant. ;-)
– marmot
Feb 4 at 15:31
1
@marmot: Yeah, that's probably wise, since it'd be hard to notice the difference. The change in water level looks more realistic now, but also less impressive somehow :).
– Circumscribe
Feb 6 at 15:31
|
show 5 more comments
The top of the pyramid should be removed so that the resulting cross-section is a square. The rope is attached to the center of that square.
– Thumbolt
Feb 4 at 6:28
3
Well, the pyramid is apparently full of holes -- the water level does not rise during the lowering of the pyramid. ;-)
– user31729
Feb 4 at 9:28
1
@ChristianHupfer Perhaps the dotted line at the bottom suggests an infinitely long cilinder?
– Servaes
Feb 4 at 12:09
2
@ChristianHupfer That's a so-called well-tempered pyramid, which changes the water temperature in such a way that the water level remains constant. ;-)
– marmot
Feb 4 at 15:31
1
@marmot: Yeah, that's probably wise, since it'd be hard to notice the difference. The change in water level looks more realistic now, but also less impressive somehow :).
– Circumscribe
Feb 6 at 15:31
The top of the pyramid should be removed so that the resulting cross-section is a square. The rope is attached to the center of that square.
– Thumbolt
Feb 4 at 6:28
The top of the pyramid should be removed so that the resulting cross-section is a square. The rope is attached to the center of that square.
– Thumbolt
Feb 4 at 6:28
3
3
Well, the pyramid is apparently full of holes -- the water level does not rise during the lowering of the pyramid. ;-)
– user31729
Feb 4 at 9:28
Well, the pyramid is apparently full of holes -- the water level does not rise during the lowering of the pyramid. ;-)
– user31729
Feb 4 at 9:28
1
1
@ChristianHupfer Perhaps the dotted line at the bottom suggests an infinitely long cilinder?
– Servaes
Feb 4 at 12:09
@ChristianHupfer Perhaps the dotted line at the bottom suggests an infinitely long cilinder?
– Servaes
Feb 4 at 12:09
2
2
@ChristianHupfer That's a so-called well-tempered pyramid, which changes the water temperature in such a way that the water level remains constant. ;-)
– marmot
Feb 4 at 15:31
@ChristianHupfer That's a so-called well-tempered pyramid, which changes the water temperature in such a way that the water level remains constant. ;-)
– marmot
Feb 4 at 15:31
1
1
@marmot: Yeah, that's probably wise, since it'd be hard to notice the difference. The change in water level looks more realistic now, but also less impressive somehow :).
– Circumscribe
Feb 6 at 15:31
@marmot: Yeah, that's probably wise, since it'd be hard to notice the difference. The change in water level looks more realistic now, but also less impressive somehow :).
– Circumscribe
Feb 6 at 15:31
|
show 5 more comments
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