Is there a (simplistic?) way to draw a 3D elevation grid like this in Tikz or PGFPlots?
The blue line should be able to move up or down and, eventually, submerge the interior blocks.
I've looked at this example, and follow it well enough that I could probably reconstruct things on my own, but it seems like at least some part of this may already exist as a package.
I would also be willing to use packages aside from TikZ or PGFPlots.
With PSTricks.
\documentclass[pstricks,border=12pt]{standalone}
\usepackage{pst-eucl}
\definecolor{myblue}{RGB}{37,111,197}
\definecolor{mybrown}{RGB}{211,200,134}
\def\rOne{0.75}
\def\rTwo{0.75}
\def\tOne{30}
\def\tTwo{-5}
\def\stripH{0.5}
\psset
{
PointName=none,
PointSymbol=none,
fillstyle=solid,
linejoin=1,
}
\def\Bar(#1,#2)#3{%
\rput(!#2 \rTwo\space mul \tTwo\space PtoC){%
\rput(!#1 \rOne\space mul \tOne\space 180 add PtoC){%
\pstGeonode{O}(\rOne;\tOne){One}(\rTwo;\tTwo){Two}
\pstTranslation{O}{Two}{One}[Three]
\pnode(0,\stripH){O'}
\pstTranslation{O}{O'}{One,Two,Three}
\pnode(0,#3){O''}
\pstTranslation{O'}{O''}{One',Two',Three'}
\psset{fillcolor=myblue}
\pspolygon(O')(O)(Two)(Two')
\pspolygon(Two')(Two)(Three)(Three')
\psset{fillcolor=mybrown}
\pspolygon(O'')(O')(Two')(Two'')
\pspolygon(Two'')(Two')(Three')(Three'')
\pspolygon(One'')(O'')(Two'')(Three'')
}%
}%
}
\newcount\OuterIndex
\def\SaveListContents#1\relax{\def\Contents{#1}}
\def\Picture{%
\begin{pspicture}[showgrid=false](-3,-2)(5,4)
\psforeach{\row}{%
{{3,2.8,2.7,3,3.1}},% <=== Only this row must use double curly braces. It is a feature!
{2.8,1,1.2,2,3},%
{2.8,1,1.2,2,2.8},%
{2.6,1.6,1.8,1.9,1.8},%
{2.4,1.5,1.7,1.9,1.5}%
}{%
\expandafter\SaveListContents\row\relax
\OuterIndex=\psLoopIndex\relax
\psforeach{\col}{\Contents}{\Bar(\the\OuterIndex,\the\psLoopIndex){\col}}%
\psLoopIndex=\OuterIndex\relax
}
\end{pspicture}}
\begin{document}
\Picture
\end{document}
\documentclass[pstricks,border=12pt]{standalone}
\usepackage{pst-eucl}
\definecolor{myblue}{RGB}{37,111,197}
\definecolor{mybrown}{RGB}{211,200,134}
\def\rOne{0.75}
\def\rTwo{0.75}
\def\tOne{30}
\def\tTwo{-15}
\def\stripH{0.5}
\psset
{
PointName=none,
PointSymbol=none,
fillstyle=solid,
linejoin=1,
}
\def\RandomBar(#1,#2){%
\rput(!#2 \rTwo\space mul \tTwo\space PtoC){%
\rput(!#1 \rOne\space mul \tOne\space 180 add PtoC){%
\pstGeonode{O}(\rOne;\tOne){One}(\rTwo;\tTwo){Two}
\pstTranslation{O}{Two}{One}[Three]
\pnode(0,\stripH){O'}
\pstTranslation{O}{O'}{One,Two,Three}
\pnode(!0 rand 201 mod 100 div 1.00 add){O''}
\pstTranslation{O'}{O''}{One',Two',Three'}
\psset{fillcolor=myblue}
\pspolygon(O')(O)(Two)(Two')
\pspolygon(Two')(Two)(Three)(Three')
\psset{fillcolor=mybrown}
\pspolygon(O'')(O')(Two')(Two'')
\pspolygon(Two'')(Two')(Three')(Three'')
\pspolygon(One'')(O'')(Two'')(Three'')
}%
}%
}
\newcount\OuterIndex
\def\SaveListContents#1\relax{\def\Contents{#1}}
\def\Picture{%
\begin{pspicture}[showgrid=false](-2.5,-3)(4.25,2.5)
\psforeach{\row}{1,2,..,5}{\psforeach{\col}{1,2,..,5}{\RandomBar(\row,\col)}}
\end{pspicture}}
\begin{document}
\psLoop{20}{\Picture}
\end{document}
\documentclass[pstricks,border=12pt]{standalone}
\usepackage{pst-eucl}
\definecolor{myblue}{RGB}{37,111,197}
\definecolor{mybrown}{RGB}{211,200,134}
\def\rOne{0.75}
\def\rTwo{0.75}
\def\tOne{30}
\def\tTwo{-15}
\def\stripH{0.5}
\psset
{
PointName=none,
PointSymbol=none,
fillstyle=solid,
linejoin=1,
}
\def\RandomBar(#1,#2){%
\rput(!#2 \rTwo\space mul \tTwo\space PtoC){%
\rput(!#1 \rOne\space mul \tOne\space 180 add PtoC){%
\pstGeonode{O}(\rOne;\tOne){One}(\rTwo;\tTwo){Two}
\pstTranslation{O}{Two}{One}[Three]
\pnode(0,\stripH){O'}
\pstTranslation{O}{O'}{One,Two,Three}
\pnode(!0 rand 201 mod 100 div 1.00 add){O''}
\pstTranslation{O'}{O''}{One',Two',Three'}
\psset{fillcolor=myblue}
\pspolygon(O')(O)(Two)(Two')
\pspolygon(Two')(Two)(Three)(Three')
\psset{fillcolor=mybrown}
\pspolygon(O'')(O')(Two')(Two'')
\pspolygon(Two'')(Two')(Three')(Three'')
\pspolygon(One'')(O'')(Two'')(Three'')
}%
}%
}
\newcount\OuterIndex
\def\SaveListContents#1\relax{\def\Contents{#1}}
\def\Picture{\psforeach{\row}{1,2,..,5}{\psforeach{\col}{1,2,..,5}{%
\begin{pspicture}[showgrid=false](-2.5,-3)(4.25,2.5)
\RandomBar(\row,\col)
\end{pspicture}}}}
\begin{document}
\psLoop{1}{\Picture}
\end{document}
\documentclass[pstricks,border=12pt]{standalone}
\usepackage{pst-eucl}
\usepackage[nomessages]{fp}
\definecolor{myblue}{RGB}{37,111,197}
\definecolor{mybrown}{RGB}{211,200,134}
\def\rOne{0.75}
\def\rTwo{0.75}
\def\tOne{20}
\def\tTwo{-45}
\FPset\RowMaxIndex{4}% because zero based index
\FPset\ColMaxIndex{4}% because zero based index
\psset
{
PointName=none,
PointSymbol=none,
fillstyle=solid,
linejoin=1,
}
\def\Bar(#1,#2)#3{%
\rput(!#2 \rTwo\space mul \tTwo\space PtoC){%
\rput(!#1 \rOne\space mul \tOne\space 180 add PtoC){%
\pstGeonode{O}(\rOne;\tOne){One}(\rTwo;\tTwo){Two}
\pstTranslation{O}{Two}{One}[Three]
\pnode(0,\stripH){O'}
\pstTranslation{O}{O'}{One,Two,Three}
\pnode(0,#3){O''}
\pstTranslation{O}{O''}{One,Two,Three}[One'',Two'',Three'']
\psset{fillcolor=mybrown}
\pspolygon(O'')(O)(Two)(Two'')
\pspolygon(Two'')(Two)(Three)(Three'')
\pspolygon(One'')(O'')(Two'')(Three'')
\psset{fillcolor=myblue,opacity=0.75,linestyle=none,linewidth=0}
\FPifeq{#1}{\RowMaxIndex}\pspolygon(O')(O)(Two)(Two')\fi
\FPifeq{#2}{\ColMaxIndex}\pspolygon(Two')(Two)(Three)(Three')\fi
\FPiflt{#3}{\stripH}\pspolygon(One')(O')(Two')(Three')\fi
}%
}%
}
\newcount\OuterIndex
\def\SaveListContents#1\relax{\def\Contents{#1}}
\def\Picture#1{%
\def\stripH{#1}%
\begin{pspicture}[showgrid=false](-2.5,-3.35)(3.05,3.05)
\psforeach{\row}{%
{{3,2.8,2.7,3,3.1}},% <=== Only this row must use double curly braces. It is a feature!
{2.8,1,1.2,2,3},%
{2.8,1,1.2,2,2.8},%
{2.6,1.6,1.8,1.9,1.8},%
{2.4,1.5,1.7,1.9,1.5}%
}{%
\expandafter\SaveListContents\row\relax
\OuterIndex=\psLoopIndex\relax
\psforeach{\col}{\Contents}{\Bar(\the\OuterIndex,\the\psLoopIndex){\col}}%
\psLoopIndex=\OuterIndex\relax
}
\end{pspicture}}
\begin{document}
\multido{\n=0.0+0.2}{17}{\Picture{\n}}
\end{document}
Undefined control sequence. <recently read> \c@lor@to@ps. Any thoughts as to why? I am using TeXLive 2012.
– Richard
Mar 25 '13 at 22:23
xelatex (slower) or latex-dvips-ps2pdf sequence (faster).
– kiss my armpit
Mar 25 '13 at 22:35
My take:
Since tikz is not well suited for this kind of graphic (which has to find intersections between planes, decomposing the figure in sub-objects and draw them in the correct order so that the nearest one hide the farthest ones) I used sketch, which can do these things and produce tikz code as result.
Next is the skecth code. The grid is a 5x5x5 cube. The water level is a real between 0 and 5. As for the height of each prism, unfortunately sketch does not provide primitives for reading numbers from files, nor to do list or array manipulation, so I had to draw each bar "one by one", instead of using a loop, and "hardcoded" their height in each case (the second number in the scale operation) :-(
def water_level 2.3
def prism {
sweep[fill style=prism]
{ 4<>, rotate(360/4,[0,1,0]) }
line[fill style=prism](0.5,0,0.5)(0.5,1,0.5)
}
def water {
sweep[fill style=water]
{ 4<>, rotate(360/4,[0,1,0]) }
line[fill style=water, style=water](2.52,0,2.52)(2.52, 1, 2.52)
}
def grid {
put { translate([0, 0, 0]) then scale([1, 5, 1])}{ {prism} }
put { translate([1, 0, 0]) then scale([1, 4.5, 1])}{ {prism} }
put { translate([2, 0, 0]) then scale([1, 4.3, 1])}{ {prism} }
put { translate([3, 0, 0]) then scale([1, 4.8, 1])}{ {prism} }
put { translate([4, 0, 0]) then scale([1, 5, 1])}{ {prism} }
put { translate([0, 0, 1]) then scale([1, 4.5, 1])}{ {prism} }
put { translate([1, 0, 1]) then scale([1, 2, 1])}{ {prism} }
put { translate([2, 0, 1]) then scale([1, 2.2, 1])}{ {prism} }
put { translate([3, 0, 1]) then scale([1, 4, 1])}{ {prism} }
put { translate([4, 0, 1]) then scale([1, 4.9, 1])}{ {prism} }
put { translate([0, 0, 2]) then scale([1, 4.5, 1])}{ {prism} }
put { translate([1, 0, 2]) then scale([1, 2, 1])}{ {prism} }
put { translate([2, 0, 2]) then scale([1, 2.2, 1])}{ {prism} }
put { translate([3, 0, 2]) then scale([1, 4, 1])}{ {prism} }
put { translate([4, 0, 2]) then scale([1, 4.5, 1])}{ {prism} }
put { translate([0, 0, 3]) then scale([1, 4.0, 1])}{ {prism} }
put { translate([1, 0, 3]) then scale([1, 3.0, 1])}{ {prism} }
put { translate([2, 0, 3]) then scale([1, 3.2, 1])}{ {prism} }
put { translate([3, 0, 3]) then scale([1, 3.5, 1])}{ {prism} }
put { translate([4, 0, 3]) then scale([1, 3.0, 1])}{ {prism} }
put { translate([0, 0, 4]) then scale([1, 3.5, 1])}{ {prism} }
put { translate([1, 0, 4]) then scale([1, 2.8, 1])}{ {prism} }
put { translate([2, 0, 4]) then scale([1, 3.0, 1])}{ {prism} }
put { translate([3, 0, 4]) then scale([1, 3.5, 1])}{ {prism} }
put { translate([4, 0, 4]) then scale([1, 2.5, 1])}{ {prism} }
put { translate([2, 0, 2]) then scale([1, water_level, 1])}{ {water} }
}
put{ view((10,20,20)) }{{grid}} % Draw it!
global { language tikz }
You save this code in a file named elevation-grid.sketch and compile it with:
$ sketch elevation-grid.sketch > tikzpicture.tex
Then, your main elevation-grid.tex document looks like this:
\documentclass{standalone}
\usepackage{tikz}
\tikzset{
prism/.style = {draw=black, fill=black!30, opacity=1},
water/.style = {draw=black, fill=blue, opacity=0.60},
}
\begin{document}
\input{tikzpicture.tex}
\end{document}
Of course this generates the graphic for a paticular water level (2.8 in the example). To generate the animation, you have to repeat the above a lot of times, for different water_level values. In order to automate this process, I removed the water_level definition from the first line of elevation-grid.sketch and wrote this small shell script (it requires convert utility from Imagemagick):
echo "def water_level $1" > aux.sketch
cat elevation-grid.sketch >> aux.sketch
sketch aux.sketch > tikzpicture.tex
pdflatex elevation-grid.tex
convert -density 300 elevation-grid.pdf elevation-grid-$1.png
If you save this code in a file named run, for example, you may call it with:
$ sh run 1.2
$ sh run 1.3
$ sh run 1.4
etc...
and you'll get a set of png files: elevation-grid-1.2.png, elevation-grid-1.3.png, and so on. Of course I also automated the above to generate values between 1.0 and 3.9. When all png figures were finally generated, I converted them to an animated gif with convert again:
$ convert -delay 20 elevation-grid*png animation.gif
Now the sketch script is generated by a python script. Currently the data for the grid
is randomly generated, but it would be trivial to read it from a file. This is the script:
import random
def randomGrid(x,y,z):
grid = []
for i in range(y):
row = []
for j in range(x):
row.append(random.random()*z+1)
grid.append(row)
return grid
def generateGraphic(grid, water_level):
code = []
code.append("def grid {")
y = 0
for row in grid:
x = 0
for cell in row:
code.append(" put { translate([%d, 0, %d]) then scale([1, %f, 1])}{ {prism} }" % (x, y, cell))
x = x + 1
code.append("")
y = y + 1
code.append("put { scale([%f, %f, %f]) then translate([%f, 0, %f])}{ {water} }" % (x+0.01, water_level, y+0.01, x/2.0-0.5, y/2.0-0.5))
code.append("}")
return "\n".join(code)
def preamble():
return """
def prism {
sweep[fill style=prism]
{ 4<>, rotate(360/4,[0,1,0]) }
line[fill style=prism](0.5,0,0.5)(0.5,1,0.5)
}
def water {
sweep[fill style=water]
{ 4<>, rotate(360/4,[0,1,0]) }
line[fill style=water, style=water](0.5,0,0.5)(0.5, 1, 0.5)
}
"""
def final(camera):
return """put{ view((%f,%f,%f)) }{{grid}} %% Draw it!
global { language tikz }""" % camera
g = randomGrid(20,20,7) % 20x20 cells, max height =7
print preamble()
print generateGraphic(g, 4.2) % 4.2 is the water level
print final(camera=(30,60,60)) % 3D position of camera, looking at origin
To be used like this:
$ python generate-sketch.py > elevation-grid.sketch
An alternative to TikZ or PGFPlots: Asymptote (part of TeXLive2012):
Source file wdem.asy:
size(6cm,0);
int frameNo;
usersetting(); // set frameNo from commandline
real[][] dem={
{3,4,7,7.5,8},
{5,5,6,6,7.5},
{4.3,4.4,3.9,4.1,6},
{4.7,4.75,2.2,2.3,6.5},
{5,6,6.2,6.2,7.3},
{4.85,7,5.2,6.1,7.2},
};
import bsp;
real u=2.5;
real v=1;
currentprojection=oblique;
path3[] bar={
plane((1,0,0),(0,1,0),(0,0,0)),
plane((0,1,0),(0,0,1),(0,0,0)),
plane((1,0,0),(0,0,1),(0,0,0)),
plane((-1,0,0),(0,-1,0),(1,1,1)),
plane((0,-1,0),(0,0,-1),(1,1,1)),
plane((-1,0,0),(0,0,-1),(1,1,1)),
};
face[] faces;
int nz=dem[0].length;
int nx=dem.length;
void barPlot(real wl){
transform3 t;
real peak;
for(int i=0;i<nx;++i){
for(int j=0;j<nz;++j){
peak=dem[nx-1-i][nz-1-j];
if(peak>0){
t=shift(i,0,j)*scale(1-1e-3,peak,1-1e-3);
for(int k=0;k<bar.length;++k){
filldraw(faces.push(t*bar[k]),project(t*bar[k]),lightgreen);//+opacity(0.5));
}
}
}
}
t=shift(1e-3,0,1e-3)*scale(nx+1e-3,wl,nz+1e-3);
for(int k=0;k<bar.length;++k){
filldraw(faces.push(t*bar[k]),project(t*bar[k]),blue+opacity(0.5));
}
add(faces);
}
real wlNow;
real wlLow=3.8;
real wlHigh=6.3;
int frames=30;
assert(frames>1,"At least two frames is a must.");
real dt=1.0/(frames-1);
real t=frameNo*dt;
wlNow=wlLow*(1-t)+wlHigh*t;
barPlot(wlNow);
shipout(format("f%02i",frameNo));
Frames were processed with batch file gen-anim.sh:
#!/bin/bash
frames=30
for((i=0;i<${frames};++i)){
echo "Frame $i begin"
asy -noV -tex=none -f pdf -noprc -u frameNo="$i" wdem.asy
echo "Frame $i end"
}
An animation was created from 30 pdf frames
by convert -colors 32 -density 200 -antialias -delay 20 f*pdf fdem0.gif and
optimized with gifsicle --colors 16 --resize 236x_ -O3 <fdem0.gif >fdem.gif.
Edit: version with individually coloured bars:
size(6cm,0);
int frameNo;
usersetting(); // set frameNo from commandline
real[][] dem={
{3,4,7,7.5,8},
{5,5,6,6,7.5},
{4.3,4.4,3.9,4.1,6},
{4.7,4.75,2.2,2.3,6.5},
{5,6,6.2,6.2,7.3},
{4.85,7,5.2,6.1,7.2},
};
int nz=dem[0].length;
int nx=dem.length;
pen[][] demColor=new pen[nx][nz];
srand(56091);
for(int i=0;i<nx;++i){
for(int j=0;j<nz;++j){
demColor[i][j]=rgb(unitrand(),unitrand(),unitrand());
}
}
import bsp;
real u=2.5;
real v=1;
currentprojection=oblique;
path3[] bar={
plane((1,0,0),(0,1,0),(0,0,0)),
plane((0,1,0),(0,0,1),(0,0,0)),
plane((1,0,0),(0,0,1),(0,0,0)),
plane((-1,0,0),(0,-1,0),(1,1,1)),
plane((0,-1,0),(0,0,-1),(1,1,1)),
plane((-1,0,0),(0,0,-1),(1,1,1)),
};
face[] faces;
void barPlot(real wl){
transform3 t;
real peak;
for(int i=0;i<nx;++i){
for(int j=0;j<nz;++j){
peak=dem[nx-1-i][nz-1-j];
if(peak>0){
t=shift(i,0,j)*scale(1-1e-3,peak,1-1e-3);
for(int k=0;k<bar.length;++k){
filldraw(faces.push(t*bar[k]),project(t*bar[k]),demColor[nx-1-i][nz-1-j]);//+opacity(0.5));
}
}
}
}
t=shift(1e-3,0,1e-3)*scale(nx+1e-3,wl,nz+1e-3);
for(int k=0;k<bar.length;++k){
filldraw(faces.push(t*bar[k]),project(t*bar[k]),blue+opacity(0.5));
}
add(faces);
}
real wlNow;
real wlLow=3.8;
real wlHigh=6.3;
int frames=30;
assert(frames>1,"At least two frames is a must.");
real dt=1.0/(frames-1);
real t=frameNo*dt;
wlNow=wlLow*(1-t)+wlHigh*t;
barPlot(wlNow);
shipout(format("f%02i",frameNo));
