That’s from my German blog TikZ.de.
Recently I played with the sine function, that “wave” that everybody knows in cartesian coordinates. Let’s take a look at a 3d polar complex sine made plot.
In polar coordinates the sine function is a simple circle:
\documentclass[border=10pt]{standalone} \usepackage{pgfplots} \usepgfplotslibrary{polar} \begin{document} \begin{tikzpicture} \begin{polaraxis}[ domain = 0:180, samples = 100, ] \addplot[thick, blue] {sin(x)}; \legend{$\sin(x)$} \end{polaraxis} \end{tikzpicture} \end{document}
![Sine function in polar coordinates](https://i0.wp.com/texwelt.de/wissen/upfiles/kreis_1.png?w=864)
When we shorten the period length, we get:
![Sine function in polar coordinates](https://i0.wp.com/texwelt.de/wissen/upfiles/sinus3.png?w=864)
We can take a rational factor:
\documentclass{standalone} \usepackage{pgfplots} \usepgfplotslibrary{polar,colormaps} \begin{document} \begin{tikzpicture} \begin{polaraxis}[ domain = -14400:14400, samples = 3000, colormap/cool, hide axis ] \addplot[no markers,mesh,opacity=0.5] {1-sin(40*x/39}; \end{polaraxis} \end{tikzpicture} \end{document}
![Sine function in polar coordinates](https://i0.wp.com/texwelt.de/wissen/upfiles/sinus4.png?w=864)
By adding another sine with other factors, we get more movement:
\documentclass{standalone} \usepackage{pgfplots} \usepgfplotslibrary{polar} \begin{document} \begin{tikzpicture} \begin{polaraxis}[ domain = -3600:3600, samples = 4000 ] \addplot[blue!50!black] {1 - sin(50*x/49) - sin(8*x)}; \end{polaraxis} \end{tikzpicture} \end{document}
![Plot in 2d](https://i0.wp.com/texwelt.de/wissen/upfiles/polar-plot-2d.png?w=864)
Let’s have a 3d view with growing angle.
We make a parametrical 3d-Plot in x and y: x runs the circle from -180 to 180 degree, we make a sampling for y for the number of rotations. We add y time 360 degrees to the function argument. y is our third dimension, while x as angle and the function value are the the original two dimensions.
\documentclass[border=10pt]{standalone} \usepackage{pgfplots} \begin{document} \begin{tikzpicture} \begin{axis}[ domain = -180:180, y domain = -19:19, samples y = 39, samples = 100, z buffer = sort, colormap/cool, grid ] \addplot3[data cs = polar, surf] ( {x}, {1 - sin(50*(x+360*y)/49) - sin(8*(x+360*y))}, {y} ); \end{axis} \end{tikzpicture} \end{document}
![Plot in 3d](https://i0.wp.com/texwelt.de/wissen/upfiles/polar-plot-3d.png?w=864)
That was my todays voyage from a circle to a rather complex function in 3d.