Commit: 49066c52522d179564d54bf487ac3d9b8e9a09fc - myprojects-hg-reborn (hg)

Commit MetaInfo

• Revision: 49066c52522d179564d54bf487ac3d9b8e9a09fc (tree)
• Zeit: 2019-10-24 17:25:59
• Autor: Lorenzo Isella <lorenzo.isella@gmai...>
• Commiter: Lorenzo Isella

Log Message

One of the most beautiful tikz images ever made.

Ändern Zusammenfassung

• add: latex-documents/casa_amorini.tex

Diff

diff -r 89685f7cffe7 -r 49066c52522d latex-documents/casa_amorini.tex
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/latex-documents/casa_amorini.tex	Thu Oct 24 10:25:59 2019 +0200
@@ -0,0 +1,122 @@
+% Author: Daniel Steger
+% Source: Mosaic from Pompeji
+% Casa degli Armorini Dorati, Living room, mosaic
+\documentclass{minimal}
+
+\usepackage{tikz}
+\usepackage{verbatim}
+
+\begin{comment}
+:Title: Mosaic from Pompeii
+
+A decorative element from a mosaic in the living room of Casa degli Armorini Dorati, Pompeii. The example shows the power of PGF's mathematical engine. 
+\end{comment}
+
+\begin{document}
+
+\begin{tikzpicture}[cap=round]
+% Colors
+\colorlet{anglecolor}{green!50!black}
+\colorlet{bordercolor}{black}
+
+%Configuration: change this to define number of intersections: 
+% 5 degree mean 360/10 = 36 elements
+\def\alpha{5} % degree
+\def\layer{5}
+
+\begin{scope}[scale=5]
+% Radius R = 1
+
+% The figure is constructed by intersecting circles Cx of radius R.
+%  M_Cx lies on the circle C with a radius \alpha degree from the outer circle R 
+%  and a distance defined by \alpha degree.
+
+% It is sufficent to calculate one special M_C, which is intersecting the x-axis 
+% at distance R from (0,0).
+\pgfmathsetmacro\sinTriDiff{sin(60-\alpha)}
+\pgfmathsetmacro\cosTriDiff{1-cos(60-\alpha)}
+% The distance from the (0,0).
+\pgfmathsetmacro\radiusC{sqrt(\cosTriDiff*\cosTriDiff + \sinTriDiff*\sinTriDiff)}
+% Angle of M_C (from x-axis)
+\pgfmathsetmacro\startAng{\alpha + atan(\sinTriDiff/\cosTriDiff)}
+
+% The segment layer are \alpha degree apart
+\pgfmathsetmacro\al{\alpha*\layer}
+
+% For each segment create the intersection parts of the circles by using arcs
+\foreach \x in {0,\alpha,...,\al}
+{
+  % Calculate the polar coordiantes of M_Cx. We take the M_C from above 
+  % and  can calculate all other M_Cx by adding \alpha
+  \pgfmathsetmacro\ang{\x + \startAng}
+  % From ths we get the (x,y) coordinates
+  \pgfmathsetmacro\xRs{\radiusC*cos(\ang)}
+  \pgfmathsetmacro\yRs{\radiusC*sin(\ang)}
+
+  % Now we intersect each new M_C with the x-axis:
+  % We can find the radius of concentric inner circles
+  \pgfmathsetmacro\radiusLayer{\xRs + sqrt( 1 - \yRs*\yRs )}
+
+  % To calculate angles for the arcs later, this angle is needed
+  \pgfmathsetmacro\angRs{acos(\yRs)}
+
+ % We need to have the angle from the previous loop as well
+  \pgfmathsetmacro\angRss{acos(\radiusC*sin(\ang-\alpha))}
+
+
+  % Add some fading by \ang
+  \colorlet{anglecolor}{black!\ang!green}
+
+  % The loop needs to run a whole.  
+  % We don't want to cope with angles > 360 degree, adapt the limits. 
+  \pgfmathsetmacro\step{2*\alpha - 180}
+  \pgfmathsetmacro\stop{180-2*\alpha}
+  \foreach \y in {-180, \step ,..., \stop}
+  {
+    \pgfmathsetmacro\deltaAng{\y-\x}
+    % This are the arcs which are definied by the intersection of 3 circles 
+    \filldraw[color=anglecolor,draw=bordercolor] 
+        (\y-\x:\radiusLayer)    
+                arc (-90+\angRs+\deltaAng : \alpha-90+\angRss+\deltaAng :1) 
+                arc (\alpha+90-\angRss+\deltaAng : 2*\alpha+90-\angRs+\deltaAng :1)
+                arc (\deltaAng+2*\alpha : \deltaAng : \radiusLayer);
+  }
+
+
+  % helper circles  & lines
+  %\draw[color=gray] (\xRs,\yRs) circle (1);
+  %\draw[color=gray] (\xRs,-\yRs) circle (1);
+  %\draw[color=blue] (0,0) circle (\radiusLayer);
+  %\draw[color=blue, very thick] (0,0) -- (0:1);
+  %\draw[color=blue, very thick] (0,0) -- (\ang:\radiusC) -- (\xRs,0);  
+  %\draw[color=blue, very thick] (\xRs,\yRs) -- (0:\radiusLayer);
+  %\filldraw[color=blue!20, very thick] (\xRs,\yRs) -- 
+  % (\xRs,\yRs-0.3) arc (-90:-90+\angRs:0.2) -- cycle;
+
+}
+% Additional inner decoration element
+\pgfmathsetmacro\xRs{\radiusC*cos(\al+\startAng)}
+\pgfmathsetmacro\yRs{\radiusC*sin(\al+\startAng)}
+\pgfmathsetmacro\radiusLayer{\xRs + sqrt( 1 - \yRs*\yRs )}
+\draw[line width=2, color=bordercolor] (0,0) circle (.8*\radiusLayer);
+\pgfmathsetmacro\radiusSmall{.7*\radiusLayer}
+% There are six elements to create. Avoid angles >360 degree.
+\foreach \x in {-60,0,...,240}
+{
+    \fill[color=anglecolor] (\x:\radiusSmall) arc (-180+\x+60: -180+\x: \radiusSmall)
+                             arc (0+\x: -60+\x: \radiusSmall)
+                             arc (120+\x: 60+\x: \radiusSmall); 
+}
+% The outer decoration
+\foreach \x in {0, 4, ..., 360}
+{
+  \fill[color=anglecolor] (\x:1) -- (\x+3:1.05) -- (\x+5:1.05) -- (\x+2:1) -- cycle;
+  \fill[color=anglecolor] (\x+5:1.05) -- (\x+7:1.05) -- (\x+4:1.1) -- (\x+2:1.1) -- cycle;
+}
+\draw[line width=1, color=bordercolor] (0,0) circle (1);
+\draw[line width=1, color=bordercolor] (0,0) circle (1.1);
+\end{scope}
+
+\end{tikzpicture}
+
+\end{document}