I would like to draw the following picture in tikz
All arcs are part of circles. I would like to specify the following information only : the coordinates of the points a and b, varying radii for the different circle portions, and fractions or percentages t to place purple and pink points along the circles at a specified fraction of the way between two previously defined points.
So for instance I would like to say that the big purple points on the right arc are 60% and 80% along the way from a to b, while the big purple points on the left arc are 40% and 70% along the way from a to b, while the pink points are midway on some circular arc joining pairs of previously defined big purple points.
If I could place some pink circles "harmoniously" in the center of the curved triangles ...
My main problem is the following : suppose I have two points a and b (given by cartesian coordinates) and a radius \rad : this specifies two circles passing through these points of given radius. How do I place a point on one of these circles that is t % along the way from a to b ?
An equivalent problem is the following : suppose I have a center point centerab and two points a and b, whose coordinates are expressed in cartesian coordinates : how do I find their polar coordinates relative to the point centerab ?
Do I have to use linear algebra (such matrix rotation, but also finding angles using arcsin), or can tikz provide me with a simple solution ?
The code below only finds the centers of such circles, but I don't know how to find the polar coordinates of a and b relative to this center, or how to place a point t percent along the way from a to b.
\documentclass[11pt]{article}
\usepackage[utf8x]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usetikzlibrary{calc, intersections}
\begin{document}
\begin{center}
\begin{tikzpicture}
\def\rad{8};
\coordinate (b) at (5,8);
\coordinate (a) at (0,0);
\draw [fill=green] (a) circle (2pt);
\draw [fill=green] (b) circle (2pt);
\path [name path = acirc] (a) circle (\rad);
\path [name path = bcirc] (b) circle (\rad);
\path [name intersections={of=acirc and bcirc}];
\coordinate (centerab) at (intersection-1);
\draw (centerab) circle (2pt);
\draw (centerab) circle (\rad);
\end{tikzpicture}
\end{center}
\end{document}
\usepackage{tkz-euclide}
.$\overbar{ab}$
, or simply use the intersections tikzlibrary for the intersections of circles (paths only) of radius\rad
centered at a and b. Use the [pos=.5] (for example) option for coordinates along a path. @Bobyandbob - Have they translated the tks-euclide manual into anything besides french yet?