Re: Venn diagram

[Aditya Mahajan <adityam@umich.edu>]

<--- On Jan 19, David Arnold wrote --->

> All,
>
> I have:
>
> \startMPpage   %figure library name: intersection
>
>  %initialize scale
>  numeric u; 10u=3in;
>
>  %ellipses
>  path A, B;
>  A:=fullcircle xyscaled (4u,3u);
>  B:=A shifted (2u,0);
>  draw A withcolor red;
>  label.ulft(btex $A$ etex, point 3 of A) withcolor red;
>  draw B withcolor blue;
>  label.urt(btex $B$ etex, point 1 of B) withcolor blue;
>
>  %bounding box
>  draw bbox currentpicture enlarged (0.5u,0.5u);
>
> \stopMPpage
>
> I need an easy way of shading these areas:
>
> 1. A intersect B
> 2. A union B
> 3. A intersect (complement of B)
> 4. (complement of A) intersect B

There is venn.mp on ctan. Using it you can do basic shading of 
intersection, union etc for 0,1,2 or 3 sets very quickly. Read the 
documentation in source for details. For example

\startMPinclusions
   input venn;
   pair A,B,T[];
   A = (.4venn_width-.5venn_circle_diameter,.5venn_height);
   B = (.6venn_width+.5venn_circle_diameter,.5venn_height);
   T1 = (.5venn_width , 0);
   T2 = (.5venn_width,.5venn_height-.5venn_circle_diameter);
   vardef venn_shade = red;
\stopMPinclusions


\startMPpage
  draw_venn_two(false,true,true,true);
  label.lft(btex $A$ etex,A);
  label.rt(btex $B$ etex,B);
  label.bot(btex $A\cup B$ etex,T2);
\stopMPpage

\startMPpage
  draw_venn_two(false,false,true,false);
  label.lft(btex $A$ etex,A);
  label.rt(btex $B$ etex,B);
  label.bot(btex $A\cap B$ etex,T2);
\stopMPpage

\startMPpage
  draw_venn_two(true,false,false,false);
  label.lft(btex $A$ etex,A);
  label.rt(btex $B$ etex,B);
  label.bot(btex $A'\cap B'$ etex,T2);
\stopMPpage


Perhaps one can combine the transparent color functionality of 
metapost with venn.mp to get really nice colors for intersections etc.

Another related question, does anyone know of a good way to hash 
(hatch) a "set" (in general, any mp closed curve). I know that there 
is hatching.mp but I was wondering if there are better solutions.

Aditya

-- 
Aditya Mahajan, EECS Systems, University of Michigan
http://www.eecs.umich.edu/~adityam || Ph: 7342624008