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I wanted to draw a convex lens in tikzpicture. I'm fairly new to writing these commands, so I drafted the following.

% Convex lens 
% \convex[R0,R1,w,h] at (x,y);
\def\convex[#1,#2,#3,#4] at (#5,#6){
    % circle-circle intersection maths
    % with adjustment for clipping at specified height
    \def\R{#1};\def\r{#2};\def\d{(\R+\r-#3)};
    \def\x{(((\d*\d)-(\r*\r)+(\R*\R))/(2*\d))};\def\c{(\d-\x)};
    \def\y{sqrt((\R*\R)-(\x*\x))};\def\yh{min(\y,#4)};
    \def\g{asin(\yh/\R)};\def\p{asin(\yh/\r)};

% sphere0 curves
\draw ({#5-\x+\R},#6) arc (0:\g:\R);
\draw ({#5-\x+\R},#6) arc (0:-\g:\R);

% sphere1 curves
\draw ({#5+\c-\r},#6) arc (180:180+\p:\r);
\draw ({#5+\c-\r},#6) arc (180:180-\p:\r);

% connecting lines (if clipped)
\def\xg{\R*cos(\g)};\def\xp{\r*cos(\p)};
\draw ({#5+\xg-\x},{\yh}) -- ({#5-\xp+\c},{\yh});
\draw ({#5+\xg-\x},{-\yh}) -- ({#5-\xp+\c},{-\yh});
}

This works, but I'd like to improve it a bit. Specific questions follow.

  1. Does it make sense to pass R0, R1, w, and h in this way? Is there a more standard way to pass arguments that is more in line with tikz/pgf philosophy?
  2. How can I pass optional arguments such as thick to my \draw commands? It seems like \def does not allow optional arguments. Is there another command I can use to define my lens?
  3. Is there a better way to do this math in tikz/pgf (i.e. can it be done in fewer commands/with less braces and parentheses)?
Zach Marin
  • 1

0 Answers0