parabolic bridge arch

I have a parabola drawn through A, B and C. There are three different equations: for the top darker border, the fill (this is a hack just using a wide line) and the lower border. It's not quite what I want.

I'd like to emphasize that there are two separate sections of the arch which are pinned together at B so I am trying to draw AB on its own. In red, I plot the function for the upper border from A to almost B, then use an arc to touch at B and reach to bottom border of the arch.

I would like to chain a function call to my statement (the last statement below) that will plot the formula of the lower border of the arch from B back to A.

I'm not sure of the syntax:

  1. How do a I chain a function call, with a different domain from the first call in the statement?
  2. When plotting the parabola of the bottom border of the arch from B back to A, I need to draw the parabola from right to left (B_x to A_x). Is this possible?
 % arch fill (central formula)
 \draw[domain=4.2:13.825, color=LightCyan3, line width=0.375cm, line cap=rect] plot[id=1] function{-3*x*x/32+3*x/2};

 % upper arch border
 \draw[domain=3.85:14.187, color=LightCyan4, thick] plot[id=2] function{-.090215*x*x+1.4425*x+0.48342};

 % lower arch border
 \draw[domain=4.15:13.813, color=LightCyan4, thick] plot[id=3] function{-0.097567*x*x+1.5621*x-0.50220};

 % incomplete red border
 \draw[domain=3.85:7.75, draw=red, fill=none, very thick]plot[id=4] function{-0.090211*x*x+1.4425*x+0.48342}arc(90:-90:0.25);

Most likely I do not fully understand or appreciate what you want. Yes, you can reverse the plot, and I do not think you need gnuplot for such a simple function.

\draw[domain=4.2:13.825, color=cyan, line width=0.375cm, line cap=rect] plot[id=1] function{-3*x*x/32+3*x/2};

 % upper arc border
 \draw[domain=3.85:14.187, color=cyan, thick] plot[variable=\x] 

 % lower arc border
 \draw[domain=4.15:13.813, color=cyan, thick] plot[variable=\x] 

 % incomplete red border
 \draw[draw=red, fill=none, very thick,fill=red!20]
 plot[domain=3.85:7.75,variable=\x] ({\x},{-0.090211*\x*\x+1.4425*\x+0.48342})
 plot[domain=7.75:3.85,variable=\x] ({\x},{-0.097567*\x*\x+1.5621*\x-0.50220})
 -- (3.85,{-0.090211*3.85*3.85+1.4425*3.85+0.48342}); 

enter image description here

For fun, I also shaded the contour. If you don't like this, just remove the fill=red!20 statement and -- (3.85,{-0.090211*3.85*3.85+1.4425*3.85+0.48342}) (but not the semicolon).

  • You understood perfectly. :) – dmorg Apr 21 '18 at 3:54

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