If statement to find the right position on a path and create a new path based on that

Question

I have a half rectangle and a circle that may intersect with each other. The circle is first at a location far above the rectangle and it moves down till it intersects with the rectangle and even passes through. I'm interested in finding the path that is created from the intersection between the two paths. So far thanks to Heiko Oberiek I know how to produce the new path for a special case. I want to be able to use conditional statements to figure out if the two shapes are intersecting and if they are where is the location of the intersection and finally produce the new path from subtracting the two shapes. Here is the code that I have for creating the two shapes:

\documentclass{standalone}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{graphicx}
\usetikzlibrary{intersections}  
\begin{document}
\begin{tikzpicture}
\pgfmathsetmacro\minX{2}
\pgfmathsetmacro\maxX{10}
\pgfmathsetmacro\minY{4}
\pgfmathsetmacro\maxY{10}
\pgfmathsetmacro\CX{11}
\pgfmathsetmacro\CY{12}
\pgfmathsetmacro\CR{2}
\pgfmathsetmacro\Roundness{0.2}
\begin{scope} [local bounding box=BoxWest]
\def\pathone{(.5*\maxX + .5*\minX,\maxY) 
    -- (-\Roundness + \maxX,\maxY)
    arc (90:0:\Roundness)
 -- (\maxX,\minY +\Roundness)
    arc (360:270:\Roundness)
    -- (.5*\maxX+ .5*\minX,\minY )}
    \path [name path=pathone, draw=green] \pathone;         
    \path [name path=pathtwo, draw=blue](\CX,\CY)
    circle (\CR);
\end{scope}
\end{tikzpicture}
\end{document}

this code produces:

changing the \CY from 12 to 10 produces:

and so on. This is the code that I have which only works when the circle has intersections with half-rectangle at the vertical line (Subtracting two TikZ paths at their intersection):

\begin{tikzpicture}[x=10pt, y=10pt]
\pgfmathsetmacro\minX{2}
\pgfmathsetmacro\maxX{10}
\pgfmathsetmacro\minY{4}
\pgfmathsetmacro\maxY{10}
\pgfmathsetmacro\CX{11}
\pgfmathsetmacro\CY{7}
\pgfmathsetmacro\CR{3}
\pgfmathsetmacro\Roundness{0.2}

\pgfmathsetmacro\OneWestX{.5*\maxX + .5*\minX}
\pgfmathsetmacro\OneEastX{\maxX}
\pgfmathsetmacro\OneNorthY{\maxY}
\pgfmathsetmacro\OneSouthY{\minY}

\pgfmathsetmacro\DiffX{\CX-\OneEastX}
\pgfmathsetmacro\DiffY{sqrt(\CR * \CR - \DiffX * \DiffX)}
\pgfmathsetmacro\DiffAngle{acos(\DiffX/\CR)}

\def\paththree{
  (\OneWestX, \OneNorthY)
  -- (\OneEastX, \OneNorthY)
  -- (\OneEastX, \CY + \DiffY) % North intersection point
  arc (180 - \DiffAngle:180 + \DiffAngle: \CR)
  -- (\OneEastX, \OneSouthY)
  -- (\OneWestX, \OneSouthY)}
\draw \paththree;
\end{tikzpicture}

can anyone help me generalize this solution for any location of the circle with respect to the half-rectangle and any radius of it?

Answer 1

Here is a proposal.

\documentclass{article}
\usepackage{tikz,pgfplots}
\pgfplotsset{compat=1.15}
\usetikzlibrary{intersections,fillbetween} 

\begin{document}
\begin{tikzpicture}
\pgfmathsetmacro\minX{2}
\pgfmathsetmacro\maxX{10}
\pgfmathsetmacro\minY{4}
\pgfmathsetmacro\maxY{10}
\pgfmathsetmacro\CX{11}
\pgfmathsetmacro\CY{12}
\pgfmathsetmacro\CR{2}
\pgfmathsetmacro\Roundness{0.2}
\begin{scope} [local bounding box=BoxWest]
\def\pathone{(.5*\maxX + .5*\minX,\maxY) 
    -- (-\Roundness + \maxX,\maxY)
    arc (90:0:\Roundness)
 -- (\maxX,\minY +\Roundness)
    arc (360:270:\Roundness)
    -- (.5*\maxX+ .5*\minX,\minY )}
    \path [name path global=pathone, draw=green] \pathone;         
    \path [name path global=pathtwo, draw=blue](\CX,\CY)
    circle (\CR);
  \path [name intersections={of=pathone and pathtwo,total=\tot}]
  \pgfextra{\pgfmathsetmacro{\NonTriv}{ifthenelse(\tot>1,1,0)}% check if there 
  %are at least two intersections
  \xdef\XNonTriv{\NonTriv}% export the result
  };
\end{scope}
  \ifnum\XNonTriv=1
    \draw[red,very thick,rounded corners, 
    intersection segments={of=pathone and pathtwo,
    sequence=L1--R2 L3}];
  \fi   
\end{tikzpicture}

\end{document}

Shifting the circle down with \pgfmathsetmacro\CY{5} yields.

Note that the intersection segments have to be drawn outside the scope.

And here is a code that finds out where the intersections are. DISCLAIMER: It does not work if the circle goes through the rounded corners. The path you are most likely after is \mypathA arc(\angleA:\angleB:\CR) --\mypathB.

\documentclass{standalone}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{graphicx}
\usetikzlibrary{intersections,calc}
\makeatletter
% from https://tex.stackexchange.com/q/56353/121799
\newcommand{\gettikzxy}[3]{%
  \tikz@scan@one@point\pgfutil@firstofone#1\relax
  \edef#2{\the\pgf@x}%
  \edef#3{\the\pgf@y}%
}
\makeatother  
\def\mytolerance{0.2}% tolerance for comparing coordinates
\begin{document}
\begin{tikzpicture}
\pgfmathsetmacro\minX{2}
\pgfmathsetmacro\maxX{10}
\pgfmathsetmacro\minY{4}
\pgfmathsetmacro\maxY{10}
\pgfmathsetmacro\CX{9}
\pgfmathsetmacro\CY{9}
\pgfmathsetmacro\CR{2}
\pgfmathsetmacro\Roundness{0.2}
\begin{scope} [local bounding box=BoxWest]
\def\pathone{(.5*\maxX + .5*\minX,\maxY) 
    -- (-\Roundness + \maxX,\maxY)
    arc (90:0:\Roundness)
 -- (\maxX,\minY +\Roundness)
    arc (360:270:\Roundness)
    -- (.5*\maxX+ .5*\minX,\minY )}
    \path [name path=pathone, draw=green] \pathone;         
    \path [name path=pathtwo, draw=blue](\CX,\CY)
    circle (\CR);
    \path [name intersections={of=pathone and pathtwo,name=myint,total=\tot}]
  \pgfextra{
  \pgfmathtruncatemacro{\NonTriv}{ifthenelse(\tot>1,1,0)}% check if there 
  \ifnum\NonTriv=1\relax
  \gettikzxy{(.5*\maxX + .5*\minX,\maxY)}{\tmpx}{\yplus}
  \gettikzxy{(\maxX,0)}{\xmax}{\tmpy}
  \gettikzxy{(.5*\maxX+ .5*\minX,\minY )}{\tmpx}{\yminus}
  \foreach \X in {1,...,\tot}
  {
    \gettikzxy{(myint-\X)}{\myx}{\myy}
    \gettikzxy{(\CX,\CY)}{\circX}{\circY}
    \ifnum\X=1
    \pgfmathparse{mod(720+atan2(+\myy-\circY,+\myx-\circX),360)}
    \xdef\angleA{\pgfmathresult}
    %\typeout{angle\space A:\angleA}
    \else
    \pgfmathparse{mod(720+atan2(+\myy-\circY,+\myx-\circX),360)}
    \xdef\angleB{\pgfmathresult}
    %\typeout{angle\space B:\angleB}
    \fi 
    \pgfmathtruncatemacro{\isontop}{ifthenelse(abs(\myy-\yplus)<\mytolerance,1,0)}
    \ifnum\isontop=1\relax%
    %\node at (myint-\X) {\X\ is on top}; 
    \ifnum\X=1
    \xdef\mypathA{(.5*\maxX + .5*\minX,\maxY)  -- ($(\CX,\CY)+(\angleA:\CR)$)}
    \else
    \xdef\mypathB{($(\CX,\CY)+(\angleB:\CR)$) -- (-\Roundness + \maxX,\maxY)
    arc (90:0:\Roundness) -- (\maxX,\minY +\Roundness)    
    arc (360:270:\Roundness)
    -- (.5*\maxX+ .5*\minX,\minY )}
    \fi
    \fi%
    \pgfmathtruncatemacro{\isonbottom}{ifthenelse(abs(\myy-\yminus)<\mytolerance,1,0)}
    \ifnum\isonbottom=1\relax%
    %\node at (myint-\X) {\X\ is on bottom}; 
    \ifnum\X=1
    \xdef\mypathA{(.5*\maxX + .5*\minX,\maxY) -- (-\Roundness + \maxX,\maxY)
    arc (90:0:\Roundness)
 -- (\maxX,\minY +\Roundness)
    arc (360:270:\Roundness)
    --  ($(\CX,\CY)+(\angleA:\CR)$)}
    \else
    \xdef\mypathB{($(\CX,\CY)+(\angleB:\CR)$) -- (.5*\maxX+ .5*\minX,\minY )}
    \fi
    \fi%
    \pgfmathtruncatemacro{\isonright}{ifthenelse(abs(\myx-\xmax)<\mytolerance,1,0)}
    \ifnum\isonright=1\relax%
    %\node at (myint-\X) {\X\ is on right}; 
    \ifnum\X=1
    \xdef\mypathA{(.5*\maxX + .5*\minX,\maxY)-- (-\Roundness + \maxX,\maxY)
    arc (90:0:\Roundness)
 --  ($(\CX,\CY)+(\angleA:\CR)$)
    }
    \else
    \xdef\mypathB{($(\CX,\CY)+(\angleB:\CR)$) -- (\maxX,\minY +\Roundness)    
    arc (360:270:\Roundness)
    -- (.5*\maxX+ .5*\minX,\minY )}
    \fi
    \fi%
    %\typeout{\X : \myx,\myy,\yplus,\yminus,\xmax}
  }
  %\typeout{\mypathA arc(\angleA:\angleB:\CR) --\mypathB}
  \draw[red] \mypathA arc(\angleA:\angleB:\CR) --\mypathB ;
  \else
  \fi
  };
\end{scope}
\end{tikzpicture}
\end{document}