# filled quarter circle

As usual I am typeseting some old exams. I ran into this image shown below

I ran into some problems when trying to tikz it up. In the minimal example below I have been able to almost recreate this image, but my method is very rough. I created a half circle, filled it. Then used some trickery with cutting the figure. My main problem is how do I fill a quarter circle? (preferably using tikz euclide) Now any help improving my figure would be greatly appreciated =)

\documentclass{standalone}
\usepackage{tkz-euclide}
\usetkzobj{all}
\begin{document}
\begin{tikzpicture}
\def\a{3} % Defines the radius for the half circle
\tkzInit[xmin=-.5,xmax=4,ymin=-.5,ymax=4] \tkzClip
\tkzDefPoint(0,0){O} \tkzDefPoint(\a,0){S1} \tkzDefPoint(0,\a){S2}
\tkzDefPoint(-\a,0){S3} \tkzDefPoint(0,-\a){S4}
\tkzDefPointBy[rotation= center O angle 45](S1) \tkzGetPoint{B}
\tkzDefPoint(\a*2^(-0.5),0){A} \tkzDefPoint(0,\a*2^(-0.5)){C}
\tkzDrawArc[fill=blue,opacity=0.3,ultra thin](O,S1)(S3)
\tkzDrawArc[color=blue,very thick](O,S1)(S2)
\tkzDrawSquare[fill=white,color=white](S3,O)
\tkzDrawSquare[fill=white](O,A) \tkzDrawSquare[thick](O,A)
\tkzDefPoint(-0.5,0){x1} \tkzDefPoint[label=above left: $x$](1+\a,0){x2}
\tkzDefPoint(0,-0.5){y1} \tkzDefPoint[label=below left: $y$](0,1+\a){y2}
\tkzDrawSegments[very thick,-stealth](x1,x2 y1,y2) \tkzDrawSegment[dashed](A,C)
\tkzDrawSegments[ultra thick,white]({-0.5,-0.5},{-0.5,4})
\tkzDrawPoints[fill=black,size=2.5](O,A,B,C)
\tkzLabelPoints[below left](O) \tkzLabelPoints[above right](B)
\tkzLabelPoints[below](A) \tkzLabelPoints[left](C)
\tkzLabelPoint[below](S1){$3$} \tkzLabelPoint[left](S2){$3$}
\end{tikzpicture}
\end{document}


EDIT: New MWE

\documentclass{standalone}
\usepackage{tkz-euclide}
\usetkzobj{all}
\begin{document}
\begin{tikzpicture}
\def\a{3} % Defines the radius and clipping.
\tkzInit[xmin=-.5,xmax=4,ymin=-.5,ymax=4] \tkzClip
% Defines all the neccecary points.
\tkzDefPoint(0,0){O} \tkzDefPoint(\a,0){S1} \tkzDefPoint(0,\a){S2}
\tkzDefPointBy[rotation= center O angle 45](S1) \tkzGetPoint{B}
\tkzDefPoint(\a*2^(-0.5),0){A} \tkzDefPoint(0,\a*2^(-0.5)){C}
% Draws the quarter cirle. (triangle + arc)
\tkzDrawPolygon[fill=blue,opacity=0.3,color=blue](O,S1,S2)
\tkzDrawArc[fill=blue,opacity=0.3,ultra thin](O,S1)(S2)
\tkzDrawArc[color=blue,very thick](O,S1)(S2) \tkzDrawSegment[color=blue!30!white](S1,S2)
% Draws the square and the dashed line.
\tkzDrawSquare[color=black,thick,fill=white](O,A) \tkzDrawSegment[dashed](A,C)
% Draws the coordinate axis.
\tkzDefPoint(-0.5,0){x1} \tkzDefPoint[label=above left: $x$](1+\a,0){x2}
\tkzDefPoint(0,-0.5){y1} \tkzDefPoint[label=below left: $y$](0,1+\a){y2}
\tkzDrawSegments[very thick,-stealth](x1,x2 y1,y2)
% Draws the points and label them.
\tkzDrawPoints[fill=black,size=2.5](O,A,B,C)
\tkzLabelPoints[below left](O) \tkzLabelPoints[above right](B)
\tkzLabelPoints[below](A) \tkzLabelPoints[left](C)
\tkzLabelPoint[below](S1){$3$} \tkzLabelPoint[left](S2){$3$}
\end{tikzpicture}
\end{document}

-

tkz-euclide manual, although is written in french, is full of examples. On page 112 you will find command \tkzFillSector. Whitin your first example you can use \tkzFillSector[fill=blue,opacity=0.3](O,S1)(S2) to fill the sector with center on O from S1 to S2.

-
I actually tried searching trough it, but I am rather weak in the french (as well as the tikz). Thanks though! That simplifies things a great deal! –  N3buchadnezzar Jun 21 '12 at 9:14

Some informations to complete Ignasi's answer.

You can find in tkz-euclide some macros about arcs, some macro about sectors. Here it's possible to draw the sector and to fill it at the same time with

   \tkzDrawSector[color=blue, thick,fill=blue,fill opacity=0.3](O,S1)(S2)


You need only to draw axis after. It's possible to use

    \tkzDrawXY[noticks,very thick]


to get axis directly.

I added \tkzClip[space=0.75] to show the tips of the axes. It's possible to reduce xmax and ymax.

You can add tkz in the tags

The complete code :

\documentclass{standalone}
\usepackage{tkz-euclide}
\usetkzobj{all}
\begin{document}
\begin{tikzpicture}
\tikzset{xlabel style/.style={below left=6 pt,
inner sep = 1pt,
outer sep = 0pt}}
\tikzset{xaxe style/.style ={>=stealth,->}}
\tikzset{ylabel style/.style={below left = 6 pt,
inner sep = 1pt,
outer sep = 0pt}}
\tikzset{yaxe style/.style ={>=stealth,->}}

\def\a{3} % Defines the radius and clipping.
\tkzInit[xmin=-.4,xmax=4,ymin=-.4,ymax=4]
% Defines all the neccecary points.
\tkzDefPoint(0,0){O} \tkzDefPoint(\a,0){S1} \tkzDefPoint(0,\a){S2}
\tkzDefPointBy[rotation= center O angle 45](S1) \tkzGetPoint{B}
\tkzDefPoint(\a*2^(-0.5),0){A} \tkzDefPoint(0,\a*2^(-0.5)){C}
% Draws the quarter cirle. (triangle + arc)
\tkzDrawSector[color=blue, thick,fill=blue,fill opacity=0.3](O,S1)(S2)
% Draws the square and the dashed line.
\tkzDrawSquare[color=black,thick,fill=white](O,A) \tkzDrawSegment[dashed](A,C)
% Draws the coordinate axis.
\tkzDrawX[noticks,very thick,below]
\tkzDrawY[noticks,very thick]
% Draws the points and label them.
\tkzDrawPoints[fill=black,size=2.5](O,A,B,C)
\tkzLabelPoints[below left](O)  \tkzLabelPoints[above right](B)
\tkzLabelPoints[below](A)       \tkzLabelPoints[left](C)
\tkzLabelPoint[below](S1){$3$}  \tkzLabelPoint[left](S2){$3$}
\end{tikzpicture}
\end{document}


The result :

-
The line S1,S2 was only there to hide the gap between the sector and the polygon(triangle). Very nice! I am learning a lot from your examples. Sorry for not being able to read your manual better, I do not know any french. Two questions: 1. is arrowstyle possible to change? I usually use stealth for consistency. 2. Using \caption beneath the image makes too much space i.imgur.com/CPDWD.png. Is there any fix? I know removing the \tkzClip[space=0.75] helps, but this removes the arrows. –  N3buchadnezzar Jun 21 '12 at 13:23
A lot of styles are in the file : tkz-base.cfg  for example \tikzset{xaxe style/.style ={>=latex,->}}  idem for yaxe style. You can modify this style with \tikzset{xaxe style/.style ={>=stealth,->}} . If you remove space=0.75 from \tkzClip[space=0.75] you need to change \tkzInit and you can use a clip with tikz \clip (a,b) rectangle (c,d);`. I updated my answer with your requests. –  Alain Matthes Jun 21 '12 at 13:43