[Tex/LaTex] filled quarter circle

tikz-pgftkz-collection

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

enter image description here

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}

Best Answer

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.

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[Tex/LaTex] way to draw TikZ lines on the “inside” or “outside” of a path

I was idling thinking how one might go about this, when I came up with a very simple solution. I wouldn't be surprised to learn that this is what Illustrator does. Looking at the diagrams, it would seem that way.

My initial plan was to figure out some sort of decoration that would "shift" a path to the left or right, but that just seemed fraught with difficulties. But I couldn't think of a way to get TikZ to treat the two halves of a path in a different manner. Then I realised that there is such a way: clipping.

When TikZ clips against a path then the two sides of that path are treated in a different manner. So that can be used to get it to only draw one side. Sort of. You draw a path, but clip it against itself. Since the clipping path has no width, this means that half the path gets drawn. The "Sort of" is because the decision about which half depends on the region that is being enclosed, not the actual side of the path. This, I think, leads to the funny look on the Illustrator images in the question.

A general solution to this would involve a command to draw and clip in the same breath. That could be done with my spath library (still in development, but available from the TeX-SX site on launchpad), and one would have to use the "reverse" clip method from somewhere around here for dealing with the other side. But to demonstrate the concept, we can just do it by hand. Here's the cube:

Cube with clipping

and here's the code:

\documentclass{article}
%\url{http://tex.stackexchange.com/q/29991/86}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}[scale=5,line width=2mm]
\draw (0,0,0) -- (1,0,0) -- (1,1,0) -- (0,1,0) -- cycle;
\draw (1,0,0) -- (1,0,-1) -- (1,1,-1) -- (1,1,0) -- cycle;
\draw (0,1,0) -- (0,1,-1) -- (1,1,-1) -- (1,1,0) -- cycle;
\begin{scope}[yshift=-2cm,line width=4mm]
\begin{scope}
\clip (0,0,0) -- (1,0,0) -- (1,1,0) -- (0,1,0) -- cycle;
\draw (0,0,0) -- (1,0,0) -- (1,1,0) -- (0,1,0) -- cycle;
\end{scope}
\begin{scope}
\clip (1,0,0) -- (1,0,-1) -- (1,1,-1) -- (1,1,0) -- cycle;
\draw (1,0,0) -- (1,0,-1) -- (1,1,-1) -- (1,1,0) -- cycle;
\end{scope}
\begin{scope}
\clip (0,1,0) -- (0,1,-1) -- (1,1,-1) -- (1,1,0) -- cycle;
\draw (0,1,0) -- (0,1,-1) -- (1,1,-1) -- (1,1,0) -- cycle;
\end{scope}
\end{scope}
\end{tikzpicture}
\end{document}

Note the scopes to limit the clips, and the doubled line width, since we lose half of it in the clip.

[Tex/LaTex] tkz-euclide changing labels and size (triangle, inscribed circle)

You could use options when drawing, such as

\tkzDrawCircle[R,very thick](S,\rSN pt)
\tkzDrawPoints[color=black,shape=circle,fill=black](D,E,F,S)

or set styles, such as by \tkzSetUpPoint and \tkzSetUpLine, which are explained in the tkz-euclide manual.

Regarding the labels, you could set their style via an option to the tikzpicture or by \tikzset, such as

\begin{tikzpicture}[scale=1.5,label style/.style={font=\Large}]

By this, the picture changes to

tikz picture

Best Answer

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[Tex/LaTex] tkz-euclide changing labels and size (triangle, inscribed circle)

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