tikz.dev / tkz-euclide Manual

tkz-euclide

Drawing, filling and clipping

28 Filling

28.1 Coloring a disc

This was possible with the macro \tkzDrawCircle, but the circle had to be drawn; this is no longer the case.

  • \tkzFillCircle[⟨local options⟩](⟨A,B⟩)

    • optionsdefaultdefinition
    radiusradiustwo points define a radius
    Rradiusa point and the measurement of a radius

    You don’t need to write radius, because it is the default option. Of course, you can add all the TikZ styles.

28.1.1 Yin and Yang

Compiled output

\begin{tikzpicture}[scale=.75]
\tkzDefPoint(0,0){O}
\tkzDefPoint(-4,0){A}
\tkzDefPoint(4,0){B}
\tkzDefPoint(-2,0){I}
\tkzDefPoint(2,0){J}
\tkzDrawSector[fill=teal](O,A)(B)
\tkzFillCircle[fill=white](J,B)
\tkzFillCircle[fill=teal](I,A)
\tkzDrawCircle(O,A)
\end{tikzpicture}
28.1.2 From a sangaku

Compiled output

\begin{tikzpicture}
\tkzDefPoint(0,0){B} \tkzDefPoint(6,0){C}%
\tkzDefSquare(B,C) \tkzGetPoints{D}{A}
\tkzClipPolygon(B,C,D,A)
\tkzDefMidPoint(A,D) \tkzGetPoint{F}
\tkzDefMidPoint(B,C) \tkzGetPoint{E}
\tkzDefMidPoint(B,D) \tkzGetPoint{Q}
\tkzDefLine[tangent from = B](F,A)
\tkzGetPoints{H}{G}
\tkzInterLL(F,G)(C,D) \tkzGetPoint{J}
\tkzInterLL(A,J)(F,E) \tkzGetPoint{K}
\tkzDefPointBy[projection=onto B--A](K)
\tkzGetPoint{M}
\tkzDrawPolygon(A,B,C,D)
\tkzFillCircle[red!20](E,B)
\tkzFillCircle[blue!20](M,A)
\tkzFillCircle[green!20](K,Q)
\tkzDrawCircles(B,A M,A E,B K,Q)
\end{tikzpicture}
28.1.3 Clipping and filling part I

Compiled output

\begin{tikzpicture}
\tkzDefPoints{0/0/A,4/0/B,2/2/O,3/4/X,4/1/Y,1/0/Z,
0/3/W,3/0/R,4/3/S,1/4/T,0/1/U}
\tkzDefSquare(A,B)\tkzGetPoints{C}{D}
\tkzDefPointWith[colinear normed=at X,K=1](O,X)
\tkzGetPoint{F}
\begin{scope}
\tkzFillCircle[fill=teal!20](O,F)
\tkzFillPolygon[white](A,...,D)
\tkzClipPolygon(A,...,D)
\foreach \c/\t in {S/C,R/B,U/A,T/D}
{\tkzFillCircle[teal!20](\c,\t)}
\end{scope}
\foreach \c/\t in {X/C,Y/B,Z/A,W/D}
{\tkzFillCircle[white](\c,\t)}
\foreach \c/\t in {S/C,R/B,U/A,T/D}
{\tkzFillCircle[teal!20](\c,\t)}
\end{tikzpicture}
28.1.4 Clipping and filling part II

Compiled output

\begin{tikzpicture}[scale=.75]
\tkzDefPoints{0/0/A,8/0/B,8/8/C,0/8/D}
\tkzDefMidPoint(A,B) \tkzGetPoint{F}
\tkzDefMidPoint(B,C) \tkzGetPoint{E}
\tkzDefMidPoint(D,B) \tkzGetPoint{I}
\tkzDefMidPoint(I,B) \tkzGetPoint{a}
\tkzInterLC(B,I)(B,C) \tkzGetSecondPoint{K}
\tkzDefMidPoint(I,K) \tkzGetPoint{b}
\begin{scope}
\tkzFillSector[fill=blue!10](B,C)(A)
\tkzDefMidPoint(A,B) \tkzGetPoint{x}
\tkzDrawSemiCircle[fill=white](x,B)
\tkzDefMidPoint(B,C) \tkzGetPoint{y}
\tkzDrawSemiCircle[fill=white](y,C)
\tkzClipCircle(E,B)
\tkzClipCircle(F,B)
\tkzFillCircle[fill=blue!10](B,A)
\end{scope}
\tkzDrawSemiCircle[thick](F,B)
\tkzDrawSemiCircle[thick](E,C)
\tkzDrawArc[thick](B,C)(A)
\tkzDrawSegments[thick](A,B B,C)
\tkzDrawPoints(A,B,C,E,F)
\tkzLabelPoints[centered](a,b)
\tkzLabelPoints(A,B,C,E,F)
\end{tikzpicture}
28.1.5 Clipping and filling part III

Compiled output

\begin{tikzpicture}
\tkzDefPoint(0,0){A} \tkzDefPoint(1,0){B}
\tkzDefPoint(2,0){C} \tkzDefPoint(-3,0){a}
\tkzDefPoint(3,0){b} \tkzDefPoint(0,3){c}
\tkzDefPoint(0,-3){d}
\begin{scope}
\tkzClipPolygon(a,b,c,d)
\tkzFillCircle[teal!20](A,C)
\end{scope}
\tkzFillCircle[white](A,B)
\tkzDrawCircle[color=red](A,C)
\tkzDrawCircle[color=red](A,B)
\end{tikzpicture}
28.2 Coloring a polygon

  • \tkzFillPolygon[⟨local options⟩](⟨points list⟩)

    • You can color a polygon while drawing it; this macro colors the inside of the polygon without drawing it.

    argumentsexampleexplanation
    (⟨pt1,pt2,…⟩)(⟨A,B,…⟩)
28.2.1 \tkzFillPolygon

Compiled output

\begin{tikzpicture}[scale=.5]
\tkzDefPoint(0,0){C} \tkzDefPoint(4,0){A}
\tkzDefPoint(0,3){B}
\tkzDefSquare(B,A) \tkzGetPoints{E}{F}
\tkzDefSquare(A,C) \tkzGetPoints{G}{H}
\tkzDefSquare(C,B) \tkzGetPoints{I}{J}
\tkzFillPolygon[color = orange!30 ](A,C,G,H)
\tkzFillPolygon[color = teal!40 ](C,B,I,J)
\tkzFillPolygon[color = purple!20](B,A,E,F)
\tkzDrawPolygon[line width = 1pt](A,B,C)
\tkzDrawPolygon[line width = 1pt](A,C,G,H)
\tkzDrawPolygon[line width = 1pt](C,B,I,J)
\tkzDrawPolygon[line width = 1pt](B,A,E,F)
\tkzLabelSegment[above](C,A){$a$}
\tkzLabelSegment[right](B,C){$b$}
\tkzLabelSegment[below left](B,A){$c$}
\end{tikzpicture}
28.3 \tkzFillSector


☞ 💣 Note that the arguments depend on the options.

  • \tkzFillSector[⟨local options⟩](⟨O,…⟩)(⟨…⟩)

    • optionsdefaultdefinition
    towardstowards\(O\) is the center and the arc from \(A\) to \((OB)\)
    rotatetowardsthe arc starts from A and the angle determines its length
    RtowardsWe give the radius and two angles
    R with nodestowardsWe give the radius and two points

    Of course, you can add all the TikZ styles for the drawings.

    optionsargumentsexample
    towards(⟨pt,pt⟩)(⟨pt⟩)\tkzFillSector(O,A)(B)
    rotate(⟨pt,pt⟩)(⟨an⟩)\tkzFillSector[rotate,color=red](O,A)(90)
    R(⟨pt,\(r\)⟩)(⟨an,an⟩)\tkzFillSector[R,color=blue](O,2)(30,90)
    R with nodes(⟨pt,\(r\)⟩)(⟨pt,pt⟩)\tkzFillSector[R with nodes](O,2)(A,B)
28.3.1 \tkzFillSector and towards

You don’t need to write towards. Note that the contours are not drawn: only the surface is colored.

Compiled output

\begin{tikzpicture}[scale=.6]
\tkzDefPoint(0,0){O}
\tkzDefPoint(-30:3){A}
\tkzDefPointBy[rotation = center O angle -60](A)
\tkzFillSector[fill=purple!20](O,A)(tkzPointResult)
\begin{scope}[shift={(-60:1)}]
\tkzDefPoint(0,0){O}
\tkzDefPoint(-30:3){A}
\tkzDefPointBy[rotation = center O angle -60](A)
\tkzGetPoint{A'}
\tkzFillSector[color=teal!40](O,A')(A)
\end{scope}
\end{tikzpicture}
28.3.2 \tkzFillSector and rotate

Compiled output

\begin{tikzpicture}[scale=1.5]
\tkzDefPoint(0,0){O} \tkzDefPoint(2,2){A}
\tkzFillSector[rotate,color=purple!20](O,A)(30)
\tkzFillSector[rotate,color=teal!40](O,A)(-30)
\end{tikzpicture}
28.4 Coloring an angle: \tkzFillAngle

The simplest case:

  • \tkzFillAngle[⟨local options⟩](⟨A,O,B⟩)

    • \(O\) is the vertex of the angle, \(OA\) and \(OB\) are its sides. Note that the angle depends on the order of the points.

    optionsdefaultdefinition
    size1this option determines the radius of the colored angular sector.

    Of course, you can add all the TikZ styles, such as fill and shade.

28.4.1 Example with size

Compiled output

\begin{tikzpicture}
\tkzInit
\tkzDefPoints{0/0/O,2.5/0/A,1.5/2/B}
\tkzFillAngle[size=2, fill=gray!10](A,O,B)
\tkzDrawLines(O,A O,B)
\tkzDrawPoints(O,A,B)
\end{tikzpicture}
28.4.2 Changing the order of items

Compiled output

\begin{tikzpicture}
\tkzInit
\tkzDefPoints{0/0/O,2.5/0/A,1.5/2/B}
\tkzFillAngle[size=2,fill=gray!10](B,O,A)
\tkzDrawLines(O,A O,B)
\tkzDrawPoints(O,A,B)
\end{tikzpicture}

Compiled output

\begin{tikzpicture}
\tkzInit
\tkzDefPoints{0/0/O,5/0/A,3/4/B}
% Don't forget {} to get, () to use
\tkzFillAngle[size=4,left color=white,
right color=red!50](A,O,B)
\tkzDrawLines(O,A O,B)
\tkzDrawPoints(O,A,B)
\end{tikzpicture}

  • \tkzFillAngles[⟨local options⟩](⟨A,O,B⟩)(⟨A’,O’,B’⟩)etc.

    • With common options, there is a macro for several angles.

28.4.3 Several angles

Compiled output

\begin{tikzpicture}[scale=0.5]
\tkzDefPoints{0/0/B,8/0/C,0/8/A,8/8/D}
\tkzDrawPolygon(B,C,D,A)
\tkzDefTriangle[equilateral](B,C) \tkzGetPoint{M}
\tkzInterLL(D,M)(A,B) \tkzGetPoint{N}
\tkzDefPointBy[rotation=center N angle -60](D)
\tkzGetPoint{L}
\tkzInterLL(N,L)(M,B) \tkzGetPoint{P}
\tkzInterLL(M,C)(D,L) \tkzGetPoint{Q}
\tkzDrawSegments(D,N N,L L,D B,M M,C)
\tkzDrawPoints(L,N,P,Q,M,A,D)
\tkzLabelPoints[left](N,P,Q)
\tkzLabelPoints[above](M,A,D)
\tkzLabelPoints(L,B,C)
\tkzMarkAngles(C,B,M B,M,C M,C,B D,L,N L,N,D N,D,L)
\tkzFillAngles[fill=red!20,opacity=.2](C,B,M
B,M,C M,C,B D,L,N L,N,D N,D,L)
\end{tikzpicture}