tikz.dev / tkz-euclide Manual

tkz-euclide

Drawing, filling and clipping

29 Controlling the bounding box

From the PgfManual:

"When you add the clip option, the current path is used for clipping subsequent drawings. Clipping never enlarges the clipping area. Thus, when you clip against a certain path and then clip again against another path, you clip against the intersection of both. The only way to enlarge the clipping path is to end the pgfscope in which the clipping was done. At the end of a pgfscope the clipping path that was in force at the beginning of the scope is reinstalled."

First of all, with TikZ you don’t have to deal with the size of the bounding box. Early versions of tkz-euclide did not control it; since version 4, the size of the bounding box is limited.

The initial bounding box after using the macro \tkzInit is defined by the rectangle based on the points \((0,0)\) and \((10,10)\). The macro \tkzInit modifies this initial bounding box with the arguments xmin, xmax, ymin and ymax. Of course, anything drawn outside modifies the bounding box, which TikZ maintains. You can influence this behavior with TikZ commands or options, such as \useasboundingbox or the option use as bounding box. You can then reserve a box for a figure, but the figure may overflow the box and spread over the main text. The command \pgfresetboundingbox clears the bounding box and starts a new one.

29.1 Utility of \tkzInit

However, it is sometimes necessary to control the size of what is displayed. To do this, you need to prepare the bounding box you are going to work in: this is the role of the macro \tkzInit. For some drawings, it is useful to fix the extreme values (xmin, xmax, ymin and ymax) and to clip this rectangle, in order to control the size of the figure as well as possible.

Two macros are useful to control the bounding box:

I have also added macros directly linked to the bounding box: you can display it or clip it (see below).

29.2 \tkzInit

  • \tkzInit[⟨local options⟩]

    • optionsdefaultdefinition
    xmin0minimum value of the abscissae in cm
    xmax10maximum value of the abscissae in cm
    xstep1difference between two graduations in \(x\)
    ymin0minimum y-axis value in cm
    ymax10maximum y-axis value in cm
    ystep1difference between two graduations in \(y\)

    The role of \tkzInit is to define an orthogonal coordinate system and a rectangular part of the plane, in which you place your drawings with Cartesian coordinates. This macro defines your working area, as on a graphing calculator. Since version 4 of tkz-euclide, \xstep and \ystep are always 1, so \tkzInit is mostly useful for actions such as clipping out.

29.3 \tkzClip

  • \tkzClip[⟨local options⟩]

    • This macro hides everything outside the rectangle defined by (xmin ; ymin) and (xmax ; ymax).

    optionsdefaultdefinition
    space1added value on the right, left, bottom and top of the background

    The option space enlarges the visible part of the drawing, which becomes the rectangle defined by (xmin-space ; ymin-space) and (xmax+space ; ymax+space). space can be negative! The unit is the cm and must not be written.

This macro clips the initial rectangle, so that only the paths inside this rectangle are drawn.

Compiled output

\begin{tikzpicture}
\tkzInit[xmax=4, ymax=3]
\tkzDefPoints{-1/-1/A,5/2/B}
\tkzDrawX \tkzDrawY
\tkzGrid
\tkzClip
\tkzDrawSegment(A,B)
\end{tikzpicture}

You can add a bit of space:

\tkzClip[space=1]
29.4 \tkzClip and the option space

This option adds some space around the clipped rectangle.

Compiled output

\begin{tikzpicture}
\tkzInit[xmax=4, ymax=3]
\tkzDefPoints{-1/-1/A,5/2/B}
\tkzDrawX \tkzDrawY
\tkzGrid
\tkzClip[space=1]
\tkzDrawSegment(A,B)
\end{tikzpicture}

The dimensions of the clipped rectangle are xmin-1, ymin-1, xmax+1 and ymax+1.

29.5 \tkzShowBB

The simplest macro.

  • \tkzShowBB[⟨local options⟩]

    • This macro displays the bounding box as a rectangular frame. It accepts TikZ options.

29.5.1 Example with \tkzShowBB

Compiled output

\begin{tikzpicture}[scale=.5]
\tkzInit[ymax=5,xmax=8]
\tkzGrid
\tkzDefPoint(3,0){A}
\begin{scope}
\tkzClipBB
\tkzDefCircle[R](A,5) \tkzGetPoint{a}
\tkzDrawCircle(A,a)
\tkzShowBB[line width = 4pt,fill=teal!10,%
opacity=.4]
\end{scope}
\tkzDefCircle[R](A,4) \tkzGetPoint{b}
\tkzDrawCircle[red](A,b)
\end{tikzpicture}
29.6 \tkzClipBB

  • \tkzClipBB

    • The idea is to limit the next constructions to the current bounding box.

29.6.1 Example with \tkzClipBB and the bisectors

Compiled output

\begin{tikzpicture}
\tkzInit[xmin=-3,xmax=6, ymin=-1,ymax=6]
\tkzDefPoint(0,0){O}\tkzDefPoint(3,1){I}
\tkzDefPoint(1,4){J}
\tkzDefLine[bisector](I,O,J) \tkzGetPoint{i}
\tkzDefLine[bisector out](I,O,J) \tkzGetPoint{j}
\tkzDrawPoints(O,I,J,i,j)
\tkzClipBB
\tkzDrawLines[add = 1 and 2,color=orange](O,I O,J)
\tkzDrawLines[add = 1 and 2](O,i O,j)
\tkzShowBB
\end{tikzpicture}

30 Clipping different objects

30.1 Clipping a polygon

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

    • This macro restricts the drawings to the given polygon.

    argumentsexampleexplanation
    (⟨pt1,pt2,pt3,…⟩)(⟨A,B,C⟩)
    optionsdefaultdefinition
    outclips the outside of the object
30.1.1 \tkzClipPolygon

Compiled output

\begin{tikzpicture}[scale=1.25]
\tkzDefPoint(0,0){A}
\tkzDefPoint(4,0){B}
\tkzDefPoint(1,3){C}
\tkzDrawPolygon(A,B,C)
\tkzDefPoint(0,2){D}
\tkzDefPoint(2,0){E}
\tkzDrawPoints(D,E)
\tkzLabelPoints(D,E)
\tkzClipPolygon(A,B,C)
\tkzDrawLine[new](D,E)
\end{tikzpicture}
30.1.2 \tkzClipPolygon[out]

Compiled output

\begin{tikzpicture}[scale=1]
\tkzDefPoint(0,0){P1}
\tkzDefPoint(4,0){P2}
\tkzDefPoint(4,4){P3}
\tkzDefPoint(0,4){P4}
\tkzDefPoint(1,1){Q1}
\tkzDefPoint(3,1){Q2}
\tkzDefPoint(3,3){Q3}
\tkzDefPoint(1,3){Q4}
\tkzDrawPolygon(P1,P2,P3,P4)
\begin{scope}
\tkzClipPolygon[out](Q1,Q2,Q3,Q4)
\tkzFillPolygon[teal!20](P1,P2,P3,P4)
\end{scope}
\tkzDrawPolygon(Q1,Q2,Q3,Q4)
\end{tikzpicture}
30.1.3 Example: use of Clip for Sangaku in a square

Compiled output

\begin{tikzpicture}[scale=.75]
\tkzDefPoint(0,0){A} \tkzDefPoint(8,0){B}
\tkzDefSquare(A,B) \tkzGetPoints{C}{D}
\tkzDefPoint(4,8){F}
\tkzDefTriangle[equilateral](C,D)
\tkzGetPoint{I}
\tkzDefPointBy[projection=onto B--C](I)
\tkzGetPoint{J}
\tkzInterLL(D,B)(I,J) \tkzGetPoint{K}
\tkzDefPointBy[symmetry=center K](B)
\tkzGetPoint{M}
\tkzClipPolygon(B,C,D,A)
\tkzFillPolygon[color = orange](A,B,C,D)
\tkzFillCircle[color = yellow](M,I)
\tkzFillCircle[color = blue!50!black](F,D)
\end{tikzpicture}
30.2 Clipping a disc

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

    • argumentsexampleexplanation
    (⟨A,B⟩)(⟨A,B⟩)AB radius
    optionsdefaultdefinition
    outclips the outside of the object

    You don’t need to write radius, because it is the default option.

30.2.1 Simple clip

Compiled output

\begin{tikzpicture}[scale=.5]
\tkzDefPoint(0,0){A} \tkzDefPoint(2,2){O}
\tkzDefPoint(4,4){B} \tkzDefPoint(5,5){C}
\tkzDrawPoints(O,A,B,C)
\tkzLabelPoints(O,A,B,C)
\tkzDrawCircle(O,A)
\tkzClipCircle(O,A)
\tkzDrawLine(A,C)
\tkzDrawCircle[fill=teal!10,opacity=.5](C,O)
\end{tikzpicture}
30.3 Clip out

Compiled output

\begin{tikzpicture}
\tkzInit[xmin=-3,ymin=-2,xmax=4,ymax=3]
\tkzDefPoint(0,0){O}
\tkzDefPoint(-4,-2){A}
\tkzDefPoint(3,1){B}
\tkzDefCircle[R](O,2) \tkzGetPoint{o}
\tkzDrawPoints(A,B) % to have a good bounding box
\begin{scope}
\tkzClipCircle[out](O,o)
\tkzDrawLines(A,B)
\end{scope}
\end{tikzpicture}
30.4 Intersection of disks

Compiled output

\begin{tikzpicture}
\tkzDefPoints{0/0/O,4/0/A,0/4/B}
\tkzDrawPolygon[fill=teal](O,A,B)
\tkzClipPolygon(O,A,B)
\tkzClipCircle(A,O)
\tkzClipCircle(B,O)
\tkzFillPolygon[white](O,A,B)
\end{tikzpicture}

See a more complex example of clipping in section 51.6.

30.5 Clipping a sector


☞ 💣 Note that the arguments depend on the options.

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

    • optionsdefaultdefinition
    towardstowards\(O\) is the center and the sector starts from \(A\) to \((OB)\)
    rotatetowardsThe sector starts from \(A\) and the angle determines its amplitude.
    RtowardsWe give the radius and two angles

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

    optionsargumentsexample
    towards(⟨pt,pt⟩)(⟨pt⟩)\tkzClipSector(O,A)(B)
    rotate(⟨pt,pt⟩)(⟨angle⟩)\tkzClipSector[rotate](O,A)(90)
    R(⟨pt,\(r\)⟩)(⟨angle 1,angle 2⟩)\tkzClipSector[R](O,2)(30,90)
30.5.1 Clipping a sector: first example

Compiled output

\begin{tikzpicture}[scale=0.5]
\tkzDefPoint(0,0){a}
\tkzDefPoint(12,0){b}
\tkzDefPoint(4,10){c}
\tkzInterCC[R](a,6)(b,8)
\tkzGetFirstPoint{AB1} \tkzGetSecondPoint{AB2}
\tkzInterCC[R](a,6)(c,6)
\tkzGetFirstPoint{AC1} \tkzGetSecondPoint{AC2}
\tkzInterCC[R](b,8)(c,6)
\tkzGetFirstPoint{BC1} \tkzGetSecondPoint{BC2}
\tkzDrawArc(a,AB2)(AB1)
\tkzDrawArc(b,AB1)(AB2)
\tkzDrawArc(a,AC2)(AC1)
\tkzDrawArc(c,AC1)(AC2)
\tkzDrawArc(b,BC2)(BC1)
\tkzDrawArc(c,BC1)(BC2)
\begin{scope}
\tkzClipSector(b,BC2)(BC1)
\tkzFillSector[teal!40!white](c,BC1)(BC2)
\end{scope}
\begin{scope}
\tkzClipSector(a,AB2)(AB1)
\tkzFillSector[teal!40!white](b,AB1)(AB2)
\end{scope}
\begin{scope}
\tkzClipSector(a,AC2)(AC1)
\tkzFillSector[teal!40!white](c,AC1)(AC2)
\end{scope}
\end{tikzpicture}
30.5.2 Clipping a sector: second example

Compiled output

\begin{tikzpicture}[scale=1.5]
\tkzDefPoint(0,0){O}
\tkzDefPoint(2,-1){A}
\tkzDefPoint(1,1){B}
\tkzDrawSector[new,dashed](O,A)(B)
\tkzDrawSector[new](O,B)(A)
\begin{scope}
\tkzClipSector(O,B)(A)
\tkzDefSquare(O,B) \tkzGetPoints{B'}{O'}
\tkzDrawPolygon[color=teal,fill=teal!20](O,B,B',O')
\end{scope}
\tkzDrawPoints(A,B,O)
\end{tikzpicture}
30.6 TikZ options: trim left or trim right

See the pgfmanual.

30.7 TikZ Controls \pgfinterruptboundingbox and \endpgfinterruptboundingbox

This command temporarily interrupts the calculation of the bounding box and starts a new one. See the pgfmanual

30.7.1 Controlling the bounding box

Compiled output

\begin{tikzpicture}
\tkzDefPoint(0,5){A}\tkzDefPoint(5,4){B}
\tkzDefPoint(0,0){C}\tkzDefPoint(5,1){D}
\tkzDrawSegments(A,B C,D A,C)
\pgfinterruptboundingbox
\tkzInterLL(A,B)(C,D)\tkzGetPoint{I}
\endpgfinterruptboundingbox
\tkzClipBB
\tkzDrawCircle(I,B)
\end{tikzpicture}
30.8 Reverse clip: tkzreverseclip

To use this option, a bounding box must be defined.

\tikzset{tkzreverseclip/.style={insert path={
(current bounding box.south west) --(current bounding box.north west)
--(current bounding box.north east) -- (current bounding box.south east)
-- cycle} }}
30.8.1 Example with \tkzClipPolygon[out]

\tkzClipPolygon[out], \tkzClipCircle[out] use this option.

Compiled output

\begin{tikzpicture}[scale=1]
\tkzInit[xmin=-5,xmax=5,ymin=-4,ymax=6]
\tkzClip
\tkzDefPoints{-.5/0/P1,.5/0/P2}
\foreach \i [count=\j from 3] in {2,...,7}{%
\tkzDefShiftPoint[P\i]({45*(\i-1)}:1){P\j}}
\tkzClipPolygon[out](P1,P...,P8)
\tkzCalcLength(P1,P5)\tkzGetLength{r}
\begin{scope}[blend group=screen]
\foreach \i in {1,...,8}{%
\tkzDefCircle[R](P\i,\r) \tkzGetPoint{x}
\tkzFillCircle[color=teal](P\i,x)}
\end{scope}
\end{tikzpicture}