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8 Specifying CoordinatesAcer H6800a (DLP-DLP Beamer (4K UHD (3.840 x 2.160 Pixel) 3.600 Lumen 10.000:1 Kontrast, 3D, Keystone, 1x 10 Watt Lautsprecher, HDMI (HDCP), Audio Anschluss) Home Cinema 4,1 von 5 Sternen 36 €831,51 € 831, 51. Resume templates 1 4 – pages templates for resumes. Clients with a valid support agreement receive all new versions including major and minor releases of codeBeamer on a regular basis, free of charge. On average, there are one major codeBeamer release and 3-4 minor releases per year, introducing new features and usability improvements.
8.1 Coordinates and Coordinate OptionsA coordinate is a position in a picture. TikZ uses a special syntax for specifying coordinates. Coordinates are alwaysput in round brackets. The general syntax is ([<options>]<coordinate specification>).
 It is possible to give options that apply only to a single coordinate, although this makes sense for transformationoptions only. To give transformation options for a single coordinate, give these options at the beginning inbrackets:
SVG-Viewer needed.

begin{tikzpicture}
 draw[style=help lines] (0,0) grid (3,2);
 draw (0,0) -- (1,1);
 draw[red] (0,0) -- ([xshift=3pt] 1,1);
 draw (1,0) -- +(30:2cm);
 draw[red] (1,0) -- +([shift=(135:5pt)] 30:2cm);
end{tikzpicture}
8.2 Simple CoordinatesThe simplest way to specify coordinates is as a comma-separated pair of TEX dimensions as in (1cm,2pt) or(2cm,textheight). As can be seen, different units can be mixed. The coordinate specified in this way means '1cmto the right and 2pt up from the origin of the picture.' You can also write things like (1cm+2pt,2pt) since the calcpackage is used.
Beamer 3 3 4 X 2 X8.3 Polar CoordinatesYou can also specify coordinates in polar coordinates. In this case, you specify an angle and a distance, separated bya colon as in (30:1cm). The angle must always be given in degrees and should be between -360 and720.
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tikz draw (0cm,0cm) -- (30:1cm) -- (60:1cm) -- (90:1cm)
 -- (120:1cm) -- (150:1cm) -- (180:1cm);
 Instead of an angle given as a number you can also use certain words. For example, up is the same as 90, so thatyou can write tikz draw (0,0) -- (2ex,0pt) -- +(up:1ex); and get Cleanmymac 3 3 2. SVG-Viewer needed.
. Apart from up you can use down,left, right, north,

$Beamer 3 3 4 X 2$

south, west, east, north east, north west, south east, south west, all of which have theirnatural meaning. 8.4 Xy- and Xyz-CoordinatesYou can specify coordinates in PGF's xy-coordinate system. In this case, you provide two unit-free numbers,separated by a comma as in (2,-3). This means 'add twice the current PGFx-vector and subtract three times they-vector.' By default, the x-vector points 1cm to the right, the y-vector points 1cm upwards, but this can bechanged arbitrarily using the x and y graphic options.
 Similarly, you can specify coordinates in the xyz-coordinate system. The only difference to the xy-coordinates isthat you specify three numbers separated by commas as in (1,2,3). This is interpreted as 'once the x-vector plustwice the y-vector plus three times the z-vector.' The default z-vector points to -cm,-cm. Consider thefollowing example:
SVG-Viewer needed.

begin{tikzpicture}[->]
 draw (0,0,0) -- (1,0,0);
 draw (0,0,0) -- (0,1,0);
 draw (0,0,0) -- (0,0,1);
end{tikzpicture}
8.5 Node CoordinatesIn PGF and in TikZ it is quite easy to define a node that you wish to reference at a later point. Once you havedefined a node, there are different ways of referencing points of the node.
8.5.1 Named Anchor CoordinatesAn anchor coordinate is a point in a node that you have previously defined using the node operation.The syntax is (<node name>.<anchor>), where <node name> is the name that was previously usedto name the node using the name=<node name> option or the special node name syntax. Here is anexample:
SVG-Viewer needed.

begin{tikzpicture}
 node (shape) at (0,2) [draw] {|class Shape|};
 node (rect) at (-2,0) [draw] {|class Rectangle|};
 node (circle) at (2,0) [draw] {|class Circle|};
 node (ellipse) at (6,0) [draw] {|class Ellipse|};
 draw (circle.north) |- (0,1);
 draw (ellipse.north) |- (0,1);
 draw[-open triangle 90] (rect.north) |- (0,1) -| (shape.south);
end{tikzpicture}
 Section 11.8 explain which anchors are available for the basic shapes.
8.5.2 Angle Anchor CoordinatesIn addition to the named anchors, it is possible to use the syntax <node name>.<angle> to name a point of thenode's border. This point is the coordinate where a ray shot from the center in the given angle hits the border. Hereis an example: 
SVG-Viewer needed.

begin{tikzpicture}
 node (start) [draw,shape=ellipse] {start};
 foreach angle in {-90, -80, .., 90}
 draw (start.angle) . controls +(angle:1cm) and +(-1,0) . (2.5,0);
 end{tikzpicture}
8.5.3 Anchor-Free Node CoordinatesIt is also possible to just 'leave out' the anchor and have TikZ calculate an appropriate border position for you.Here is an example:
SVG-Viewer needed.

begin{tikzpicture}[fill=blue!20]
 draw[style=help lines] (-1,-2) grid (6,3);
 path (0,0) node(a) [ellipse,rotate=10,draw,fill] {An ellipse}
 (3,-1) node(b) [circle,draw,fill] {A circle}
 (2,2) node(c) [rectangle,rotate=20,draw,fill] {A rectangle}
 (5,2) node(d) [rectangle,rotate=-30,draw,fill] {Another rectangle};
 draw[thick] (a) -- (b) -- (c) -- (d);
 draw[thick,red,->] (a) |- +(1,3) -| (c) |- (b);
 draw[thick,blue,<->] (b) . controls +(right:2cm) and +(down:1cm) . (d);
end{tikzpicture}
 TikZ will be reasonably clever at determining the border points that you 'mean,' but, naturally, this may failin some situations. If TikZ fails to determine an appropriate border point, the center will be usedinstead.
 Automatic computation of anchors works only with the line-to operations --, the vertical/horizontalversions |- and -|, and with the curve-to operation .. For other path commands, such as parabolaor plot, the center will be used. If this is not desired, you should give a named anchor or an angleanchor.
 Note that if you use an automatic coordinate for both the start and the end of a line-to, as in --(b)--, then twoborder coordinates are computed with a move-to between them. This is usually exactly what youwant.
 If you use relative coordinates together with automatic anchor coordinates, the relative coordinates are alwayscomputed relative to the node's center, not relative to the border point. Here is an example:
SVG-Viewer needed.

tikz draw (0,0) node(x) [draw] {Text}
 rectangle (1,1)
 (x) -- +(1,1);
 Similarly, in the following examples both control points are (1,1): 
SVG-Viewer needed.

tikz draw (0,0) node(x) [draw] {X}
 (2,0) node(y) {Y}
 (x) . controls +(1,1) and +(-1,1) . (y);
8.6 Intersection Coordinates8.6.1 Intersection of Two LinesOften you wish to specify a point that is on the intersection of two lines. The first way to specify such anintersection is the following: You can use the special syntax (intersection of<p1>--<p2> and<q1>--<q2>). Thiswill yield the intersection point of the line going through p1 and p2 and the line through q1 and q2. If the lines donot meet or if they are identical and arithmetical overflow error will result.

south, west, east, north east, north west, south east, south west, all of which have theirnatural meaning. 8.4 Xy- and Xyz-CoordinatesYou can specify coordinates in PGF's xy-coordinate system. In this case, you provide two unit-free numbers,separated by a comma as in (2,-3). This means 'add twice the current PGFx-vector and subtract three times they-vector.' By default, the x-vector points 1cm to the right, the y-vector points 1cm upwards, but this can bechanged arbitrarily using the x and y graphic options.
 Similarly, you can specify coordinates in the xyz-coordinate system. The only difference to the xy-coordinates isthat you specify three numbers separated by commas as in (1,2,3). This is interpreted as 'once the x-vector plustwice the y-vector plus three times the z-vector.' The default z-vector points to -cm,-cm. Consider thefollowing example:
SVG-Viewer needed.

begin{tikzpicture}[->]
 draw (0,0,0) -- (1,0,0);
 draw (0,0,0) -- (0,1,0);
 draw (0,0,0) -- (0,0,1);
end{tikzpicture}
8.5 Node CoordinatesIn PGF and in TikZ it is quite easy to define a node that you wish to reference at a later point. Once you havedefined a node, there are different ways of referencing points of the node.
8.5.1 Named Anchor CoordinatesAn anchor coordinate is a point in a node that you have previously defined using the node operation.The syntax is (<node name>.<anchor>), where <node name> is the name that was previously usedto name the node using the name=<node name> option or the special node name syntax. Here is anexample:
SVG-Viewer needed.

begin{tikzpicture}
 node (shape) at (0,2) [draw] {|class Shape|};
 node (rect) at (-2,0) [draw] {|class Rectangle|};
 node (circle) at (2,0) [draw] {|class Circle|};
 node (ellipse) at (6,0) [draw] {|class Ellipse|};
 draw (circle.north) |- (0,1);
 draw (ellipse.north) |- (0,1);
 draw[-open triangle 90] (rect.north) |- (0,1) -| (shape.south);
end{tikzpicture}
 Section 11.8 explain which anchors are available for the basic shapes.
8.5.2 Angle Anchor CoordinatesIn addition to the named anchors, it is possible to use the syntax <node name>.<angle> to name a point of thenode's border. This point is the coordinate where a ray shot from the center in the given angle hits the border. Hereis an example: 
SVG-Viewer needed.

begin{tikzpicture}
 node (start) [draw,shape=ellipse] {start};
 foreach angle in {-90, -80, .., 90}
 draw (start.angle) . controls +(angle:1cm) and +(-1,0) . (2.5,0);
 end{tikzpicture}
8.5.3 Anchor-Free Node CoordinatesIt is also possible to just 'leave out' the anchor and have TikZ calculate an appropriate border position for you.Here is an example:
SVG-Viewer needed.

begin{tikzpicture}[fill=blue!20]
 draw[style=help lines] (-1,-2) grid (6,3);
 path (0,0) node(a) [ellipse,rotate=10,draw,fill] {An ellipse}
 (3,-1) node(b) [circle,draw,fill] {A circle}
 (2,2) node(c) [rectangle,rotate=20,draw,fill] {A rectangle}
 (5,2) node(d) [rectangle,rotate=-30,draw,fill] {Another rectangle};
 draw[thick] (a) -- (b) -- (c) -- (d);
 draw[thick,red,->] (a) |- +(1,3) -| (c) |- (b);
 draw[thick,blue,<->] (b) . controls +(right:2cm) and +(down:1cm) . (d);
end{tikzpicture}
 TikZ will be reasonably clever at determining the border points that you 'mean,' but, naturally, this may failin some situations. If TikZ fails to determine an appropriate border point, the center will be usedinstead.
 Automatic computation of anchors works only with the line-to operations --, the vertical/horizontalversions |- and -|, and with the curve-to operation .. For other path commands, such as parabolaor plot, the center will be used. If this is not desired, you should give a named anchor or an angleanchor.
 Note that if you use an automatic coordinate for both the start and the end of a line-to, as in --(b)--, then twoborder coordinates are computed with a move-to between them. This is usually exactly what youwant.
 If you use relative coordinates together with automatic anchor coordinates, the relative coordinates are alwayscomputed relative to the node's center, not relative to the border point. Here is an example:
SVG-Viewer needed.

tikz draw (0,0) node(x) [draw] {Text}
 rectangle (1,1)
 (x) -- +(1,1);
 Similarly, in the following examples both control points are (1,1): 
SVG-Viewer needed.

tikz draw (0,0) node(x) [draw] {X}
 (2,0) node(y) {Y}
 (x) . controls +(1,1) and +(-1,1) . (y);
8.6 Intersection Coordinates8.6.1 Intersection of Two LinesOften you wish to specify a point that is on the intersection of two lines. The first way to specify such anintersection is the following: You can use the special syntax (intersection of<p1>--<p2> and<q1>--<q2>). Thiswill yield the intersection point of the line going through p1 and p2 and the line through q1 and q2. If the lines donot meet or if they are identical and arithmetical overflow error will result.
SVG-Viewer needed.

begin{tikzpicture}
 draw[help lines] (0,0) grid (3,2);
 draw (0,0) coordinate (A) -- (3,2) coordinate (B)
 (1,2) -- (3,0);
 fill[red] (intersection of A--B and 1,2--3,0) circle (2pt);
end{tikzpicture}
8.6.2 Intersection of Horizontal and Vertical LinesA frequent special case of intersections is the intersection of a vertical line going through a point p and a horizontalline going through some other point q. For this situation there is a special, shorter, syntax: You can say either(<p> |-<q>) or (<q> -|<p>).
 For example, (2,1 |- 3,4) and (3,4 -| 2,1) both yield the same as (2,4) (provided the xy-coordinatesystem has not been modified).
 The most useful application of the syntax is to draw a line up to some point on a vertical or horizontal line. Hereis an example:
SVG-Viewer needed.

begin{tikzpicture}
 path (30:1cm) node(p1) {$p_1$} (75:1cm) node(p2) {$p_2$};
 draw (-0.2,0) -- (1.2,0) node(xline)[right] {$q_1$};
 draw (2,-0.2) -- (2,1.2) node(yline)[above] {$q_2$};
 draw[->] (p1) -- (p1 |- xline);
 draw[->] (p2) -- (p2 |- xline);
 draw[->] (p1) -- (p1 -| yline);
 draw[->] (p2) -- (p2 -| yline);
end{tikzpicture}
8.7 Relative and Incremental CoordinatesYou can prefix coordinates by ++ to make them 'relative.' A coordinate such as ++(1cm,0pt) means '1cm to theright of the previous position.' Relative coordinates are often useful in 'local' contexts:
SVG-Viewer needed.

begin{tikzpicture}
 draw (0,0) -- ++(1,0) -- ++(0,1) -- ++(-1,0) -- cycle;
 draw (2,0) -- ++(1,0) -- ++(0,1) -- ++(-1,0) -- cycle;
 draw (1.5,1.5) -- ++(1,0) -- ++(0,1) -- ++(-1,0) -- cycle;
end{tikzpicture}
 Instead of ++ you can also use a single +. This also specifies a relative coordinate, but it does not 'update' thecurrent point for subsequent usages of relative coordinates. Thus, you can use this notation to specify numerouspoints, all relative to the same 'initial' point:
Beamer 3 3 4 X 2 FreeSVG-Viewer needed.

begin{tikzpicture}
 draw (0,0) -- +(1,0) -- +(1,1) -- +(0,1) -- cycle;
 draw (2,0) -- +(1,0) -- +(1,1) -- +(0,1) -- cycle;
 draw (1.5,1.5) -- +(1,0) -- +(1,1) -- +(0,1) -- cycle;
end{tikzpicture}
 There is one special situation, where relative coordinates are interpreted differently. If you use a relativecoordinate as a control point of a Bézier curve, the following rule applies: First, a relative first control point istaken relative to the beginning of the curve. Second, a relative second control point is taken relativeto the end of the curve. Third, a relative end point of a curve is taken relative to the start of thecurve.
 This special behavior makes it easy to specify that a curve should 'leave or arrives from a certaindirection' at the start or end. In the following example, the curve 'leaves' at 30o and 'arrives' at60o:
SVG-Viewer needed.

begin{tikzpicture}
 draw (1,0) . controls +(30:1cm) and +(60:1cm) . (3,-1);
 draw[gray,->] (1,0) -- +(30:1cm);
 draw[gray,<-] (3,-1) -- +(60:1cm);
end{tikzpicture}
A formula is made up by combining various constructs. Some of them are explained below:
1. Arithmetic Operations:
Arithmetic equations are typed with a dollar sign. For example, $a + b$, $a - b$, $-a$, $a / b$, $a b$. There are different forms for multiplication and division that are $a cdot b$, $a times b$, $a div b$.
Fractions are typed with the frac command by putting the denominator and numerator with separate curly brackets.
The display style fraction inline command dfrac can be used with the tfrac environment for basically matrices so that the entries look small.
For subscripts and superscripts, we use ‘_' and ‘^' respectively. For example, a_{1}, a_{i_{1}}, a^{2}, a^{b^{c}} will yield the result.
There is one symbol that can be automatically superscripted that is, '. For example, $f'(x)$ will yield and to get we input $f^{prime 2}$.
For indicating dualspace, use the command ${}^{dagger}$ where the {} means empty group.
The commands sb and sp are used for subscripts and superscripts respectively.
2. Binomial Coefficients:
Binomial coefficients are written with command binom by putting the expression between curly brackets.
We can use the display style inline command dbinom by using the tbinom environment.
Beamer 3 3 4 X 243. Ellipses:
There are two ellipses low or on the line ellipses and centered ellipses.
The low or on the line ellipses are types as F(x_{1}, x_{2}, dots, x_{n}) and the centered ellipses are typed as x_{1} + x_{2} + dots + x_{n}.
LaTeX gives ldots command to distinguish between low and bdots for centered ellipses.
The other variants for dots command are dotsc for an ellipse followed by comma, dotsb for an ellipse followed by a binary operation, dotsm if followed by multiplication, dotsi for an ellipse with integral and dotso for an 'other' ellipse.
Beamer 3 3 4 X 204. Integral:
In an integral math equation in LaTeX, the lower limit is taken as a subscript and the upper limit is taken as a superscript. For example, the code $intlimits_{-infty}^{infty} e^{-x^{2}} , dx = sqrt{pi}$ yields.
The commands oint, iint, iiint and idotsint yield and respectively.
For complicated bounds, we use substack command or the subarray environment.
5. Roots:
The command sqrt produces the square root. For example, $sqrt{5}$ and $sqrt{a + 2b + c^{2}}$ gives and respectively.
Can be typed using the expression $sqrt[g]{5}$ and the position of ‘g' can be adjusted by providing the additional commands: leftroot moves ‘g' left or right with negative argument and uproot moves ‘g' up or down with negative attribute.