How does TikZ render an arc?












4















With the sample MWE below, TikZ generates the following diagram:



1. Drawing an arc



documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
coordinate[label=below:$a$] (a) at (0,0);

draw (a) arc(0:180:2);
end{tikzpicture}
end{document}


enter image description here



2. Drawing a circle



documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
coordinate[label=below:$a$] (a) at (0,0);
coordinate[label=below:$b$] (b) at (5,5);

draw (a) arc(0:180:2);
draw (b) circle [radius=2cm];
end{tikzpicture}
end{document}


enter image description here



With draw <coordinate> circle command, TikZ draws a circle, with the <coordinate> at its center.



With draw <coordinate> arc command, TikZ draws an arc, with the <coordinate> as one of its endpoints.



I wish to understand, why this difference of behavior and how is TikZ drawing the arc with draw (a) arc(0:180:2);.



Why does TikZ does not use (a) as its center point while drawing an arc similar to drawing a circle.



How does TikZ actually draw the arc with point a.



What is the reference and center point, when TikZ draws an arc.










share|improve this question























  • May I draw your attention to this question? IMHO the question "Why does TikZ does not use (a) as its center point while drawing an arc similar to drawing a circle?" is not really answerable, and there are more than enough answers that show you how you can get whatever behavior you want.

    – marmot
    2 hours ago








  • 1





    The mathematical geometry of an arc and a circle? Judging from the question you seem to understand it very well. (Internally TikZ approximates them with Bezier curves, if that's your question.)

    – marmot
    2 hours ago






  • 1





    What is the geometry here? It is just simply the beginning angle and the ending angle.

    – JouleV
    2 hours ago






  • 1





    The logic is very simple: consider draw (x,y) arc(alpha:beta:r); Now draw a circle of radius r such that (x,y) is at the position specified by the angle alpha, Now TikZ draws an arc from that point to the point with angle beta along that circle.

    – marmot
    2 hours ago






  • 1





    @marmot Yes, but I have to "update" myself right now

    – JouleV
    1 hour ago
















4















With the sample MWE below, TikZ generates the following diagram:



1. Drawing an arc



documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
coordinate[label=below:$a$] (a) at (0,0);

draw (a) arc(0:180:2);
end{tikzpicture}
end{document}


enter image description here



2. Drawing a circle



documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
coordinate[label=below:$a$] (a) at (0,0);
coordinate[label=below:$b$] (b) at (5,5);

draw (a) arc(0:180:2);
draw (b) circle [radius=2cm];
end{tikzpicture}
end{document}


enter image description here



With draw <coordinate> circle command, TikZ draws a circle, with the <coordinate> at its center.



With draw <coordinate> arc command, TikZ draws an arc, with the <coordinate> as one of its endpoints.



I wish to understand, why this difference of behavior and how is TikZ drawing the arc with draw (a) arc(0:180:2);.



Why does TikZ does not use (a) as its center point while drawing an arc similar to drawing a circle.



How does TikZ actually draw the arc with point a.



What is the reference and center point, when TikZ draws an arc.










share|improve this question























  • May I draw your attention to this question? IMHO the question "Why does TikZ does not use (a) as its center point while drawing an arc similar to drawing a circle?" is not really answerable, and there are more than enough answers that show you how you can get whatever behavior you want.

    – marmot
    2 hours ago








  • 1





    The mathematical geometry of an arc and a circle? Judging from the question you seem to understand it very well. (Internally TikZ approximates them with Bezier curves, if that's your question.)

    – marmot
    2 hours ago






  • 1





    What is the geometry here? It is just simply the beginning angle and the ending angle.

    – JouleV
    2 hours ago






  • 1





    The logic is very simple: consider draw (x,y) arc(alpha:beta:r); Now draw a circle of radius r such that (x,y) is at the position specified by the angle alpha, Now TikZ draws an arc from that point to the point with angle beta along that circle.

    – marmot
    2 hours ago






  • 1





    @marmot Yes, but I have to "update" myself right now

    – JouleV
    1 hour ago














4












4








4


1






With the sample MWE below, TikZ generates the following diagram:



1. Drawing an arc



documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
coordinate[label=below:$a$] (a) at (0,0);

draw (a) arc(0:180:2);
end{tikzpicture}
end{document}


enter image description here



2. Drawing a circle



documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
coordinate[label=below:$a$] (a) at (0,0);
coordinate[label=below:$b$] (b) at (5,5);

draw (a) arc(0:180:2);
draw (b) circle [radius=2cm];
end{tikzpicture}
end{document}


enter image description here



With draw <coordinate> circle command, TikZ draws a circle, with the <coordinate> at its center.



With draw <coordinate> arc command, TikZ draws an arc, with the <coordinate> as one of its endpoints.



I wish to understand, why this difference of behavior and how is TikZ drawing the arc with draw (a) arc(0:180:2);.



Why does TikZ does not use (a) as its center point while drawing an arc similar to drawing a circle.



How does TikZ actually draw the arc with point a.



What is the reference and center point, when TikZ draws an arc.










share|improve this question














With the sample MWE below, TikZ generates the following diagram:



1. Drawing an arc



documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
coordinate[label=below:$a$] (a) at (0,0);

draw (a) arc(0:180:2);
end{tikzpicture}
end{document}


enter image description here



2. Drawing a circle



documentclass{article}
usepackage{tikz}
begin{document}
begin{tikzpicture}
coordinate[label=below:$a$] (a) at (0,0);
coordinate[label=below:$b$] (b) at (5,5);

draw (a) arc(0:180:2);
draw (b) circle [radius=2cm];
end{tikzpicture}
end{document}


enter image description here



With draw <coordinate> circle command, TikZ draws a circle, with the <coordinate> at its center.



With draw <coordinate> arc command, TikZ draws an arc, with the <coordinate> as one of its endpoints.



I wish to understand, why this difference of behavior and how is TikZ drawing the arc with draw (a) arc(0:180:2);.



Why does TikZ does not use (a) as its center point while drawing an arc similar to drawing a circle.



How does TikZ actually draw the arc with point a.



What is the reference and center point, when TikZ draws an arc.







tikz-pgf






share|improve this question













share|improve this question











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share|improve this question










asked 2 hours ago









subham sonisubham soni

5,05983189




5,05983189













  • May I draw your attention to this question? IMHO the question "Why does TikZ does not use (a) as its center point while drawing an arc similar to drawing a circle?" is not really answerable, and there are more than enough answers that show you how you can get whatever behavior you want.

    – marmot
    2 hours ago








  • 1





    The mathematical geometry of an arc and a circle? Judging from the question you seem to understand it very well. (Internally TikZ approximates them with Bezier curves, if that's your question.)

    – marmot
    2 hours ago






  • 1





    What is the geometry here? It is just simply the beginning angle and the ending angle.

    – JouleV
    2 hours ago






  • 1





    The logic is very simple: consider draw (x,y) arc(alpha:beta:r); Now draw a circle of radius r such that (x,y) is at the position specified by the angle alpha, Now TikZ draws an arc from that point to the point with angle beta along that circle.

    – marmot
    2 hours ago






  • 1





    @marmot Yes, but I have to "update" myself right now

    – JouleV
    1 hour ago



















  • May I draw your attention to this question? IMHO the question "Why does TikZ does not use (a) as its center point while drawing an arc similar to drawing a circle?" is not really answerable, and there are more than enough answers that show you how you can get whatever behavior you want.

    – marmot
    2 hours ago








  • 1





    The mathematical geometry of an arc and a circle? Judging from the question you seem to understand it very well. (Internally TikZ approximates them with Bezier curves, if that's your question.)

    – marmot
    2 hours ago






  • 1





    What is the geometry here? It is just simply the beginning angle and the ending angle.

    – JouleV
    2 hours ago






  • 1





    The logic is very simple: consider draw (x,y) arc(alpha:beta:r); Now draw a circle of radius r such that (x,y) is at the position specified by the angle alpha, Now TikZ draws an arc from that point to the point with angle beta along that circle.

    – marmot
    2 hours ago






  • 1





    @marmot Yes, but I have to "update" myself right now

    – JouleV
    1 hour ago

















May I draw your attention to this question? IMHO the question "Why does TikZ does not use (a) as its center point while drawing an arc similar to drawing a circle?" is not really answerable, and there are more than enough answers that show you how you can get whatever behavior you want.

– marmot
2 hours ago







May I draw your attention to this question? IMHO the question "Why does TikZ does not use (a) as its center point while drawing an arc similar to drawing a circle?" is not really answerable, and there are more than enough answers that show you how you can get whatever behavior you want.

– marmot
2 hours ago






1




1





The mathematical geometry of an arc and a circle? Judging from the question you seem to understand it very well. (Internally TikZ approximates them with Bezier curves, if that's your question.)

– marmot
2 hours ago





The mathematical geometry of an arc and a circle? Judging from the question you seem to understand it very well. (Internally TikZ approximates them with Bezier curves, if that's your question.)

– marmot
2 hours ago




1




1





What is the geometry here? It is just simply the beginning angle and the ending angle.

– JouleV
2 hours ago





What is the geometry here? It is just simply the beginning angle and the ending angle.

– JouleV
2 hours ago




1




1





The logic is very simple: consider draw (x,y) arc(alpha:beta:r); Now draw a circle of radius r such that (x,y) is at the position specified by the angle alpha, Now TikZ draws an arc from that point to the point with angle beta along that circle.

– marmot
2 hours ago





The logic is very simple: consider draw (x,y) arc(alpha:beta:r); Now draw a circle of radius r such that (x,y) is at the position specified by the angle alpha, Now TikZ draws an arc from that point to the point with angle beta along that circle.

– marmot
2 hours ago




1




1





@marmot Yes, but I have to "update" myself right now

– JouleV
1 hour ago





@marmot Yes, but I have to "update" myself right now

– JouleV
1 hour ago










2 Answers
2






active

oldest

votes


















5














Here is an attempt to use attempt to explain step by step what's going on. I use the non-deprecated syntax, as suggested by Joule V.



documentclass{beamer}
usepackage{tikz}
usetikzlibrary{overlay-beamer-styles}
begin{document}
begin{frame}[t]
frametitle{The arc construction}
textbackslashtexttt{draw (P) arc[start angle=$alpha$,end
angle=$beta$,radius=$r$];}

centering
begin{tikzpicture}
node[circle,fill,inner sep=1pt,label=right:{$P=(x,y)$}] (P){};
draw[dashed,visible on=<2-4>] (P) ++ (210:2) coordinate (O) circle[radius=2cm];
draw[visible on=<2>] (O) + (1,0) arc[start angle=00,end angle=30,radius=1cm]
node[midway,right] {$alpha$};
draw[visible on=<2>] (P) -- (O) -- ++(2,0) node[midway,below]{$r$};
draw[visible on=<3>,thick] (P) arc[start angle=30,end angle=135,radius=2cm]
coordinate (Q);
draw[visible on=<3>] (O) + (1,0) arc[start angle=00,end angle=135,radius=1cm]
node[midway,below] {$beta$} (Q) -- (O) -- ++(2,0) ;
path (O) -- ++ (0,2.5); % only for the bounding box
end{tikzpicture}
begin{itemize}
item<+-> Consider a point $P=(x,y)$.
item<+-> Imagine now a circle of radius $r$ for which $P$ sits at the angle
$alpha$.
item<+-> The arc runs along this circle between the angles $alpha$ and
$beta$;
end{itemize}
end{frame}
end{document}


enter image description here






share|improve this answer


























  • +1, very clear!

    – CarLaTeX
    1 hour ago



















3














Short answer: arc has nothing to do with circle. circle is drawn with four curves, arc is drawn with one curve, that is all.



Let's start with tikz.code.tex. In lines 3673–3706, there is the definition of tikz@do@arc, based on pgfpatharc, which is defined in pgfcorepathconstruct.code.tex. Circles and ellipses are defined in the same way.



In pgfcorepathconstruct.code.tex, pgfpatharc is defined as a curve with a starting point and an ending point, based on pgf@nlt@curveto (line 401).



Meanwhile, you can see that any kind of curves, even circles, are defined based on pgf@nlt@curveto. Circles and ellipses is defined in pgfpathellipse as a set of four connected curves: line 926, line 947, line 968, and line 989 — each of these curves has its own pgf@nlt@curveto.



That is why the arc does not take its coordinate as the center, but a starting point.






share|improve this answer
























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    2 Answers
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    active

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    2 Answers
    2






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    5














    Here is an attempt to use attempt to explain step by step what's going on. I use the non-deprecated syntax, as suggested by Joule V.



    documentclass{beamer}
    usepackage{tikz}
    usetikzlibrary{overlay-beamer-styles}
    begin{document}
    begin{frame}[t]
    frametitle{The arc construction}
    textbackslashtexttt{draw (P) arc[start angle=$alpha$,end
    angle=$beta$,radius=$r$];}

    centering
    begin{tikzpicture}
    node[circle,fill,inner sep=1pt,label=right:{$P=(x,y)$}] (P){};
    draw[dashed,visible on=<2-4>] (P) ++ (210:2) coordinate (O) circle[radius=2cm];
    draw[visible on=<2>] (O) + (1,0) arc[start angle=00,end angle=30,radius=1cm]
    node[midway,right] {$alpha$};
    draw[visible on=<2>] (P) -- (O) -- ++(2,0) node[midway,below]{$r$};
    draw[visible on=<3>,thick] (P) arc[start angle=30,end angle=135,radius=2cm]
    coordinate (Q);
    draw[visible on=<3>] (O) + (1,0) arc[start angle=00,end angle=135,radius=1cm]
    node[midway,below] {$beta$} (Q) -- (O) -- ++(2,0) ;
    path (O) -- ++ (0,2.5); % only for the bounding box
    end{tikzpicture}
    begin{itemize}
    item<+-> Consider a point $P=(x,y)$.
    item<+-> Imagine now a circle of radius $r$ for which $P$ sits at the angle
    $alpha$.
    item<+-> The arc runs along this circle between the angles $alpha$ and
    $beta$;
    end{itemize}
    end{frame}
    end{document}


    enter image description here






    share|improve this answer


























    • +1, very clear!

      – CarLaTeX
      1 hour ago
















    5














    Here is an attempt to use attempt to explain step by step what's going on. I use the non-deprecated syntax, as suggested by Joule V.



    documentclass{beamer}
    usepackage{tikz}
    usetikzlibrary{overlay-beamer-styles}
    begin{document}
    begin{frame}[t]
    frametitle{The arc construction}
    textbackslashtexttt{draw (P) arc[start angle=$alpha$,end
    angle=$beta$,radius=$r$];}

    centering
    begin{tikzpicture}
    node[circle,fill,inner sep=1pt,label=right:{$P=(x,y)$}] (P){};
    draw[dashed,visible on=<2-4>] (P) ++ (210:2) coordinate (O) circle[radius=2cm];
    draw[visible on=<2>] (O) + (1,0) arc[start angle=00,end angle=30,radius=1cm]
    node[midway,right] {$alpha$};
    draw[visible on=<2>] (P) -- (O) -- ++(2,0) node[midway,below]{$r$};
    draw[visible on=<3>,thick] (P) arc[start angle=30,end angle=135,radius=2cm]
    coordinate (Q);
    draw[visible on=<3>] (O) + (1,0) arc[start angle=00,end angle=135,radius=1cm]
    node[midway,below] {$beta$} (Q) -- (O) -- ++(2,0) ;
    path (O) -- ++ (0,2.5); % only for the bounding box
    end{tikzpicture}
    begin{itemize}
    item<+-> Consider a point $P=(x,y)$.
    item<+-> Imagine now a circle of radius $r$ for which $P$ sits at the angle
    $alpha$.
    item<+-> The arc runs along this circle between the angles $alpha$ and
    $beta$;
    end{itemize}
    end{frame}
    end{document}


    enter image description here






    share|improve this answer


























    • +1, very clear!

      – CarLaTeX
      1 hour ago














    5












    5








    5







    Here is an attempt to use attempt to explain step by step what's going on. I use the non-deprecated syntax, as suggested by Joule V.



    documentclass{beamer}
    usepackage{tikz}
    usetikzlibrary{overlay-beamer-styles}
    begin{document}
    begin{frame}[t]
    frametitle{The arc construction}
    textbackslashtexttt{draw (P) arc[start angle=$alpha$,end
    angle=$beta$,radius=$r$];}

    centering
    begin{tikzpicture}
    node[circle,fill,inner sep=1pt,label=right:{$P=(x,y)$}] (P){};
    draw[dashed,visible on=<2-4>] (P) ++ (210:2) coordinate (O) circle[radius=2cm];
    draw[visible on=<2>] (O) + (1,0) arc[start angle=00,end angle=30,radius=1cm]
    node[midway,right] {$alpha$};
    draw[visible on=<2>] (P) -- (O) -- ++(2,0) node[midway,below]{$r$};
    draw[visible on=<3>,thick] (P) arc[start angle=30,end angle=135,radius=2cm]
    coordinate (Q);
    draw[visible on=<3>] (O) + (1,0) arc[start angle=00,end angle=135,radius=1cm]
    node[midway,below] {$beta$} (Q) -- (O) -- ++(2,0) ;
    path (O) -- ++ (0,2.5); % only for the bounding box
    end{tikzpicture}
    begin{itemize}
    item<+-> Consider a point $P=(x,y)$.
    item<+-> Imagine now a circle of radius $r$ for which $P$ sits at the angle
    $alpha$.
    item<+-> The arc runs along this circle between the angles $alpha$ and
    $beta$;
    end{itemize}
    end{frame}
    end{document}


    enter image description here






    share|improve this answer















    Here is an attempt to use attempt to explain step by step what's going on. I use the non-deprecated syntax, as suggested by Joule V.



    documentclass{beamer}
    usepackage{tikz}
    usetikzlibrary{overlay-beamer-styles}
    begin{document}
    begin{frame}[t]
    frametitle{The arc construction}
    textbackslashtexttt{draw (P) arc[start angle=$alpha$,end
    angle=$beta$,radius=$r$];}

    centering
    begin{tikzpicture}
    node[circle,fill,inner sep=1pt,label=right:{$P=(x,y)$}] (P){};
    draw[dashed,visible on=<2-4>] (P) ++ (210:2) coordinate (O) circle[radius=2cm];
    draw[visible on=<2>] (O) + (1,0) arc[start angle=00,end angle=30,radius=1cm]
    node[midway,right] {$alpha$};
    draw[visible on=<2>] (P) -- (O) -- ++(2,0) node[midway,below]{$r$};
    draw[visible on=<3>,thick] (P) arc[start angle=30,end angle=135,radius=2cm]
    coordinate (Q);
    draw[visible on=<3>] (O) + (1,0) arc[start angle=00,end angle=135,radius=1cm]
    node[midway,below] {$beta$} (Q) -- (O) -- ++(2,0) ;
    path (O) -- ++ (0,2.5); % only for the bounding box
    end{tikzpicture}
    begin{itemize}
    item<+-> Consider a point $P=(x,y)$.
    item<+-> Imagine now a circle of radius $r$ for which $P$ sits at the angle
    $alpha$.
    item<+-> The arc runs along this circle between the angles $alpha$ and
    $beta$;
    end{itemize}
    end{frame}
    end{document}


    enter image description here







    share|improve this answer














    share|improve this answer



    share|improve this answer








    edited 1 hour ago

























    answered 1 hour ago









    marmotmarmot

    120k6154290




    120k6154290













    • +1, very clear!

      – CarLaTeX
      1 hour ago



















    • +1, very clear!

      – CarLaTeX
      1 hour ago

















    +1, very clear!

    – CarLaTeX
    1 hour ago





    +1, very clear!

    – CarLaTeX
    1 hour ago











    3














    Short answer: arc has nothing to do with circle. circle is drawn with four curves, arc is drawn with one curve, that is all.



    Let's start with tikz.code.tex. In lines 3673–3706, there is the definition of tikz@do@arc, based on pgfpatharc, which is defined in pgfcorepathconstruct.code.tex. Circles and ellipses are defined in the same way.



    In pgfcorepathconstruct.code.tex, pgfpatharc is defined as a curve with a starting point and an ending point, based on pgf@nlt@curveto (line 401).



    Meanwhile, you can see that any kind of curves, even circles, are defined based on pgf@nlt@curveto. Circles and ellipses is defined in pgfpathellipse as a set of four connected curves: line 926, line 947, line 968, and line 989 — each of these curves has its own pgf@nlt@curveto.



    That is why the arc does not take its coordinate as the center, but a starting point.






    share|improve this answer




























      3














      Short answer: arc has nothing to do with circle. circle is drawn with four curves, arc is drawn with one curve, that is all.



      Let's start with tikz.code.tex. In lines 3673–3706, there is the definition of tikz@do@arc, based on pgfpatharc, which is defined in pgfcorepathconstruct.code.tex. Circles and ellipses are defined in the same way.



      In pgfcorepathconstruct.code.tex, pgfpatharc is defined as a curve with a starting point and an ending point, based on pgf@nlt@curveto (line 401).



      Meanwhile, you can see that any kind of curves, even circles, are defined based on pgf@nlt@curveto. Circles and ellipses is defined in pgfpathellipse as a set of four connected curves: line 926, line 947, line 968, and line 989 — each of these curves has its own pgf@nlt@curveto.



      That is why the arc does not take its coordinate as the center, but a starting point.






      share|improve this answer


























        3












        3








        3







        Short answer: arc has nothing to do with circle. circle is drawn with four curves, arc is drawn with one curve, that is all.



        Let's start with tikz.code.tex. In lines 3673–3706, there is the definition of tikz@do@arc, based on pgfpatharc, which is defined in pgfcorepathconstruct.code.tex. Circles and ellipses are defined in the same way.



        In pgfcorepathconstruct.code.tex, pgfpatharc is defined as a curve with a starting point and an ending point, based on pgf@nlt@curveto (line 401).



        Meanwhile, you can see that any kind of curves, even circles, are defined based on pgf@nlt@curveto. Circles and ellipses is defined in pgfpathellipse as a set of four connected curves: line 926, line 947, line 968, and line 989 — each of these curves has its own pgf@nlt@curveto.



        That is why the arc does not take its coordinate as the center, but a starting point.






        share|improve this answer













        Short answer: arc has nothing to do with circle. circle is drawn with four curves, arc is drawn with one curve, that is all.



        Let's start with tikz.code.tex. In lines 3673–3706, there is the definition of tikz@do@arc, based on pgfpatharc, which is defined in pgfcorepathconstruct.code.tex. Circles and ellipses are defined in the same way.



        In pgfcorepathconstruct.code.tex, pgfpatharc is defined as a curve with a starting point and an ending point, based on pgf@nlt@curveto (line 401).



        Meanwhile, you can see that any kind of curves, even circles, are defined based on pgf@nlt@curveto. Circles and ellipses is defined in pgfpathellipse as a set of four connected curves: line 926, line 947, line 968, and line 989 — each of these curves has its own pgf@nlt@curveto.



        That is why the arc does not take its coordinate as the center, but a starting point.







        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 1 hour ago









        JouleVJouleV

        14.7k22665




        14.7k22665






























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