Tangent Lines Intersecting Curves

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Why I am only getting one point of intersection read by the program? Solution is to breaking to two parts with tangent lines drawn at different lengths.



documentclass{article}
usepackage{tikz}
usetikzlibrary{calc,intersections}
usetikzlibrary{decorations.markings}
begin{document}
pgfkeys{tikz/.cd,
tangent length/.store in=TangentLength,
tangent length=3.14cm,
normal length/.store in=NormalLength,
normal length=7mm}
newcounter{tangent}
newcounter{normal}
tikzset{tangent/.style={red,thin},normal/.style={blue,thin},
tangent at/.style={postaction={decorate,decoration={markings,
mark=at position #1 with {stepcounter{tangent}
draw[tangent,name path=tangent-thetangent] (-TangentLength,0) --
(9cm,0);
fill[tangent] (0,0) circle (2pt);}}}},
normal at/.style={postaction={decorate,decoration={markings,
mark=at position #1 with {stepcounter{normal}
draw[normal,name path=normal-thenormal] (0,-NormalLength) --
(0,NormalLength);
fill[normal] (0,0) circle (2pt);}}}},
}
begin{tikzpicture}
% Axes
draw [-latex] (-1,0) -- (11,0) node [right] {$x$};
draw [-latex] (0,-1) -- (0,6) node [above] {$y$};
% Origin
node at (0,0) [below left] {$0$};
% Points
coordinate (start) at (1,-0.8);
coordinate (c1) at (3,3);
coordinate (c2) at (5.5,1.5);
coordinate (c3) at (8,4);
coordinate (end) at (10.5,-0.8);
% show the points
% foreach n in {start,c1,c2,c3,end} fill [black] (n)
% circle (2pt) node [below] {};
% join the coordinates
draw [name path=curve,thick,tangent at/.list={0.3,0.3},
normal at/.list={}] (start) to[out=70,in=180] (c1) to[out=0,in=180]
(c2) to[out=0,in=180] (c3) to[out=0,in=150] (end);
fill[name intersections={of=curve and tangent-2,total=t},cyan]
(intersection-t) circle (2pt);
fill[name intersections={of=curve and tangent-1,total=t},cyan]
(intersection-t) circle (2pt);
end{tikzpcicture}
end{document}


This outputs:



enter image description here










share|improve this question






















  • Please replace ` end{tikzpcicture}` by ` end{tikzpicture}`.
    – marmot
    Nov 25 at 0:04















up vote
1
down vote

favorite












Why I am only getting one point of intersection read by the program? Solution is to breaking to two parts with tangent lines drawn at different lengths.



documentclass{article}
usepackage{tikz}
usetikzlibrary{calc,intersections}
usetikzlibrary{decorations.markings}
begin{document}
pgfkeys{tikz/.cd,
tangent length/.store in=TangentLength,
tangent length=3.14cm,
normal length/.store in=NormalLength,
normal length=7mm}
newcounter{tangent}
newcounter{normal}
tikzset{tangent/.style={red,thin},normal/.style={blue,thin},
tangent at/.style={postaction={decorate,decoration={markings,
mark=at position #1 with {stepcounter{tangent}
draw[tangent,name path=tangent-thetangent] (-TangentLength,0) --
(9cm,0);
fill[tangent] (0,0) circle (2pt);}}}},
normal at/.style={postaction={decorate,decoration={markings,
mark=at position #1 with {stepcounter{normal}
draw[normal,name path=normal-thenormal] (0,-NormalLength) --
(0,NormalLength);
fill[normal] (0,0) circle (2pt);}}}},
}
begin{tikzpicture}
% Axes
draw [-latex] (-1,0) -- (11,0) node [right] {$x$};
draw [-latex] (0,-1) -- (0,6) node [above] {$y$};
% Origin
node at (0,0) [below left] {$0$};
% Points
coordinate (start) at (1,-0.8);
coordinate (c1) at (3,3);
coordinate (c2) at (5.5,1.5);
coordinate (c3) at (8,4);
coordinate (end) at (10.5,-0.8);
% show the points
% foreach n in {start,c1,c2,c3,end} fill [black] (n)
% circle (2pt) node [below] {};
% join the coordinates
draw [name path=curve,thick,tangent at/.list={0.3,0.3},
normal at/.list={}] (start) to[out=70,in=180] (c1) to[out=0,in=180]
(c2) to[out=0,in=180] (c3) to[out=0,in=150] (end);
fill[name intersections={of=curve and tangent-2,total=t},cyan]
(intersection-t) circle (2pt);
fill[name intersections={of=curve and tangent-1,total=t},cyan]
(intersection-t) circle (2pt);
end{tikzpcicture}
end{document}


This outputs:



enter image description here










share|improve this question






















  • Please replace ` end{tikzpcicture}` by ` end{tikzpicture}`.
    – marmot
    Nov 25 at 0:04













up vote
1
down vote

favorite









up vote
1
down vote

favorite











Why I am only getting one point of intersection read by the program? Solution is to breaking to two parts with tangent lines drawn at different lengths.



documentclass{article}
usepackage{tikz}
usetikzlibrary{calc,intersections}
usetikzlibrary{decorations.markings}
begin{document}
pgfkeys{tikz/.cd,
tangent length/.store in=TangentLength,
tangent length=3.14cm,
normal length/.store in=NormalLength,
normal length=7mm}
newcounter{tangent}
newcounter{normal}
tikzset{tangent/.style={red,thin},normal/.style={blue,thin},
tangent at/.style={postaction={decorate,decoration={markings,
mark=at position #1 with {stepcounter{tangent}
draw[tangent,name path=tangent-thetangent] (-TangentLength,0) --
(9cm,0);
fill[tangent] (0,0) circle (2pt);}}}},
normal at/.style={postaction={decorate,decoration={markings,
mark=at position #1 with {stepcounter{normal}
draw[normal,name path=normal-thenormal] (0,-NormalLength) --
(0,NormalLength);
fill[normal] (0,0) circle (2pt);}}}},
}
begin{tikzpicture}
% Axes
draw [-latex] (-1,0) -- (11,0) node [right] {$x$};
draw [-latex] (0,-1) -- (0,6) node [above] {$y$};
% Origin
node at (0,0) [below left] {$0$};
% Points
coordinate (start) at (1,-0.8);
coordinate (c1) at (3,3);
coordinate (c2) at (5.5,1.5);
coordinate (c3) at (8,4);
coordinate (end) at (10.5,-0.8);
% show the points
% foreach n in {start,c1,c2,c3,end} fill [black] (n)
% circle (2pt) node [below] {};
% join the coordinates
draw [name path=curve,thick,tangent at/.list={0.3,0.3},
normal at/.list={}] (start) to[out=70,in=180] (c1) to[out=0,in=180]
(c2) to[out=0,in=180] (c3) to[out=0,in=150] (end);
fill[name intersections={of=curve and tangent-2,total=t},cyan]
(intersection-t) circle (2pt);
fill[name intersections={of=curve and tangent-1,total=t},cyan]
(intersection-t) circle (2pt);
end{tikzpcicture}
end{document}


This outputs:



enter image description here










share|improve this question













Why I am only getting one point of intersection read by the program? Solution is to breaking to two parts with tangent lines drawn at different lengths.



documentclass{article}
usepackage{tikz}
usetikzlibrary{calc,intersections}
usetikzlibrary{decorations.markings}
begin{document}
pgfkeys{tikz/.cd,
tangent length/.store in=TangentLength,
tangent length=3.14cm,
normal length/.store in=NormalLength,
normal length=7mm}
newcounter{tangent}
newcounter{normal}
tikzset{tangent/.style={red,thin},normal/.style={blue,thin},
tangent at/.style={postaction={decorate,decoration={markings,
mark=at position #1 with {stepcounter{tangent}
draw[tangent,name path=tangent-thetangent] (-TangentLength,0) --
(9cm,0);
fill[tangent] (0,0) circle (2pt);}}}},
normal at/.style={postaction={decorate,decoration={markings,
mark=at position #1 with {stepcounter{normal}
draw[normal,name path=normal-thenormal] (0,-NormalLength) --
(0,NormalLength);
fill[normal] (0,0) circle (2pt);}}}},
}
begin{tikzpicture}
% Axes
draw [-latex] (-1,0) -- (11,0) node [right] {$x$};
draw [-latex] (0,-1) -- (0,6) node [above] {$y$};
% Origin
node at (0,0) [below left] {$0$};
% Points
coordinate (start) at (1,-0.8);
coordinate (c1) at (3,3);
coordinate (c2) at (5.5,1.5);
coordinate (c3) at (8,4);
coordinate (end) at (10.5,-0.8);
% show the points
% foreach n in {start,c1,c2,c3,end} fill [black] (n)
% circle (2pt) node [below] {};
% join the coordinates
draw [name path=curve,thick,tangent at/.list={0.3,0.3},
normal at/.list={}] (start) to[out=70,in=180] (c1) to[out=0,in=180]
(c2) to[out=0,in=180] (c3) to[out=0,in=150] (end);
fill[name intersections={of=curve and tangent-2,total=t},cyan]
(intersection-t) circle (2pt);
fill[name intersections={of=curve and tangent-1,total=t},cyan]
(intersection-t) circle (2pt);
end{tikzpcicture}
end{document}


This outputs:



enter image description here







intersections






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked Nov 25 at 0:02









MathScholar

4608




4608












  • Please replace ` end{tikzpcicture}` by ` end{tikzpicture}`.
    – marmot
    Nov 25 at 0:04


















  • Please replace ` end{tikzpcicture}` by ` end{tikzpicture}`.
    – marmot
    Nov 25 at 0:04
















Please replace ` end{tikzpcicture}` by ` end{tikzpicture}`.
– marmot
Nov 25 at 0:04




Please replace ` end{tikzpcicture}` by ` end{tikzpicture}`.
– marmot
Nov 25 at 0:04










1 Answer
1






active

oldest

votes

















up vote
1
down vote



accepted










The style tangent at=<pos> attaches a tangent at position pos. So tangent at/.list={0.3,0.3} will just create two identical tangents. However, this has nothing to do with the intersections. Rather, you want to mark the last two intersections of the tangent with the curve. (TikZ finds more intersections since a tangent of course runs very close to the curve, so some of the additional intersections are not true intersections but result from numerical inaccuracies.)



documentclass{article}
usepackage{tikz}
usetikzlibrary{calc,intersections}
usetikzlibrary{decorations.markings}
begin{document}
pgfkeys{tikz/.cd,
tangent length/.store in=TangentLength,
tangent length=3.14cm,
normal length/.store in=NormalLength,
normal length=7mm}
newcounter{tangent}
newcounter{normal}
tikzset{tangent/.style={red,thin},normal/.style={blue,thin},
tangent at/.style={postaction={decorate,decoration={markings,
mark=at position #1 with {stepcounter{tangent}
draw[tangent,name path=tangent-thetangent] (-TangentLength,0) --
(9cm,0);
fill[tangent] (0,0) circle (2pt);}}}},
normal at/.style={postaction={decorate,decoration={markings,
mark=at position #1 with {stepcounter{normal}
draw[normal,name path=normal-thenormal] (0,-NormalLength) --
(0,NormalLength);
fill[normal] (0,0) circle (2pt);}}}},
}
begin{tikzpicture}
% Axes
draw [-latex] (-1,0) -- (11,0) node [right] {$x$};
draw [-latex] (0,-1) -- (0,6) node [above] {$y$};
% Origin
node at (0,0) [below left] {$0$};
% Points
coordinate (start) at (1,-0.8);
coordinate (c1) at (3,3);
coordinate (c2) at (5.5,1.5);
coordinate (c3) at (8,4);
coordinate (end) at (10.5,-0.8);
% show the points
% foreach n in {start,c1,c2,c3,end} fill [black] (n)
% circle (2pt) node [below] {};
% join the coordinates
draw [name path=curve,thick,tangent at=0.3] (start) to[out=70,in=180] (c1) to[out=0,in=180]
(c2) to[out=0,in=180] (c3) to[out=0,in=150] (end);
fill[name intersections={of=curve and tangent-1,total=t},cyan]
pgfextra{pgfmathtruncatemacro{prevt}{t-1}}
foreach i in {prevt,t} {(intersection-i) circle (2pt)};
end{tikzpicture}
end{document}


enter image description here






share|improve this answer





















  • @Thank Marmot. You are a tremendous help to me!
    – MathScholar
    Nov 25 at 0:23











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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
1
down vote



accepted










The style tangent at=<pos> attaches a tangent at position pos. So tangent at/.list={0.3,0.3} will just create two identical tangents. However, this has nothing to do with the intersections. Rather, you want to mark the last two intersections of the tangent with the curve. (TikZ finds more intersections since a tangent of course runs very close to the curve, so some of the additional intersections are not true intersections but result from numerical inaccuracies.)



documentclass{article}
usepackage{tikz}
usetikzlibrary{calc,intersections}
usetikzlibrary{decorations.markings}
begin{document}
pgfkeys{tikz/.cd,
tangent length/.store in=TangentLength,
tangent length=3.14cm,
normal length/.store in=NormalLength,
normal length=7mm}
newcounter{tangent}
newcounter{normal}
tikzset{tangent/.style={red,thin},normal/.style={blue,thin},
tangent at/.style={postaction={decorate,decoration={markings,
mark=at position #1 with {stepcounter{tangent}
draw[tangent,name path=tangent-thetangent] (-TangentLength,0) --
(9cm,0);
fill[tangent] (0,0) circle (2pt);}}}},
normal at/.style={postaction={decorate,decoration={markings,
mark=at position #1 with {stepcounter{normal}
draw[normal,name path=normal-thenormal] (0,-NormalLength) --
(0,NormalLength);
fill[normal] (0,0) circle (2pt);}}}},
}
begin{tikzpicture}
% Axes
draw [-latex] (-1,0) -- (11,0) node [right] {$x$};
draw [-latex] (0,-1) -- (0,6) node [above] {$y$};
% Origin
node at (0,0) [below left] {$0$};
% Points
coordinate (start) at (1,-0.8);
coordinate (c1) at (3,3);
coordinate (c2) at (5.5,1.5);
coordinate (c3) at (8,4);
coordinate (end) at (10.5,-0.8);
% show the points
% foreach n in {start,c1,c2,c3,end} fill [black] (n)
% circle (2pt) node [below] {};
% join the coordinates
draw [name path=curve,thick,tangent at=0.3] (start) to[out=70,in=180] (c1) to[out=0,in=180]
(c2) to[out=0,in=180] (c3) to[out=0,in=150] (end);
fill[name intersections={of=curve and tangent-1,total=t},cyan]
pgfextra{pgfmathtruncatemacro{prevt}{t-1}}
foreach i in {prevt,t} {(intersection-i) circle (2pt)};
end{tikzpicture}
end{document}


enter image description here






share|improve this answer





















  • @Thank Marmot. You are a tremendous help to me!
    – MathScholar
    Nov 25 at 0:23















up vote
1
down vote



accepted










The style tangent at=<pos> attaches a tangent at position pos. So tangent at/.list={0.3,0.3} will just create two identical tangents. However, this has nothing to do with the intersections. Rather, you want to mark the last two intersections of the tangent with the curve. (TikZ finds more intersections since a tangent of course runs very close to the curve, so some of the additional intersections are not true intersections but result from numerical inaccuracies.)



documentclass{article}
usepackage{tikz}
usetikzlibrary{calc,intersections}
usetikzlibrary{decorations.markings}
begin{document}
pgfkeys{tikz/.cd,
tangent length/.store in=TangentLength,
tangent length=3.14cm,
normal length/.store in=NormalLength,
normal length=7mm}
newcounter{tangent}
newcounter{normal}
tikzset{tangent/.style={red,thin},normal/.style={blue,thin},
tangent at/.style={postaction={decorate,decoration={markings,
mark=at position #1 with {stepcounter{tangent}
draw[tangent,name path=tangent-thetangent] (-TangentLength,0) --
(9cm,0);
fill[tangent] (0,0) circle (2pt);}}}},
normal at/.style={postaction={decorate,decoration={markings,
mark=at position #1 with {stepcounter{normal}
draw[normal,name path=normal-thenormal] (0,-NormalLength) --
(0,NormalLength);
fill[normal] (0,0) circle (2pt);}}}},
}
begin{tikzpicture}
% Axes
draw [-latex] (-1,0) -- (11,0) node [right] {$x$};
draw [-latex] (0,-1) -- (0,6) node [above] {$y$};
% Origin
node at (0,0) [below left] {$0$};
% Points
coordinate (start) at (1,-0.8);
coordinate (c1) at (3,3);
coordinate (c2) at (5.5,1.5);
coordinate (c3) at (8,4);
coordinate (end) at (10.5,-0.8);
% show the points
% foreach n in {start,c1,c2,c3,end} fill [black] (n)
% circle (2pt) node [below] {};
% join the coordinates
draw [name path=curve,thick,tangent at=0.3] (start) to[out=70,in=180] (c1) to[out=0,in=180]
(c2) to[out=0,in=180] (c3) to[out=0,in=150] (end);
fill[name intersections={of=curve and tangent-1,total=t},cyan]
pgfextra{pgfmathtruncatemacro{prevt}{t-1}}
foreach i in {prevt,t} {(intersection-i) circle (2pt)};
end{tikzpicture}
end{document}


enter image description here






share|improve this answer





















  • @Thank Marmot. You are a tremendous help to me!
    – MathScholar
    Nov 25 at 0:23













up vote
1
down vote



accepted







up vote
1
down vote



accepted






The style tangent at=<pos> attaches a tangent at position pos. So tangent at/.list={0.3,0.3} will just create two identical tangents. However, this has nothing to do with the intersections. Rather, you want to mark the last two intersections of the tangent with the curve. (TikZ finds more intersections since a tangent of course runs very close to the curve, so some of the additional intersections are not true intersections but result from numerical inaccuracies.)



documentclass{article}
usepackage{tikz}
usetikzlibrary{calc,intersections}
usetikzlibrary{decorations.markings}
begin{document}
pgfkeys{tikz/.cd,
tangent length/.store in=TangentLength,
tangent length=3.14cm,
normal length/.store in=NormalLength,
normal length=7mm}
newcounter{tangent}
newcounter{normal}
tikzset{tangent/.style={red,thin},normal/.style={blue,thin},
tangent at/.style={postaction={decorate,decoration={markings,
mark=at position #1 with {stepcounter{tangent}
draw[tangent,name path=tangent-thetangent] (-TangentLength,0) --
(9cm,0);
fill[tangent] (0,0) circle (2pt);}}}},
normal at/.style={postaction={decorate,decoration={markings,
mark=at position #1 with {stepcounter{normal}
draw[normal,name path=normal-thenormal] (0,-NormalLength) --
(0,NormalLength);
fill[normal] (0,0) circle (2pt);}}}},
}
begin{tikzpicture}
% Axes
draw [-latex] (-1,0) -- (11,0) node [right] {$x$};
draw [-latex] (0,-1) -- (0,6) node [above] {$y$};
% Origin
node at (0,0) [below left] {$0$};
% Points
coordinate (start) at (1,-0.8);
coordinate (c1) at (3,3);
coordinate (c2) at (5.5,1.5);
coordinate (c3) at (8,4);
coordinate (end) at (10.5,-0.8);
% show the points
% foreach n in {start,c1,c2,c3,end} fill [black] (n)
% circle (2pt) node [below] {};
% join the coordinates
draw [name path=curve,thick,tangent at=0.3] (start) to[out=70,in=180] (c1) to[out=0,in=180]
(c2) to[out=0,in=180] (c3) to[out=0,in=150] (end);
fill[name intersections={of=curve and tangent-1,total=t},cyan]
pgfextra{pgfmathtruncatemacro{prevt}{t-1}}
foreach i in {prevt,t} {(intersection-i) circle (2pt)};
end{tikzpicture}
end{document}


enter image description here






share|improve this answer












The style tangent at=<pos> attaches a tangent at position pos. So tangent at/.list={0.3,0.3} will just create two identical tangents. However, this has nothing to do with the intersections. Rather, you want to mark the last two intersections of the tangent with the curve. (TikZ finds more intersections since a tangent of course runs very close to the curve, so some of the additional intersections are not true intersections but result from numerical inaccuracies.)



documentclass{article}
usepackage{tikz}
usetikzlibrary{calc,intersections}
usetikzlibrary{decorations.markings}
begin{document}
pgfkeys{tikz/.cd,
tangent length/.store in=TangentLength,
tangent length=3.14cm,
normal length/.store in=NormalLength,
normal length=7mm}
newcounter{tangent}
newcounter{normal}
tikzset{tangent/.style={red,thin},normal/.style={blue,thin},
tangent at/.style={postaction={decorate,decoration={markings,
mark=at position #1 with {stepcounter{tangent}
draw[tangent,name path=tangent-thetangent] (-TangentLength,0) --
(9cm,0);
fill[tangent] (0,0) circle (2pt);}}}},
normal at/.style={postaction={decorate,decoration={markings,
mark=at position #1 with {stepcounter{normal}
draw[normal,name path=normal-thenormal] (0,-NormalLength) --
(0,NormalLength);
fill[normal] (0,0) circle (2pt);}}}},
}
begin{tikzpicture}
% Axes
draw [-latex] (-1,0) -- (11,0) node [right] {$x$};
draw [-latex] (0,-1) -- (0,6) node [above] {$y$};
% Origin
node at (0,0) [below left] {$0$};
% Points
coordinate (start) at (1,-0.8);
coordinate (c1) at (3,3);
coordinate (c2) at (5.5,1.5);
coordinate (c3) at (8,4);
coordinate (end) at (10.5,-0.8);
% show the points
% foreach n in {start,c1,c2,c3,end} fill [black] (n)
% circle (2pt) node [below] {};
% join the coordinates
draw [name path=curve,thick,tangent at=0.3] (start) to[out=70,in=180] (c1) to[out=0,in=180]
(c2) to[out=0,in=180] (c3) to[out=0,in=150] (end);
fill[name intersections={of=curve and tangent-1,total=t},cyan]
pgfextra{pgfmathtruncatemacro{prevt}{t-1}}
foreach i in {prevt,t} {(intersection-i) circle (2pt)};
end{tikzpicture}
end{document}


enter image description here







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answered Nov 25 at 0:11









marmot

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  • @Thank Marmot. You are a tremendous help to me!
    – MathScholar
    Nov 25 at 0:23


















  • @Thank Marmot. You are a tremendous help to me!
    – MathScholar
    Nov 25 at 0:23
















@Thank Marmot. You are a tremendous help to me!
– MathScholar
Nov 25 at 0:23




@Thank Marmot. You are a tremendous help to me!
– MathScholar
Nov 25 at 0:23


















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