Tangent Lines Intersecting Curves
Multi tool use
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1
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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:
intersections
add a comment |
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:
intersections
Please replace ` end{tikzpcicture}` by ` end{tikzpicture}`.
– marmot
Nov 25 at 0:04
add a comment |
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:
intersections
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:
intersections
intersections
asked Nov 25 at 0:02
MathScholar
4608
4608
Please replace ` end{tikzpcicture}` by ` end{tikzpicture}`.
– marmot
Nov 25 at 0:04
add a comment |
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
add a comment |
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}
@Thank Marmot. You are a tremendous help to me!
– MathScholar
Nov 25 at 0:23
add a comment |
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}
@Thank Marmot. You are a tremendous help to me!
– MathScholar
Nov 25 at 0:23
add a comment |
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}
@Thank Marmot. You are a tremendous help to me!
– MathScholar
Nov 25 at 0:23
add a comment |
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}
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}
answered Nov 25 at 0:11
marmot
79.5k490168
79.5k490168
@Thank Marmot. You are a tremendous help to me!
– MathScholar
Nov 25 at 0:23
add a comment |
@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
add a comment |
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});
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StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
KOuNe 78MoBOD6zaa,2 5L
Please replace ` end{tikzpcicture}` by ` end{tikzpicture}`.
– marmot
Nov 25 at 0:04