tikz-pgf
When teaching trigonometry, sometimes it is useful to represent angles greater than 360º with some kind of "spiral arc". For example:
the angle of -440º in the figure.
My question is:
How can I do this in nicely TikZ?
I can do it by using several consecutive arcs, but I wish to know if is there a more elegant solution to this.
The trigonometric functions in PGF use degrees, so you'll have to use 360 instead of 2*pi, and you'll have to deduct the full circle from the angle, not the other way round.
This becomes clear if you make a minimal example and look at the angles. The delta angle of the arc is the end angle minus the start angle. In your case, you have a delta angle that's larger than 180°, so you get the large arc. By subtracting a full circle from the end angle, the absolute value of the difference angle becomes smaller than 180°:
\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
\coordinate [label=right:O] (O) at (0,0);
\coordinate [label=below:A] (A) at (-1,-1.5);
\coordinate [label=left:B] (B) at (-2,1);
\draw (A) -- (O) -- (B);
\draw [-latex]
let
\p0 = (O),
\p1 = (A),
\p2 = (B),
\n1 = {atan2(\x1 - \x0, \y1 - \y0)},
\n2 = {atan2(\x2 - \x0, \y2 - \y0)},
\n3 = {1cm}
in
(\p0) + (\n1:\n3) arc [radius=\n3, start angle=\n1, end angle=\n2]
node [anchor=west, align=right] at (1.5,0) {\verb|\n1|: \pgfmathparse{\n1}\pgfmathprintnumber{\pgfmathresult}\\ \verb|\n2|: \pgfmathparse{\n2}\pgfmathprintnumber{\pgfmathresult}\\
delta: \pgfmathparse{\n2-\n1}\pgfmathprintnumber{\pgfmathresult}};
\end{tikzpicture}
\begin{tikzpicture}
\coordinate [label=right:O] (O) at (0,0);
\coordinate [label=below:A] (A) at (-1,-1.5);
\coordinate [label=left:B] (B) at (-2,1);
\draw (A) -- (O) -- (B);
\draw [-latex]
let
\p0 = (O),
\p1 = (A),
\p2 = (B),
\n1 = {atan2(\x1 - \x0, \y1 - \y0)},
\n2 = {atan2(\x2 - \x0, \y2 - \y0) - 360},
\n3 = {1cm}
in
(\p0) + (\n1:\n3) arc [radius=\n3, start angle=\n1, end angle=\n2]
node [anchor=west, align=right] at (1.5,0) {\verb|\n1|: \pgfmathparse{\n1}\pgfmathprintnumber{\pgfmathresult}\\ \verb|\n2|: \pgfmathparse{\n2}\pgfmathprintnumber{\pgfmathresult}\\
delta: \pgfmathparse{\n2-\n1}\pgfmathprintnumber{\pgfmathresult}};
\end{tikzpicture}
\end{document}
\documentclass[convert = false]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc, intersections, backgrounds, arrows}
\begin{document}
\tikzset{circle with radius/.style = {shape = circle, inner sep = 0pt,
outer sep = 0pt, minimum size = {2 * (#1)}}}
\begin{tikzpicture}[line join = round, line cap = round,
every label/.append style = {font = \scriptsize},
dot/.style = {inner sep = +0pt, shape = circle,
draw = black, label = {#1}},
small dot/.style = {minimum size = .05cm, dot = {#1}},
big dot/.style = {minimum size = .1cm, dot = {#1}},
]
\begin{scope}
%\clip ($(B) + (1.5, -2)$) rectangle ($(B) + (-3, 2)$);
\coordinate (O) at (0, 0);
\pgfmathsetmacro{\as}{3}
\pgfmathsetmacro{\bs}{2.25}
\pgfmathsetmacro{\c}{sqrt(\as^2 - \bs^2)}
\pgfmathsetmacro{\al}{3.75}
\pgfmathsetmacro{\bl}{2.9}
\pgfmathsetmacro{\cl}{sqrt(\al^2 - \bl^2)}
\pgfmathsetmacro{\xs}{abs(\c - \cl)}
\coordinate (O) at (0, 0);
\node[fill = black, big dot = {below left: \(F\)}] (F) at (\c, 0) {};
\path[name path global = line1] (\c, 0) -- ++(60:{\as} and \bs);
\path[name path global = line2] (\c, 0) -- ++(150:6cm);
\draw[name path global = ell1, blue] (O) ellipse
(\as cm and \bs cm);
\draw[name path global = ell2, red] (-\xs, 0)
ellipse (\al cm and \bl cm);
\path[name intersections = {of = line1 and ell1, by = P1}];
\node[fill = black, big dot = {right: \(A\)}] (A) at (P1) {};
\path[name intersections = {of = line2 and ell2, by = P2}];
\node[fill = black, big dot = {above: \(B\)}] (B) at (P2) {};
\begin{scope}[declare function = {doubleA = 5.8cm;},
]
\clip ($(A.center) + (1, 0)$) rectangle ($(B.center) + (0, 1)$);
\begin{pgfinterruptboundingbox}
\path let
\p1 = ($(A) - (F)$),
\p2 = ($(B) - (F)$),
\n1 = {veclen(\x1, \y1)},
\n2 = {veclen(\x2, \y2)}
in
(A) node[name path global = aCircle, circle with radius = doubleA-\n1]
{}
(B) node[name path global = bCircle, circle with radius = doubleA-\n2]
{}
(F) node[name path global = fCircle,
circle with radius = .5 * doubleA] {};
\tikzset{name intersections = {of = aCircle and bCircle, name = F'} }
\foreach \solA in {2} {
\path ($(F)!.5!(F'-\solA)$) coordinate (C'-\solA)
($(C'-\solA)!doubleA/2!(F)$) coordinate (xDir-\solA)
(F'-\solA) node[name path global/.expanded = f'Circle-\solA,
circle with radius = .5 * doubleA] {};
} %!?
\foreach \solA in {2} { %!?
\path[name intersections = {of = fCircle and f'Circle-\solA,
by = {yDir-\solA}}]
($(xDir-\solA)-(C'-\solA)$) coordinate (xDir'-\solA)
($(yDir-\solA)-(C'-\solA)$) coordinate (yDir'-\solA)
;
}
\end{pgfinterruptboundingbox}
\foreach \solA in {2}
\draw[x = (xDir'-\solA), y = (yDir'-\solA), name path global = traj]
(C'-\solA) circle [radius = 1];
\end{scope}
\path[name path = circ] (B) circle [radius = 1bp];
\draw[name intersections = {of = circ and traj}, -latex] (B) --
($(intersection-1)!1.25cm!(intersection-2)$) coordinate (P3);
\draw[name intersections = {of = circ and ell2}, -latex, red] (B) --
($(intersection-1)!2cm!(intersection-2)$) coordinate (P4);
\draw[-latex, name path = line3] (P3) -- (P4);
\draw[name path = line4] (B) -- ($(B)!2.1cm!-90:(F)$) coordinate (P5);
\path[name path = circ2] (P3) circle [radius = 1bp];
\path[name intersections = {of = circ2 and line3}, name path = line5]
(P3) -- ($(intersection-1)!2cm!(P3)$);
\path[name intersections = {of = line5 and line4, by = P6}];
\path[name intersections = {of = circ and traj}] (B) --
($(intersection-1)!1.5cm!(intersection-2)$) coordinate (P7);
\path[name intersections = {of = circ and ell2}] (B) --
($(intersection-1)!2.5cm!(intersection-2)$) coordinate (P8);
\draw[-latex] let
\p0 = (P6),
\p1 = (P5),
\p2 = (P4),
\n1 = {atan2(\x1 - \x0, \y1 - \y0)},
\n2 = {atan2(\x2 - \x0, \y2 - \y0)-360},
\n3 = {.75cm}
in (P6) +(\n1:\n3) arc[radius = \n3, start angle = \n1, end angle = \n2];
\end{scope}
\end{tikzpicture}
\end{document}
\draw (x,y) arc (start:stop:radius); draws an arc
radius(x,y)(x-r*cos(start), y-r*sin(start)) and(x-r*cos(start)+r*cos(stop), y-r*sin(start)+r*sin(stop)).For example,
\draw[red] (0,0) arc (30:60:3);
draws an arc
3(0,0)(0-3*cos(30),0-3*sin(30)) and(0-3*cos(30)+3*cos(60),0-3*sin(30)+3*sin(60)).\draw[blue] (0,0) -- ++(30+180:3) -- +(60:3);
draw a blue line to the arc to make a complete sector as shown in the following figure.
\documentclass[tikz,border=12pt]{standalone}
\begin{document}
\foreach \start/\stop in {30/60,45/90,135/180,0/180,45/315}
{
\begin{tikzpicture}
\draw[lightgray,ultra thin] (-6,-6) grid (6,6);
\draw[red] (0,0) arc (\start:\stop:3);
\draw[blue] (0,0) -- ++(\start+180:3) -- +(\stop:3);
\node[anchor=north] at (0,6) {$(\start:\stop:3)$};
\end{tikzpicture}
}
\end{document}
Best Answer