[Tex/LaTex] How is arc defined in TikZ

arctikz-pgf

Several questions about how arc is computed:

1. The start and end angles seem to be defined relative to the y axis, yet in the Tikz manual they are defined relative to the x axis. Is this right?

2. Is the end angle defined between the y (or x) axis and the incoming path, or between the y (or x) axis and the extension of the path beyond the endpoint?

3. Geometrically speaking, providing just the start and end angles (and radius) is not enough to define an arc unambiguously. Is there some other assumption, such as: Arcs must be less than 180 degrees? Or arcs must always curve counterclockwise?

\draw (x,y) arc (start:stop:radius); draws an arc

• with radius radius
• starts from (x,y)
• with center (x-r*cos(start), y-r*sin(start)) and
• ends at (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

• of radius 3
• starting from (0,0)
• with center (0-3*cos(30),0-3*sin(30)) and
• ending at (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.

Minimal Working Example

\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}