shapes: Add arc-through documentation

src/draw/shapes.typ

@@ -304,39 +304,77 @@
   },)
 }
 
+/// Draw an arc that passes through three points a, b and c.
+///
+/// Note that all three points must not lay on a straight line, otherwise
+/// the function fails.
+///
+/// #example(```
+/// arc-through((0,0), (1,0), (2,0))
+/// ```)
+///
+/// *Style Root* `arc` \
+/// *Style Keys* \
+///   For style keys, see `arc`.
+///
+/// *Anchors* \
+///   For anchors see `arc`.
+///
+/// - a (coordinate): Start position of the arc
+/// - b (coordinate): Position the arc passes through
+/// - c (coordinate): End position of the arc
+/// - name (none,string): The arc elements node name that, if set can be used to query anchors
+/// - ..style (style): Style key value pairs. The function `arc-through` uses
+///   all keys that `arc` uses, but `radius`, as this is determined by the
+///   three input points.
 #let arc-through(
   a,
   b,
   c,
   name: none,
   ..style,
 ) = get-ctx(ctx => {
-  let (ctx, a) = coordinate.resolve(ctx, a)
-  let (ctx, b) = coordinate.resolve(ctx, b)
-  let (ctx, c) = coordinate.resolve(ctx, c)
+  let (ctx, a, b, c) = coordinate.resolve(ctx, a, b, c)
   assert(a.at(2) == b.at(2) and b.at(2) == c.at(2),
     message: "The z coordinate of all points must be equal, but is: " + repr((a, b, c).map(v => v.at(2))))
 
+  // Calculate the circle center from three points or fails if all
+  // three points are on one straight line.
   let center = util.calculate-circle-center-3pt(a, b, c)
   let radius = vector.dist(center, a)
-  let start = {
-    let (x, y, ..) = vector.sub(a, center)
-    calc.atan2(x, y) // Typst's atan2 is (x,y) order!
-  }
+
+  // Find the start and inner angle between a-center-c
+  let start = vector.angle2(center, a)
   let delta = vector.angle(a, center, c)
 
+  // Returns a negative number if pt is left of the line a-b,
+  // if pt is right to a-b, a positive number is returned,
+  // otherwise zero.
   let side-on-line(a, b, pt) = {
     let (x1, y1, ..) = a
     let (x2, y2, ..) = b
     let (x,  y, ..)  = pt
     return (x - x1) * (y2 - y1) - (y - y1) * (x2 - x1)
   }
 
+  // Center & b     b is left,
+  //  are left      center not
+  //
+  //    +-b-+          +-b-+
+  //   /     \        /     \
+  //  |   C   |    --a-------c--
+  //   \     /        \  C  /
+  // ---a---c---       +---+
+  //
+  // If b and C are on the same side of a-c, the arcs radius is >= 180deg,
+  // otherwise the radius is < 180deg.
   let center-is-left = side-on-line(a, c, center) < 0
   let b-is-left = side-on-line(a, c, b) < 0
 
   // If the center and point b are on the same side of a-c,
-  // the arcs delta must be > 180deg
+  // the arcs delta must be > 180deg. Note, that delta is
+  // the inner angle between a-center-c, so we need to calculate
+  // the outer angle by subtracting from 360deg.
   if center-is-left == b-is-left {
     delta = 360deg - delta
   }