shapes: Add arc-through

Thanks to Matthew Brown for the implementation.

src/draw.typ

@@ -1,4 +1,4 @@
 #import "draw/grouping.typ": intersections, group, anchor, copy-anchors, place-anchors, set-ctx, get-ctx, for-each-anchor, on-layer, place-marks
 #import "draw/transformations.typ": set-transform, rotate, translate, scale, set-origin, move-to, set-viewport
 #import "draw/styling.typ": set-style, fill, stroke
-#import "draw/shapes.typ": circle, circle-through, arc, mark, line, grid, content, rect, bezier, bezier-through, catmull, hobby, merge-path, shadow
+#import "draw/shapes.typ": circle, circle-through, arc, arc-through, mark, line, grid, content, rect, bezier, bezier-through, catmull, hobby, merge-path, shadow

src/draw/shapes.typ

@@ -304,6 +304,52 @@
  },)
 }
 
+#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)
+ 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))))
+
+ 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!
+ }
+ let delta = vector.angle(a, center, c)
+
+ 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)
+ }
+
+ 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
+ if center-is-left == b-is-left {
+ delta = 360deg - delta
+ }
+
+ // If b is left of a-c, swap a-c to c-a by using a negative delta
+ if b-is-left {
+ delta *= -1
+ }
+
+ return arc(a, start: start, delta: delta, radius: radius,
+ anchor: "arc-start", name: name, ..style)
+})
+
 #let mark(from, to, ..style) = {
  assert.eq(
  style.pos(),

src/util.typ

@@ -89,7 +89,8 @@
  return (calc.cos(angle) * rx + x, calc.sin(angle) * ry + y, z)
 }
 
-/// Calculate circle center from 3 points
+/// Calculate circle center from 3 points. The z coordinate
+/// is taken from point a.
 ///
 /// - a (vector): Point 1
 /// - b (vector): Point 2
@@ -129,11 +130,11 @@
  }
  let x = (d - c)/(a - b)
  let y = a * x + c
- return (x, y, 0)
+ return (x, y)
  }
 
  assert(args.len() == 4, message: "Could not find circle center")
- return line-intersection-2d(..args)
+ return vector.as-vec(line-intersection-2d(..args), init: (0, 0, a.at(2)))
 }
 
 #let resolve-number(ctx, num) = {

tests/arc/arc-through/test.typ

@@ -0,0 +1,65 @@
+#set page(width: auto, height: auto)
+#import "/src/lib.typ": *
+
+#let show-points(..pts) = {
+ import draw: *
+ for pt in pts.pos() {
+ circle(pt, radius: .1)
+ }
+}
+
+#let test(a, b, c) = {
+ import draw: *
+ group({
+ anchor("center", (0,0,0))
+ show-points(a, b, c)
+ arc-through(a, b, c)
+ }, name: "g", anchor: "west", padding: .1)
+ set-origin("g.east")
+}
+
+#box(stroke: 2pt + red, canvas(length: 1cm, {
+ import draw: *
+
+ test((0,0), (1, 1), (2, 0))
+ test((0,0), (1,-1), (2, 0))
+ test((0,1), (1, 0), (0,-1))
+ test((0,1), (-1,0), (0,-1))
+}))
+
+#box(stroke: 2pt + red, canvas(length: 1cm, {
+ import draw: *
+
+ for a in range(36, 360 + 36, step: 36) {
+ let a = a * 1deg
+ test((1,0),
+ (calc.cos(a / 2), calc.sin(a / 2)),
+ (calc.cos(a), calc.sin(a)))
+ }
+}))
+
+#box(stroke: 2pt + red, canvas(length: 1cm, {
+ import draw: *
+
+ for d in range(0, 8 + 1) {
+ let d = (d - 2) / 5
+ test((0,0), (1,d), (2,.5))
+ }
+}))
+
+#box(stroke: 2pt + red, canvas(length: 1cm, {
+ import draw: *
+
+ // The style radius must not influence the
+ // arc radius!
+ set-style(radius: 5)
+ set-style(arc: (radius: 5))
+ test((0,0), (1, 1), (2, 0))
+}))
+
+#box(stroke: 2pt + red, canvas(length: 1cm, {
+ import draw: *
+
+ arc-through((0,0), (1,1), (2,0))
+ arc-through((0,0,1), (1,1,1), (2,0,1), stroke: blue)
+}))

tests/arc/test.typ

@@ -34,3 +34,11 @@
  content((rel: (0, .5), to: "c." + a), [#a], frame: "rect", fill: white, stroke: none)
  })
 }))
+
+
+#box(stroke: 2pt + red, canvas(length: 1cm, {
+ import draw: *
+
+ arc((0,0), start: 45deg, delta: 90deg)
+ arc((0,0,1), start: 45deg, delta: 90deg, stroke: blue)
+}))