draw: Function for finding closest point

Author: johannes-wolf

CHANGES.md

@@ -22,6 +22,8 @@ package called `cetz-plot`.
 
 ## Draw
 - Added `floating` function for drawing elements without affecting bounding boxes.
+- Added `closest-point` for creating an anchor at the closest point between a
+  reference point and one or more elements.
 
 ## Marks
 - Added support for mark `anchor` style key, to adjust mark placement and

src/bezier.typ

@@ -586,3 +586,30 @@
   }
   return pts
 }
+
+/// Find the closest point on a bezier to a given point
+/// by using a binary search along the curve.
+#let cubic-closest-point(pt, s, e, c1, c2, max-recursion: 1) = {
+  let probe(low, high, depth) = {
+    let min = calc.inf
+    let min-t = 0
+
+    for t in range(0, 11) {
+      t = low + t / 10 * (high - low)
+      let d = vector.dist(pt, cubic-point(s, e, c1, c2, t))
+      if d < min {
+        min = d
+        min-t = t
+      }
+    }
+
+    if depth < max-recursion {
+      let step = (high - low) / 10
+      return probe(calc.max(0, min-t - step), calc.min(min-t + step, 1), depth + 1)
+    }
+
+    return cubic-point(s, e, c1, c2, min-t)
+  }
+
+  return probe(0, 1, 0)
+}

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, hide, floating
+#import "draw/grouping.typ": intersections, group, anchor, copy-anchors, place-anchors, set-ctx, get-ctx, for-each-anchor, on-layer, place-marks, hide, floating, closest-point
 #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, arc-through, mark, line, grid, content, rect, bezier, bezier-through, catmull, hobby, merge-path

src/draw/grouping.typ

@@ -198,6 +198,90 @@
   },)
 }
 
+/// Finds the closest point on one or more elements to a coordinate and
+/// creates an anchor. Transformations insides the body are scoped and do
+/// not get applied outsides.
+///
+/// - name (string): Anchor name.
+/// - reference-point (coordinate): Coordinate to find the closest point to.
+/// - body (element): One or more elements to consider. A least one is required. A function that accepts `ctx` and returns elements is also accepted.
+#let closest-point(name, reference-point, body) = {
+  import "/src/bezier.typ": cubic-closest-point
+
+  assert(type(name) == str,
+    message: "Anchor name must be of type string, got " + repr(name))
+  coordinate.resolve-system(reference-point)
+
+  return (ctx => {
+    let (_, pt) = coordinate.resolve(ctx, reference-point)
+    pt = util.apply-transform(ctx.transform, pt)
+
+    let group-ctx = ctx
+    group-ctx.groups.push(())
+    let (ctx: group-ctx, drawables, bounds) = process.many(group-ctx, util.resolve-body(ctx, body))
+    ctx.nodes += group-ctx.nodes
+
+    let min = calc.inf
+    let min-pt = none
+
+    // Compute the closest point on line a-b to point pt
+    let line-closest-pt(pt, a, b) = {
+      let n = vector.sub(b, a)
+      let d = vector.dot(n, pt)
+      d -= vector.dot(a, n)
+
+      let f = d / vector.dot(n, n)
+      return if f < 0 {
+        a
+      } else if f > 1 {
+        b
+      } else  {
+        vector.add(a, vector.scale(n, f))
+      }
+    }
+
+    for d in drawables {
+      if not "segments" in d { continue }
+
+      for ((kind, ..pts)) in d.segments {
+        if kind == "cubic" {
+          let tmp-pt = cubic-closest-point(pt, ..pts)
+          let tmp-min = vector.dist(tmp-pt, pt)
+          if tmp-min < min {
+            min-pt = tmp-pt
+            min = tmp-min
+          }
+        } else {
+          for i in range(1, pts.len()) {
+            let tmp-pt = line-closest-pt(pt, pts.at(i - 1), pts.at(i))
+            let tmp-min = vector.dist(tmp-pt, pt)
+            if tmp-min < min {
+              min-pt = tmp-pt
+              min = tmp-min
+            }
+          }
+        }
+      }
+    }
+
+    let (transform, anchors) = anchor_.setup(
+      anchor => min-pt,
+      ("default",),
+      default: "default",
+      name: name,
+      transform: none
+    )
+
+    return (
+      ctx: ctx,
+      name: name,
+      anchors: anchors,
+      drawables: drawables,
+      bounds: bounds
+    )
+  },)
+}
+
 /// Groups one or more elements together. This element acts as a scope, all state changes such as transformations and styling only affect the elements in the group. Elements after the group are not affected by the changes inside the group.
 ///
 /// #example(```