From 23aaaf38f1b21569be64fa59b7f497ec616071a3 Mon Sep 17 00:00:00 2001
From: David Thompson <dthompson2@worcester.edu>
Date: Mon, 4 Oct 2021 08:23:17 -0400
Subject: graphics: path: Add clockwise arcs.

---
 chickadee/graphics/path.scm | 19 ++++++++++++-------
 1 file changed, 12 insertions(+), 7 deletions(-)

diff --git a/chickadee/graphics/path.scm b/chickadee/graphics/path.scm
index c4e2b89..66617db 100644
--- a/chickadee/graphics/path.scm
+++ b/chickadee/graphics/path.scm
@@ -129,7 +129,7 @@
 ;; So in addition to our primitives, we need one more: expand. The
 ;; expand command is like a trivial macro expander.  It accepts a proc
 ;; with a single argument: The previous point in the path.
-(define (arc center rx ry angle-start angle-end)
+(define* (arc center rx ry angle-start angle-end #:optional (counter-clockwise? #t))
   ;; This algorithm is based on "Approximating Arcs Using Cubic Bézier
   ;; Curves" by Joe Cridge:
   ;; https://web.archive.org/web/20170829122313/https://www.joecridge.me/content/pdf/bezier-arcs.pdf
@@ -147,10 +147,13 @@
        (else
         (+ adjusted tau)))))
   (let* ((angle-start (adjust-angle angle-start))
-         (angle-end* (adjust-angle angle-end))
-         (angle-end (if (> angle-start angle-end*)
-                        (+ angle-end* tau)
-                        angle-end*))
+         (angle-end** (adjust-angle angle-end))
+         (angle-end* (if (> angle-start angle-end**)
+                         (+ angle-end** tau)
+                         angle-end**))
+         (angle-end (if counter-clockwise?
+                        angle-end*
+                        (- angle-end* (* 2.0 pi))))
          ;; Don't bother making a curve for an angle smaller than
          ;; this.
          (min-angle .00001)
@@ -167,13 +170,15 @@
                  (x1 #f)
                  (y1 #f))
         (let ((delta (- angle-end start)))
-          (if (> delta min-angle)
+          (if (> (abs delta) min-angle)
               (if x1
                   ;; Iteration 2+: Create a bezier curve for up to pi/2
                   ;; radians of the arc.  Limiting a curve to <= pi/2
                   ;; radians creates a very close approximation of the
                   ;; true curve.
-                  (let* ((size (min delta pi/2)) ; max segment angle is pi/2
+                  (let* ((size (if counter-clockwise? ; max segment angle is pi/2
+                                   (min delta pi/2)
+                                   (max delta (- pi/2))))
                          ;; This curve segment spans the range [start,
                          ;; end] radians.
                          (end (+ start size))
-- 
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