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+;;; Chickadee Game Toolkit
+;;; Copyright © 2018 David Thompson <davet@gnu.org>
+;;;
+;;; Chickadee is free software: you can redistribute it and/or modify
+;;; it under the terms of the GNU General Public License as published
+;;; by the Free Software Foundation, either version 3 of the License,
+;;; or (at your option) any later version.
+;;;
+;;; Chickadee is distributed in the hope that it will be useful, but
+;;; WITHOUT ANY WARRANTY; without even the implied warranty of
+;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+;;; General Public License for more details.
+;;;
+;;; You should have received a copy of the GNU General Public License
+;;; along with this program.  If not, see
+;;; <http://www.gnu.org/licenses/>.
+
+;;; Commentary:
+;;
+;; Cubic Bezier curves in 2D space.
+;;
+;;; Code:
+
+(define-module (chickadee math bezier)
+  #:use-module (ice-9 match)
+  #:use-module (srfi srfi-9)
+  #:use-module (chickadee math vector)
+  #:export (make-bezier-curve
+            bezier-curve?
+            bezier-curve-p0
+            bezier-curve-p1
+            bezier-curve-p2
+            bezier-curve-p3
+            bezier-curve-point-at!
+            bezier-curve-point-at
+            bezier-path))
+
+(define-record-type <bezier-curve>
+  (make-bezier-curve p0 p1 p2 p3)
+  bezier-curve?
+  (p0 bezier-curve-p0)
+  (p1 bezier-curve-p1)
+  (p2 bezier-curve-p2)
+  (p3 bezier-curve-p3))
+
+(define (bezier-curve-point-at! dest bezier t)
+  "Write the coordinates for BEZIER at T (a value in the range [0, 1])
+to the 2D vector DEST."
+  (let* ((u (- 1.0 t))
+         (tt (* t t))
+         (uu (* u u))
+         (uuu (* uu u))
+         (ttt (* tt t))
+         (p0 (bezier-curve-p0 bezier))
+         (p1 (bezier-curve-p1 bezier))
+         (p2 (bezier-curve-p2 bezier))
+         (p3 (bezier-curve-p3 bezier)))
+    (set-vec2-x! dest (+ (* uuu (vec2-x p0))
+                         (* 3 uu t (vec2-x p1))
+                         (* 3 u tt (vec2-x p2))
+                         (* ttt (vec2-x p3))))
+    (set-vec2-y! dest (+ (* uuu (vec2-y p0))
+                         (* 3 uu t (vec2-y p1))
+                         (* 3 u tt (vec2-y p2))
+                         (* ttt (vec2-y p3))))))
+
+(define (bezier-curve-point-at bezier t)
+  "Return the coordinates for BEZIER at T (a value in the range [0,
+1]) as a 2D vector."
+  (let ((v #v(0.0 0.0)))
+    (bezier-curve-point-at! v bezier t)
+    v))
+
+(define (bezier-path . control-points)
+  "Return a list of connected bezier curves defined by CONTROL-POINTS.
+The first curve is defined by the first 4 arguments and every
+additional curve thereafter requires 3 additional arguments."
+  (match control-points
+    ((_) '())
+    ((p0 p1 p2 p3 . prest)
+     (cons (make-bezier-curve p0 p1 p2 p3)
+           (apply bezier-path p3 prest)))))