Emacs Lisp implementation of Graham scan

contents/graham_scan/code/elisp/graham-scan.el

@@ -0,0 +1,56 @@
+(require 'cl-seq)
+
+(defun snoc (list elem)
+  "Append ELEM to the end of the list.
+
+This is like `cons', but operates on the end of list.
+
+Adapted from dash.el."
+  (append list (list elem)))
+
+(defun nthrev (n lst)
+  "Return the Nth element of LST from the end."
+  (nth (- (length lst) (1+ n)) lst))
+
+(defun is-ccw (a b c)
+  "Determines if a turn between three points is counterclockwise."
+  (>= (* (- (nth 1 c) (nth 1 a)) (- (nth 0 b) (nth 0 a)))
+      (* (- (nth 1 b) (nth 1 a)) (- (nth 0 c) (nth 0 a)))))
+
+(defun polar-angle (ref point)
+  "Returns the polar angle from a point relative to a reference point"
+  (atan (- (nth 1 point) (nth 1 ref)) (- (nth 0 point) (nth 0 ref))))
+
+(defun graham-scan (initial-gift)
+  "Finds the convex hull of a distribution of points with a Graham scan."
+  (let* ((gift (cl-remove-duplicates initial-gift))
+         ;; This is /only/ to get the starting point.
+         (min-sorted-gift (sort gift (lambda (p1 p2) (< (nth 1 p1) (nth 1 p2)))))
+         (start (car min-sorted-gift))
+         (trimmed-gift (cdr min-sorted-gift))
+         (points (sort trimmed-gift (lambda (p1 p2) (< (polar-angle start p1)
+                                                       (polar-angle start p2)))))
+         (hull (list start (car points) (cadr points))))
+    (dolist (point (cddr points))
+      (while (not (is-ccw (nthrev 1 hull) (nthrev 0 hull) point))
+        (setq hull (reverse (cdr (reverse hull)))))
+      (setq hull (snoc hull point)))
+    hull))
+
+(princ
+ (graham-scan
+  '((-5 2)
+    (5 7)
+    (-6 -12)
+    (-14 -14)
+    (9 9)
+    (-1 -1)
+    (-10 11)
+    (-6 15)
+    (-6 -8)
+    (15 -9)
+    (7 -7)
+    (-2 -9)
+    (6 -5)
+    (0 14)
+    (2 8))))

contents/graham_scan/graham_scan.md

@@ -32,6 +32,8 @@ We can find whether a rotation is counter-clockwise with trigonometric functions
 [import:18-20, lang="cpp"](code/c++/graham_scan.cpp)
 {% sample lang="coco" %}
 [import:4-8, lang="coconut"](code/coconut/graham_scan.coco)
+{%sample lang="elisp" %}
+[import:15-22, lang="elisp"](code/elisp/graham-scan.el)
 {% endmethod %}
 
 If the output of this function is 0, the points are collinear.
@@ -66,6 +68,8 @@ In the end, the code should look something like this:
 [import:26-62, lang="cpp"](code/c++/graham_scan.cpp)
 {% sample lang="coco" %}
 [import:17-30, lang="coconut"](code/coconut/graham_scan.coco)
+{%sample lang="elisp" %}
+[import:24-38, lang="elisp"](code/elisp/graham-scan.el)
 {% endmethod %}
 
 ### Bibliography
@@ -95,6 +99,8 @@ In the end, the code should look something like this:
 [import, lang="cpp"](code/c++/graham_scan.cpp)
 {%sample lang="coco" %}
 [import, lang="coconut"](code/coconut/graham_scan.coco)
+{%sample lang="elisp" %}
+[import, lang="elisp"](code/elisp/graham-scan.el)
 {% endmethod %}
 
 <script>