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+;;; guile-2d
+;;; Copyright (C) 2013 David Thompson <dthompson2@worcester.edu>
+;;;
+;;; Guile-2d is free software: you can redistribute it and/or modify it
+;;; under the terms of the GNU Lesser General Public License as
+;;; published by the Free Software Foundation, either version 3 of the
+;;; License, or (at your option) any later version.
+;;;
+;;; Guile-2d 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
+;;; Lesser General Public License for more details.
+;;;
+;;; You should have received a copy of the GNU Lesser General Public
+;;; License along with this program.  If not, see
+;;; <http://www.gnu.org/licenses/>.
+
+;;; Commentary:
+;;
+;; 2D vector math operations.
+;;
+;;; Code:
+
+(define-module (2d vector2)
+  #:use-module (srfi srfi-1)
+  #:use-module (srfi srfi-9)
+  #:export (<vector2>
+            vector2
+            vector2?
+            vx
+            vy
+            null-vector2
+            identity-vector2
+            vector2-polar
+            v+
+            v*
+            vscale
+            vmag
+            vnorm
+            vdot
+            vcross))
+
+(define-record-type <vector2>
+  (vector2 x y)
+  vector2?
+  (x vx)
+  (y vy))
+
+(define null-vector2 (vector2 0 0))
+(define identity-vector2 (vector2 1 1))
+
+(define (vector2-polar r theta)
+  "Converts polar coordinates into a cartesian vector."
+  (vector2 (* r (cos theta))
+           (* r (sin theta))))
+
+(define (v+ . vectors)
+  "Adds vectors."
+  (define (add-vectors x y vectors)
+    (cond ((null? vectors)
+           (vector2 x y))
+          (else
+           (add-vectors (+ x (vx (car vectors)))
+                        (+ y (vy (car vectors)))
+                        (cdr vectors)))))
+  (add-vectors 0 0 vectors))
+
+(define (v* . vectors)
+  "Multiplies vectors."
+  (define (multiply-vectors x y vectors)
+    (cond ((null? vectors)
+           (vector2 x y))
+          (else
+           (multiply-vectors (* x (vx (car vectors)))
+                             (* y (vy (car vectors)))
+                             (cdr vectors)))))
+  (multiply-vectors 1 1 vectors))
+
+(define (vscale v scalar)
+  "Multiply vector by a scalar."
+  (vector2 (* (vx v) scalar)
+           (* (vy v) scalar)))
+
+(define (vmag v)
+  "Returns the magnitude of a vector"
+  (sqrt (+ (expt (vx v) 2)
+           (expt (vy v) 2))))
+
+(define (vnorm v)
+  "Normalizes a vector."
+  (let ((m (vmag v)))
+    (if (zero? m)
+        null-vector2
+        (vector2 (/ (vx v) m)
+                 (/ (vy v) m)))))
+
+(define (vdot v1 v2)
+  "Returns the dot product of two vectors."
+  (+ (* (vx v1) (vx v2))
+     (* (vy v1) (vy v2))))
+
+(define (vcross v1 v2)
+  "Returns the cross product of two vectors. The cross product of a 2D
+vector is not defined. This function instead returns the Z coordinate
+of the cross product as if the vectors were in 3D space."
+  (- (* (vx v1) (vy v2))
+     (* (vy v1) (vx v2))))