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;;; guile-2d
;;; Copyright (C) 2013, 2014 David Thompson <dthompson2@worcester.edu>
;;;
;;; This program 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.
;;;
;;; This program 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:
;;
;; 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
vector2-translate
vector2-scale))
(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)
"Convert the polar coordinates (R, THETA) into a cartesian vector."
(vector2 (* r (cos theta))
(* r (sin theta))))
(define (v+ . vectors)
"Return the sum of all 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)
"Return the product of all 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 the vector V by a scalar value."
(vector2 (* (vx v) scalar)
(* (vy v) scalar)))
(define (vmag v)
"Return the magnitude of the vector V."
(sqrt (+ (expt (vx v) 2)
(expt (vy v) 2))))
(define (vnorm v)
"Normalize the vector V."
(let ((m (vmag v)))
(if (zero? m)
null-vector2
(vector2 (/ (vx v) m)
(/ (vy v) m)))))
(define (vdot v1 v2)
"Return the dot product of the vectors V1 and V2."
(+ (* (vx v1) (vx v2))
(* (vy v1) (vy v2))))
(define (vcross v1 v2)
"Return the cross product of the vectors V1 and V2. Technically, 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))))
(define (vector2-translate v)
"Perform an OpenGL translate operation with the vector V."
(gl-translate (vx v) (vy v) 0))
(define (vector2-scale v)
"Perform an OpenGL scale operation with the vector V."
(gl-scale (vx v) (vy v) 1))
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