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;;; Sly
;;; Copyright (C) 2014 David Thompson <davet@gnu.org>
;;;
;;; 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:
;;
;; Vector math.
;;
;;; Code:
(define-module (sly math vector)
#:use-module (ice-9 match)
#:use-module (srfi srfi-1)
#:use-module (srfi srfi-9)
#:use-module (sly math)
#:export (<vector2>
<vector3>
<vector4>
vector2 vector3 vector4
vector2? vector3? vector4?
polar2
vx vy vz vw
vmap v+ v- v* vdot vcross
magnitude normalize vlerp
anchor-vector)
#:replace (magnitude))
(define-record-type <vector2>
(vector2 x y)
vector2?
(x vector2-x)
(y vector2-y))
(define-record-type <vector3>
(vector3 x y z)
vector3?
(x vector3-x)
(y vector3-y)
(z vector3-z))
(define-record-type <vector4>
(vector4 x y z w)
vector4?
(x vector4-x)
(y vector4-y)
(z vector4-z)
(w vector4-w))
(define vx
(match-lambda
((or ($ <vector2> x _)
($ <vector3> x _ _)
($ <vector4> x _ _ _))
x)))
(define vy
(match-lambda
((or ($ <vector2> _ y)
($ <vector3> _ y _)
($ <vector4> _ y _ _))
y)))
(define vz
(match-lambda
((or ($ <vector3> _ _ z)
($ <vector4> _ _ z _))
z)))
(define vw vector4-w)
(define (polar2 r theta)
"Create a new 2D vector from the polar coordinate (R, THETA) where R
is the radius and THETA is the angle."
(vector2 (* r (cos theta))
(* r (sin theta))))
(define (vmap proc v)
"Return a new vector that is the result of applying PROC to each
element of the 2D/3D/4D vector V."
(match v
(($ <vector2> x y)
(vector2 (proc x) (proc y)))
(($ <vector3> x y z)
(vector3 (proc x) (proc y) (proc z)))
(($ <vector4> x y z w)
(vector4 (proc x) (proc y) (proc z) (proc w)))))
(define-syntax-rule (vector-lambda proc)
(match-lambda*
((($ <vector2> x1 y1) ($ <vector2> x2 y2))
(vector2 (proc x1 x2) (proc y1 y2)))
((($ <vector2> x y) (? number? k))
(vector2 (proc x k) (proc y k)))
(((? number? k) ($ <vector2> x y))
(vector2 (proc k x) (proc k y)))
((($ <vector3> x1 y1 z1) ($ <vector3> x2 y2 z2))
(vector3 (proc x1 x2) (proc y1 y2) (proc z1 z2)))
((($ <vector3> x y z) (? number? k))
(vector3 (proc x k) (proc y k) (proc z k)))
(((? number? k) ($ <vector3> x y z))
(vector3 (proc k x) (proc k y) (proc k z)))
((($ <vector4> x1 y1 z1 w1) ($ <vector4> x2 y2 z2 w2))
(vector4 (proc x1 x2) (proc y1 y2) (proc z1 z2) (proc w1 w2)))
((($ <vector4> x y z w) (? number? k))
(vector4 (proc x k) (proc y k) (proc z k) (proc w k)))
(((? number? k) ($ <vector4> x y z w))
(vector4 (proc k x) (proc k y) (proc k z) (proc k w)))))
(define (v+ . vectors)
(reduce (vector-lambda +) 0 vectors))
(define v-
(match-lambda*
((v) (v- 0 v))
((v v* ...)
(fold-right (let ((- (vector-lambda -)))
(lambda (prev v)
(- v prev)))
v v*))))
(define (v* . vectors)
(reduce (vector-lambda *) 1 vectors))
(define vdot
(match-lambda*
((($ <vector2> x1 y1) ($ <vector2> x2 y2))
(+ (* x1 x2) (* y1 y2)))
((($ <vector3> x1 y1 z1) ($ <vector3> x2 y2 z2))
(+ (* x1 x2) (* y1 y2) (* z1 z2)))
((($ <vector4> x1 y1 z1 w1) ($ <vector4> x2 y2 z2 w2))
(+ (* x1 x2) (* y1 y2) (* z1 z2) (* w1 w2)))))
(define vcross
(match-lambda*
((($ <vector3> x1 y1 z1) ($ <vector3> x2 y2 z2))
(vector3 (- (* y1 z2) (* z1 y2))
(- (* z1 x2) (* x1 z2))
(- (* x1 y2) (* y1 x2))))))
(define (magnitude v)
"Return the magnitude of the vector V."
(sqrt
(match v
(($ <vector2> x y)
(+ (square x) (square y)))
(($ <vector3> x y z)
(+ (square x) (square y) (square z)))
(($ <vector4> x y z w)
(+ (square x) (square y) (square z) (square w))))))
(define (normalize v)
"Return the normalized form of the vector V."
(let ((m (magnitude v)))
(if (zero? m)
v
(match v
(($ <vector2> x y)
(vector2 (/ x m) (/ y m)))
(($ <vector3> x y z)
(vector3 (/ x m) (/ y m) (/ z m)))
(($ <vector4> x y z w)
(vector4 (/ x m) (/ y m) (/ z m) (/ w m)))))))
(define vlerp (make-lerp v+ v*))
(define (anchor-vector width height anchor)
"Create an anchor point vector from the description ANCHOR within
the rectangular defined by WIDTH and HEIGHT. Valid values for ANCHOR
are: 'center', 'top-left', 'top-right', 'bottom-left', 'bottom-right',
'top-center', 'bottom-center', or any 2D vector. When ANCHOR is a 2D
vector, the return value is simply the same vector."
(match anchor
((? vector2? anchor)
anchor)
('center
(vector2 (/ width 2)
(/ height 2)))
('top-left
(vector2 0 height))
('top-right
(vector2 width height))
('bottom-left
(vector2 0 0))
('bottom-right
(vector2 width 0))
('top-center
(vector2 (/ width 2) height))
('bottom-center
(vector2 (/ width 2) 0))
(_ (error "Invalid anchor type: " anchor))))
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