1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
|
;;; 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 (rnrs bytevectors)
#:use-module (srfi srfi-1)
#:use-module (srfi srfi-9)
#:use-module (sly math)
#:use-module (sly records)
#:export (vector2 vector3 vector4
vector2? vector3? vector4?
vx vy vz vw
vector2-x vector2-y
vector3-x vector3-y vector3-z
vector4-x vector4-y vector4-z vector4-w
vmap v+ v- v* vdot vcross
magnitude normalize vlerp))
(define-packed-f64-record-type <vector2>
vector2
bytevector->vector2 vector2->bytevector
vector2?
(x 0 vector2-x set-vector2-x!)
(y 1 vector2-y set-vector2-y!))
(define-packed-f64-record-type <vector3>
vector3
bytevector->vector3 vector3->bytevector
vector3?
(x 0 vector3-x set-vector3-x!)
(y 1 vector3-y set-vector3-y!)
(z 2 vector3-z set-vector3-z!))
(define-packed-f64-record-type <vector4>
vector4
bytevector->vector4 vector4->bytevector
vector4?
(x 0 vector4-x set-vector4-x!)
(y 1 vector4-y set-vector4-y!)
(z 2 vector4-z set-vector4-z!)
(w 3 vector4-w set-vector4-w!))
(define-inlinable (vx v)
(cond
((vector2? v) (vector2-x v))
((vector3? v) (vector3-x v))
((vector4? v) (vector4-x v))))
(define-inlinable (vy v)
(cond
((vector2? v) (vector2-y v))
((vector3? v) (vector3-y v))
((vector4? v) (vector4-y v))))
(define-inlinable (vz v)
(cond
((vector3? v) (vector3-z v))
((vector4? v) (vector4-z v))))
(define-inlinable (vw v)
(vector4-w v))
(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)))))
;; Hoo boy, the things we do for efficiency. ;)
(define-syntax-rule (vector-arithmetic vectors op identity)
(match vectors
;; Common cases: Adding just 2 vectors of the same type.
;; Matching against them here means avoiding the more expensive,
;; more general loops later on.
(((and (? vector2?) (= vector2->bytevector bv1))
(and (? vector2?) (= vector2->bytevector bv2)))
(bytevector->vector2
(f64vector (op (f64vector-ref bv1 0)
(f64vector-ref bv2 0))
(op (f64vector-ref bv1 1)
(f64vector-ref bv2 1)))))
(((and (? vector3?) (= vector3->bytevector bv1))
(and (? vector3?) (= vector3->bytevector bv2)))
(bytevector->vector3
(f64vector (op (f64vector-ref bv1 0)
(f64vector-ref bv2 0))
(op (f64vector-ref bv1 1)
(f64vector-ref bv2 1))
(op (f64vector-ref bv1 2)
(f64vector-ref bv2 2)))))
(((and (? vector4?) (= vector4->bytevector bv1))
(and (? vector4?) (= vector4->bytevector bv2)))
(bytevector->vector4
(f64vector (op (f64vector-ref bv1 0)
(f64vector-ref bv2 0))
(op (f64vector-ref bv1 1)
(f64vector-ref bv2 1))
(op (f64vector-ref bv1 2)
(f64vector-ref bv2 2))
(op (f64vector-ref bv1 3)
(f64vector-ref bv2 3)))))
;; Special cases for a list with a a single element, to handle use
;; with subtraction.
(((and (? vector2?) (= vector2->bytevector head)))
(vector2 (op (f64vector-ref head 0))
(op (f64vector-ref head 1))))
(((and (? vector3?) (= vector3->bytevector head)))
(vector3 (op (f64vector-ref head 0))
(op (f64vector-ref head 1))
(op (f64vector-ref head 2))))
(((and (? vector4?) (= vector4->bytevector head)))
(vector4 (op (f64vector-ref head 0))
(op (f64vector-ref head 1))
(op (f64vector-ref head 2))
(op (f64vector-ref head 3))))
(((? number? x))
(op x))
;; General case:
(vectors*
(let outer ((scalar-sum #f)
(vectors* vectors*))
(match vectors*
;; First, add up all of the scalars that appear at the head of
;; the list, before we've been able to determine which vector
;; type to specialize on.
(() (or scalar-sum identity))
(((? number? x) . tail)
(outer (if scalar-sum (op scalar-sum x) x) tail))
;; Specialize based on vector type once we actually encounter a
;; vector.
;;
;; 2D vectors, possibly mixed with scalars:
(((and (? vector2?) (= vector2->bytevector head)) . tail)
(let ((bv (if scalar-sum
(f64vector (op scalar-sum
(f64vector-ref head 0))
(op scalar-sum
(f64vector-ref head 1)))
(bytevector-copy head))))
(let inner ((vectors* tail))
(match vectors*
(() (bytevector->vector2 bv))
(((? number? x) . tail)
(f64vector-set! bv 0 (op (f64vector-ref bv 0) x))
(f64vector-set! bv 1 (op (f64vector-ref bv 1) x))
(inner tail))
(((and (? vector2?) (= vector2->bytevector head)) . tail)
(f64vector-set! bv 0 (op (f64vector-ref bv 0)
(f64vector-ref head 0)))
(f64vector-set! bv 1 (op (f64vector-ref bv 1)
(f64vector-ref head 1)))
(inner tail))))))
;; 3D vectors, possibly mixed with scalars:
(((and (? vector3?) (= vector3->bytevector head)) . tail)
(let ((bv (if scalar-sum
(f64vector (op scalar-sum
(f64vector-ref head 0))
(op scalar-sum
(f64vector-ref head 1))
(op scalar-sum
(f64vector-ref head 2)))
(bytevector-copy head))))
(let inner ((vectors* tail))
(match vectors*
(() (bytevector->vector3 bv))
(((? number? x) . tail)
(f64vector-set! bv 0 (op (f64vector-ref bv 0) x))
(f64vector-set! bv 1 (op (f64vector-ref bv 1) x))
(f64vector-set! bv 2 (op (f64vector-ref bv 2) x))
(inner tail))
(((and (? vector3?) (= vector3->bytevector head)) . tail)
(f64vector-set! bv 0 (op (f64vector-ref bv 0)
(f64vector-ref head 0)))
(f64vector-set! bv 1 (op (f64vector-ref bv 1)
(f64vector-ref head 1)))
(f64vector-set! bv 2 (op (f64vector-ref bv 2)
(f64vector-ref head 2)))
(inner tail))))))
;; 4D vectors, possibly mixed with scalars:
(((and (? vector4?) (= vector4->bytevector head)) . tail)
(let ((bv (if scalar-sum
(f64vector (op scalar-sum
(f64vector-ref head 0))
(op scalar-sum
(f64vector-ref head 1))
(op scalar-sum
(f64vector-ref head 2))
(op scalar-sum
(f64vector-ref head 3)))
(bytevector-copy head))))
(let inner ((vectors* tail))
(match vectors*
(() (bytevector->vector4 bv))
(((? number? x) . tail)
(f64vector-set! bv 0 (op (f64vector-ref bv 0) x))
(f64vector-set! bv 1 (op (f64vector-ref bv 1) x))
(f64vector-set! bv 2 (op (f64vector-ref bv 2) x))
(f64vector-set! bv 3 (op (f64vector-ref bv 3) x))
(inner tail))
(((and (? vector4?) (= vector4->bytevector head)) . tail)
(f64vector-set! bv 0 (op (f64vector-ref bv 0)
(f64vector-ref head 0)))
(f64vector-set! bv 1 (op (f64vector-ref bv 1)
(f64vector-ref head 1)))
(f64vector-set! bv 2 (op (f64vector-ref bv 2)
(f64vector-ref head 2)))
(f64vector-set! bv 3 (op (f64vector-ref bv 3)
(f64vector-ref head 3)))
(inner tail)))))))))))
(define (v+ . vectors)
"Compute the sum of VECTORS."
(vector-arithmetic vectors + 0))
(define (v* . vectors)
"Compute the product of VECTORS."
(vector-arithmetic vectors * 1))
(define (v- vectors . rest)
"Compute the difference of VECTORS."
(vector-arithmetic (cons vectors rest) - 0))
(define (vdot v1 v2)
"Compute the dot product of the vectors V1 and V2."
(cond
((and (vector2? v1) (vector2? v2))
(+ (* (vector2-x v1) (vector2-x v2))
(* (vector2-y v1) (vector2-y v2))))
((and (vector3? v1) (vector3? v2))
(+ (* (vector3-x v1) (vector3-x v2))
(* (vector3-y v1) (vector3-y v2))
(* (vector3-z v1) (vector3-z v2))))
((and (vector4? v1) (vector4? v2))
(+ (* (vector4-x v1) (vector4-x v2))
(* (vector4-y v1) (vector4-y v2))
(* (vector4-z v1) (vector4-z v2))
(* (vector4-w v1) (vector4-w v2))))))
(define (vcross v1 v2)
"Compute the cross product of the 3D vectors V1 and V2."
(vector3 (- (* (vector3-y v1) (vector3-z v2))
(* (vector3-z v1) (vector3-y v2)))
(- (* (vector3-z v1) (vector3-x v2))
(* (vector3-x v1) (vector3-z v2)))
(- (* (vector3-x v1) (vector3-y v2))
(* (vector3-y v1) (vector3-x v2)))))
(define (magnitude v)
"Return the magnitude of the vector V."
(sqrt
(cond
((vector2? v)
(+ (square (vector2-x v))
(square (vector2-y v))))
((vector3? v)
(+ (square (vector3-x v))
(square (vector3-y v))
(square (vector3-z v))))
((vector4? v)
(+ (square (vector4-x v))
(square (vector4-y v))
(square (vector4-z v))
(square (vector4-w v)))))))
(define (normalize v)
"Return the normalized form of the vector V."
(let ((m (magnitude v)))
(cond
((zero? m) v)
((vector2? v)
(vector2 (/ (vector2-x v) m)
(/ (vector2-y v) m)))
((vector3? v)
(vector3 (/ (vector3-x v) m)
(/ (vector3-y v) m)
(/ (vector3-z v) m)))
((vector4? v)
(vector4 (/ (vector4-x v) m)
(/ (vector4-y v) m)
(/ (vector4-z v) m)
(/ (vector4-w v) m))))))
(define vlerp (make-lerp v+ v*))
|
