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
|
; libctl: flexible Guile-based control files for scientific software
; Copyright (C) 1998, 1999, 2000, 2001, 2002, Steven G. Johnson
;
; This library 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 2 of the License, or (at your option) any later version.
;
; This library 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 library; if not, write to the
; Free Software Foundation, Inc., 59 Temple Place - Suite 330,
; Boston, MA 02111-1307, USA.
;
; Steven G. Johnson can be contacted at stevenj@alum.mit.edu.
; ****************************************************************
(if (not (defined? 'material-type))
(define-class material-type no-parent)) ; define dummy class
(define-class geometric-object no-parent
(define-property material no-default 'material-type)
(define-property center no-default 'vector3))
(define (non-negative? x) (not (negative? x)))
(define-class cylinder geometric-object
(define-post-processed-property axis (vector3 0 0 1) 'vector3 unit-vector3)
(define-property radius no-default 'number non-negative?)
(define-property height no-default 'number non-negative?))
(define-class cone cylinder
(define-property radius2 0 'number))
(define-class sphere geometric-object
(define-property radius no-default 'number non-negative?))
(define-class block geometric-object
(define-post-processed-property e1 (vector3 1 0 0) 'vector3 unit-vector3)
(define-post-processed-property e2 (vector3 0 1 0) 'vector3 unit-vector3)
(define-post-processed-property e3 (vector3 0 0 1) 'vector3 unit-vector3)
(define-property size no-default 'vector3)
(define-derived-property projection-matrix 'matrix3x3
(lambda (object)
(matrix3x3-inverse
(matrix3x3
(object-property-value object 'e1)
(object-property-value object 'e2)
(object-property-value object 'e3))))))
(define-class ellipsoid block
(define-derived-property inverse-semi-axes 'vector3
(lambda (object)
(vector-map (lambda (x) (/ 2.0 x))
(object-property-value object 'size)))))
; ****************************************************************
(define-class lattice no-parent
(define-post-processed-property basis1 (vector3 1 0 0) 'vector3 unit-vector3)
(define-post-processed-property basis2 (vector3 0 1 0) 'vector3 unit-vector3)
(define-post-processed-property basis3 (vector3 0 0 1) 'vector3 unit-vector3)
(define-property size (vector3 1 1 1) 'vector3)
(define-property basis-size (vector3 1 1 1) 'vector3)
(define-derived-property b1 'vector3
(lambda (object)
(vector3-scale (vector3-x (object-property-value object 'basis-size))
(object-property-value object 'basis1))))
(define-derived-property b2 'vector3
(lambda (object)
(vector3-scale (vector3-y (object-property-value object 'basis-size))
(object-property-value object 'basis2))))
(define-derived-property b3 'vector3
(lambda (object)
(vector3-scale (vector3-z (object-property-value object 'basis-size))
(object-property-value object 'basis3))))
(define-derived-property basis 'matrix3x3
(lambda (object)
(let ((B (matrix3x3
(object-property-value object 'b1)
(object-property-value object 'b2)
(object-property-value object 'b3))))
(if (zero? (matrix3x3-determinant B))
(error "lattice basis vectors must be linearly independent!"))
B)))
(define-derived-property metric 'matrix3x3
(lambda (object)
(let ((B (object-property-value object 'basis)))
(matrix3x3* (matrix3x3-transpose B) B)))))
; ****************************************************************
; Define some utility functions:
(define (shift-geometric-object go shift-vector)
(let ((c (object-property-value go 'center)))
(modify-object go (center (vector3+ c shift-vector)))))
(define (geometric-object-duplicates shift-vector min-multiple max-multiple go)
(define (g-o-d min-multiple L)
(if (<= min-multiple max-multiple)
(g-o-d (+ min-multiple 1)
(cons (shift-geometric-object
go (vector3-scale min-multiple shift-vector))
L))
L))
(g-o-d min-multiple '()))
(define (geometric-objects-duplicates shift-vector min-multiple max-multiple
go-list)
(fold-left append '()
(map (lambda (go)
(geometric-object-duplicates
shift-vector min-multiple max-multiple go))
go-list)))
(define (geometric-objects-lattice-duplicates go-list . usize)
(let ((u1 (if (>= (length usize) 1) (list-ref usize 0) 1))
(u2 (if (>= (length usize) 2) (list-ref usize 1) 1))
(u3 (if (>= (length usize) 3) (list-ref usize 2) 1))
(s (object-property-value geometry-lattice 'size)))
(let ((b1 (vector3 u1 0 0)) (b2 (vector3 0 u2 0)) (b3 (vector3 0 0 u3))
(n1 (ceiling (/ (vector3-x s) u1)))
(n2 (ceiling (/ (vector3-y s) u2)))
(n3 (ceiling (/ (vector3-z s) u3))))
(geometric-objects-duplicates
b1 (- (floor (/ (- n1 1) 2))) (ceiling (/ (- n1 1) 2))
(geometric-objects-duplicates
b2 (- (floor (/ (- n2 1) 2))) (ceiling (/ (- n2 1) 2))
(geometric-objects-duplicates
b3 (- (floor (/ (- n3 1) 2))) (ceiling (/ (- n3 1) 2))
go-list))))))
; ****************************************************************
(define-input-var dimensions 3 'integer)
(define-input-var default-material '() 'material-type)
(define-input-var geometry-lattice (make lattice) 'lattice)
(define-input-var geometry '() (make-list-type 'geometric-object))
(define-input-var ensure-periodicity true 'boolean)
(define-external-function point-in-object? true false
'boolean 'vector3 'geometric-object)
(define-external-function point-in-periodic-object? true false
'boolean 'vector3 'geometric-object)
; (define-external-function material-of-point true false
; 'material-type 'vector3)
(define-external-function display-geometric-object-info false false
no-return-value 'integer 'geometric-object)
(define-external-function square-basis false false
'matrix3x3 'matrix3x3 'vector3)
; ****************************************************************
; Functions and variables for determining the grid size
(define no-size 1e-20) ; for when a particular lattice dimension has no size
(define-param resolution 10) ; the resolution (may be a vector3)
(define-param grid-size false) ; force grid size, if set
(define (get-grid-size)
(if grid-size
grid-size
(let ((res (if (vector3? resolution)
resolution
(vector3 resolution resolution resolution))))
(vector-map
(lambda (x) (inexact->exact (max (ceiling x) 1)))
(vector-map * res (object-property-value geometry-lattice 'size))))))
(define (get-grid-size-prod)
(let ((s (get-grid-size)))
(* (vector3-x s) (vector3-y s) (vector3-z s))))
; ****************************************************************
; Cartesian conversion and rotation for lattice and reciprocal coords:
; The following conversion routines work for vector3 and matrix3x3 arguments:
(define (lattice->cartesian x)
(if (vector3? x)
(matrix3x3*
(object-property-value geometry-lattice 'basis) x)
(matrix3x3*
(matrix3x3*
(object-property-value geometry-lattice 'basis) x)
(matrix3x3-inverse (object-property-value geometry-lattice 'basis)))))
(define (cartesian->lattice x)
(if (vector3? x)
(matrix3x3*
(matrix3x3-inverse (object-property-value geometry-lattice 'basis)) x)
(matrix3x3*
(matrix3x3*
(matrix3x3-inverse (object-property-value geometry-lattice 'basis)) x)
(object-property-value geometry-lattice 'basis))))
(define (reciprocal->cartesian x)
(let ((s (vector-map
(lambda (x) (if (= x no-size) 1 x))
(object-property-value geometry-lattice 'size))))
(let ((Rst
(matrix3x3-transpose
(matrix3x3* (object-property-value geometry-lattice 'basis)
(matrix3x3 (vector3 (vector3-x s) 0 0)
(vector3 0 (vector3-y s) 0)
(vector3 0 0 (vector3-z s)))))))
(if (vector3? x)
(matrix3x3* (matrix3x3-inverse Rst) x)
(matrix3x3* (matrix3x3* (matrix3x3-inverse Rst) x) Rst)))))
(define (cartesian->reciprocal x)
(let ((s (vector-map
(lambda (x) (if (= x no-size) 1 x))
(object-property-value geometry-lattice 'size))))
(let ((Rst
(matrix3x3-transpose
(matrix3x3* (object-property-value geometry-lattice 'basis)
(matrix3x3 (vector3 (vector3-x s) 0 0)
(vector3 0 (vector3-y s) 0)
(vector3 0 0 (vector3-z s)))))))
(if (vector3? x)
(matrix3x3* Rst x)
(matrix3x3* (matrix3x3* Rst x) (matrix3x3-inverse Rst))))))
(define (lattice->reciprocal x) (cartesian->reciprocal (lattice->cartesian x)))
(define (reciprocal->lattice x) (cartesian->lattice (reciprocal->cartesian x)))
; rotate vectors in lattice/reciprocal coords (note that the axis
; is also given in the corresponding basis):
(define (rotate-lattice-vector3 axis theta v)
(cartesian->lattice
(rotate-vector3 (lattice->cartesian axis) theta
(lattice->cartesian v))))
(define (rotate-reciprocal-vector3 axis theta v)
(cartesian->reciprocal
(rotate-vector3 (reciprocal->cartesian axis) theta
(reciprocal->cartesian v))))
; ****************************************************************
|
