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
|
;;; Modifications to the basic R-tree following "THE R+-TREE: A
;;; DYNAMIC INDEX FOR MULTI-DIMENSIONAL OBJECTS", Sellis, Roussopoulos
;;; and Faloutsos, Proc. 15th Int. Conf. on Very Large Databases,
;;; 1987
;;;
;;; By this stage, not very much of the original R-tree is left, mind
;;; you.
(in-package "SPATIAL-TREES-IMPL")
(defclass r+-tree (r-tree)
((fill-factor :initarg :fill-factor :accessor fill-factor)))
(defmethod make-spatial-tree :around ((kind (eql :r+)) &rest initargs)
(declare (ignore initargs))
(cerror "Make an R+-tree nevertheless"
"R+-trees' dynamic insertion is broken.")
(call-next-method))
(defmethod make-spatial-tree ((kind (eql :r+)) &rest initargs)
(apply #'make-instance 'r+-tree
:root-node (make-instance 'spatial-tree-leaf-node :records nil)
initargs))
(defmethod initialize-instance :after ((tree r+-tree) &rest args)
(declare (ignore args))
(unless (slot-boundp tree 'fill-factor)
(setf (slot-value tree 'fill-factor)
(round (* (max-per-node tree) 1/3)))))
(defmethod search :around ((r rectangle) (tree r+-tree))
(remove-duplicates (call-next-method)))
;;; 3.3. Insertion
(defmethod insert ((r t) (tree r+-tree))
(labels ((%insert (r node tree)
(cond
((typep node 'spatial-tree-leaf-node)
(if (>= (length (records node)) (max-per-node tree))
(split-node tree r node)
(push r (records node))))
(t (dolist (child (children node))
(when (intersectp (mbr child tree) (mbr r tree))
(%insert r child tree)))))))
(%insert r (root-node tree) tree)
tree))
;;; 3.4. Deletion
(defun unlink-node (node tree)
(cond
((eq node (root-node tree)))
(t (let ((parent (parent node)))
(cond
((= (length (children parent)) 1)
(if (eq parent (root-node tree))
(setf (root-node tree)
(make-instance 'spatial-tree-leaf-node :records nil))
(unlink-node parent tree)))
(t
(setf (children parent) (remove node (children parent))
(slot-value parent 'mbr) (minimum-bound-of (children parent) tree))))))))
(defmethod delete ((r t) (tree r+-tree))
(labels ((%delete (r node tree)
(cond
((typep node 'spatial-tree-leaf-node)
(setf (records node) (remove r (records node)))
(when (null (records node))
(unlink-node node tree)))
(t (dolist (child (children node))
(when (intersectp (mbr child tree) (mbr r tree))
(%delete r child tree)))))))
(%delete r (root-node tree) tree)
tree))
;;; 3.5. Node Splitting
(defun cost (r1 r2)
(+ (area r1) (area r2)))
(defun generate-partition-rectangles (entries tree)
(let ((mbr (minimum-bound-of entries tree)))
(do* ((lows (lows (mbr (car entries) tree)) (cdr lows))
(axis 0 (1+ axis))
(mincost)
(low)
(high))
((null lows) (values low high))
(let ((sorted (sort (copy-list entries) #'<
:key (lambda (x) (nth axis (lows (mbr x tree)))))))
(cond
;; FIXME: this is the wrong way to write a loop which needs
;; initialization. There are a number of these dotted around
;; now.
((null mincost)
(let* ((one (subseq sorted 0 (fill-factor tree)))
(two (subseq sorted (fill-factor tree)))
(new-low-coordinate
(/ (+ (nth axis (highs (mbr (car (last one)) tree)))
(nth axis (lows (mbr (car two) tree))))
2)))
;; FIXME: this does not guarantee optimality, because if
;; one and two do not overlap we can shrink this high
;; rectangle to the MBR of two.
(setf low (make-rectangle
:lows (lows mbr)
:highs (substitute-if new-low-coordinate (constantly t)
(highs mbr) :start axis :count 1))
high (make-rectangle
:lows (substitute-if new-low-coordinate (constantly t)
(lows mbr) :start axis :count 1)
:highs (highs mbr))
mincost (cost low high))))
(t
(let* ((one (subseq sorted 0 (fill-factor tree)))
(two (subseq sorted (fill-factor tree)))
(new-low-coordinate
(/ (+ (nth axis (highs (mbr (car (last one)) tree)))
(nth axis (lows (mbr (car two) tree))))
2))
(new-low (make-rectangle
:lows (lows mbr)
:highs (substitute-if
new-low-coordinate (constantly t)
(highs mbr) :start axis :count 1)))
(new-high (make-rectangle
:lows (substitute-if
new-low-coordinate (constantly t)
(lows mbr) :start axis :count 1)
:highs (highs mbr)))
(cost (cost new-low new-high)))
(when (< cost mincost)
(setf mincost cost
low new-low
high new-high)))))))))
(defun split-node-by (tree node entries rone rtwo)
(let ((new-node (make-node-like node)))
(setf (children node) nil
(children new-node) nil)
(dolist (entry entries)
(cond
((null (intersection rone (mbr entry tree)))
(push entry (children new-node))
(unless (typep node 'spatial-tree-leaf-node)
(setf (parent entry) new-node)))
((null (intersection rtwo (mbr entry tree)))
(push entry (children node))
(unless (typep node 'spatial-tree-leaf-node)
(setf (parent entry) node)))
((typep node 'spatial-tree-leaf-node)
(push entry (records new-node))
(push entry (records node)))
(t (let ((new (split-node-by tree entry (children entry) rone rtwo)))
(push new (children new-node))
(setf (parent new) new-node)
(push entry (children node))
(setf (parent entry) node)))))
(setf (slot-value node 'mbr) (intersection rone (minimum-bound-of (children node) tree))
(slot-value new-node 'mbr) (intersection rtwo (minimum-bound-of (children new-node) tree)))
new-node))
(defmethod split-node ((tree r+-tree) new node)
(let ((entries (cons new (children node))))
(multiple-value-bind (rone rtwo)
(generate-partition-rectangles entries tree)
(let ((new-node (split-node-by tree node entries rone rtwo)))
(if (eq (root-node tree) node)
(let ((new-root (make-instance 'spatial-tree-node
:children (list node new-node))))
(setf (root-node tree) new-root
(parent node) new-root
(parent new-node) new-root))
(let ((pr (parent node)))
(if (>= (length (children pr)) (max-per-node tree))
(split-node tree new-node pr)
(progn
(push new-node (children pr))
(setf (parent new-node) pr)))))))))
|
