├── __init__.py ├── Readme.txt ├── pm1quadtree_use.py ├── use_rtree.py ├── pm3quadtree.py ├── kdtree3.py ├── pointquadtree3.py ├── prkdtree2.py ├── prkdtree3.py ├── kdtree2a.py ├── kdtree2b.py ├── pm1quadtree.py ├── rtree1.py ├── pointquadtree1.py ├── extent.py ├── pointquadtree2.py ├── pmquadtree.py ├── pm2quadtree.py ├── prkdtree1.py ├── bst.py ├── kdtree1.py ├── rtree2.py └── LICENSE /__init__.py: -------------------------------------------------------------------------------- 1 | -------------------------------------------------------------------------------- /Readme.txt: -------------------------------------------------------------------------------- 1 | Algorithms for indexing spatial data 2 | -------------------------------------------------------------------------------- /pm1quadtree_use.py: -------------------------------------------------------------------------------- 1 | import pickle 2 | from pm1quadtree import * 3 | from xdcel import * 4 | 5 | import sys 6 | sys.path.append('../contrib') 7 | from dcel import * 8 | 9 | D = pickle.load(open('../data/mydcel.pickle')) 10 | XD = Xdcel(D) 11 | 12 | X = [v.x for v in D.vertices] 13 | Y = [v.y for v in D.vertices] 14 | xmin,xmax,ymin,ymax = min(X)-1, max(X)+1, min(Y)-1, max(Y)+1 15 | maxmax = max(xmax,ymax) 16 | xmax=ymax=maxmax 17 | extent = Extent(xmin, xmax, ymin, ymax) 18 | 19 | pmq = PMQuadTreeNode(extent.getcenter(), extent) 20 | split_by_points(XD.vertices, pmq) 21 | split_by_edges_pm1(XD.edges, pmq) 22 | print search_pmquadtree(pmq, 1, 1) 23 | print search_pmquadtree(pmq, 1, 2) 24 | print search_pmquadtree(pmq, 6, 5) 25 | -------------------------------------------------------------------------------- /use_rtree.py: -------------------------------------------------------------------------------- 1 | """ 2 | Example of using R-tree 3 | 4 | Contact: 5 | Ningchuan Xiao 6 | The Ohio State University 7 | Columbus, OH 8 | """ 9 | 10 | __author__ = "Ningchuan Xiao " 11 | 12 | from rtree1 import * 13 | from rtree2 import * 14 | 15 | MBRs = [ [10,17,3,7], # R14 16 | [12,16,4,6], # R12 17 | [7,9,0,5], # R10 18 | [1,8,1,4], # R11 19 | [1,2,6,11], # R8 20 | [15,18,0,2], # R13 21 | [0,3,3,12], # R9 22 | [13,15,14,18], # R16 23 | [10,18,12,15], # R15 24 | [14,17,9,16] ] # R17 25 | 26 | M = 3 27 | root = RTreeNode(M, None) 28 | 29 | extents = [Extent(mbr[0], mbr[1], mbr[2], mbr[3]) 30 | for mbr in MBRs] 31 | for e in extents: 32 | n = search_rtree_extent(root, e) 33 | insert(n, e) 34 | 35 | root.get_all_leaves() 36 | -------------------------------------------------------------------------------- /pm3quadtree.py: -------------------------------------------------------------------------------- 1 | from xdcel import * 2 | from pmquadtree import * 3 | import pickle 4 | 5 | def split_by_edges_pm3(edges, pmq): 6 | subedges = [] 7 | for e in edges: 8 | if is_intersect(pmq.extent, e): 9 | subedges.append(e) 10 | elif pmq.extent.contains(e.fr) and\ 11 | pmq.extent.contains(e.to): 12 | subedges.append(e) 13 | if not pmq.is_leaf(): 14 | for i in range(4): 15 | split_by_edges_pm3(subedges, pmq.quads[i]) 16 | return 17 | if len(subedges) == 0: 18 | pmq.type = WHITE 19 | return 20 | else: 21 | pmq.type = BLACK 22 | for e in subedges: 23 | pmq.edges.append(e) 24 | return 25 | 26 | def test(): 27 | D = pickle.load(open('../data/mydcel.pickle')) 28 | XD = Xdcel(D) 29 | 30 | X = [v.x for v in D.vertices] 31 | Y = [v.y for v in D.vertices] 32 | xmin,xmax,ymin,ymax = min(X)-1, max(X)+1,\ 33 | min(Y)-1, max(Y)+1 34 | maxmax = max(xmax,ymax) 35 | xmax=ymax=maxmax 36 | extent = Extent(xmin, xmax, ymin, ymax) 37 | 38 | pm3q = PMQuadTreeNode(extent.getcenter(), extent) 39 | split_by_points(XD.vertices, pm3q) 40 | split_by_edges_pm3(XD.edges, pm3q) 41 | print search_pmquadtree(pm3q, 1, 1) 42 | 43 | if __name__ == '__main__': 44 | test() 45 | -------------------------------------------------------------------------------- /kdtree3.py: -------------------------------------------------------------------------------- 1 | """ 2 | k-D trees. Part 3. 3 | 4 | Nearest neighbor search using point k-D trees 5 | 6 | Contact: 7 | Ningchuan Xiao 8 | The Ohio State University 9 | Columbus, OH 10 | """ 11 | 12 | __author__ = "Ningchuan Xiao " 13 | 14 | INF = float('inf') 15 | maxdist = INF 16 | 17 | def update_neighbors(p0, p, neighbors, n): 18 | d = p0.distance(p) 19 | for i, x in enumerate(neighbors): 20 | if i == n: 21 | return neighbors[n-1][1] 22 | if d < x[1]: 23 | neighbors.insert(i, [p0, d]) 24 | if len(neighbors) < n: 25 | return INF 26 | return neighbors[n-1][1] 27 | neighbors.append([p0, d]) 28 | return INF 29 | 30 | def nnquery(t, p, n, found, depth=0): 31 | global maxdist 32 | if t is None: 33 | return 34 | if t.left == None and t.right == None: 35 | maxdist = update_neighbors(t.point, p, found, n) 36 | return 37 | axis = depth % len(p) 38 | if p[axis] < t.point[axis]: 39 | nearer_tree, farther_tree = t.left, t.right 40 | else: 41 | nearer_tree, farther_tree = t.right, t.left 42 | nnquery(nearer_tree, p, n, found, depth+1) 43 | maxdist = update_neighbors(t.point, p, found, n) 44 | if abs(t.point[axis]-p[axis]) < maxdist: # must check the far side 45 | nnquery(farther_tree, p, n, found, depth+1) 46 | return 47 | 48 | def kdtree_nearest_neighbor_query(t, p, n=1): 49 | nearest_neighbors = [] 50 | nnquery(t, p, n, nearest_neighbors) 51 | return nearest_neighbors[:n] 52 | -------------------------------------------------------------------------------- /pointquadtree3.py: -------------------------------------------------------------------------------- 1 | """ 2 | Point quadtree. Part 3. 3 | 4 | Nearest neighbor query 5 | 6 | Contact: 7 | Ningchuan Xiao 8 | The Ohio State University 9 | Columbus, OH 10 | """ 11 | 12 | __author__ = "Ningchuan Xiao " 13 | 14 | INF = float('inf') 15 | pqmaxdist = INF 16 | 17 | import sys 18 | sys.path.append('..') 19 | from indexing.kdtree3 import * 20 | 21 | # returns the quad of t where p is located 22 | # 0-NW, 1-NE, 2-SE, 3-SW 23 | def pqcompare(t, p): 24 | if p.x=t.point.y: 27 | return 0 28 | elif p.x>=t.point.x and p.y 0: 12 | rquery(t.right, p, r, found, depth+1) 13 | return 14 | if prkdcompare(t, Point(p.x+r+w, p.y+r+h), 15 | depth)[1] < 0: 16 | rquery(t.left, p, r, found, depth+1) 17 | return 18 | if t.point is not None: 19 | if p.distance(t.point) <= r: 20 | found.append(t.point) 21 | rquery(t.left, p, r, found, depth+1) 22 | rquery(t.right, p, r, found, depth+1) 23 | return 24 | found = [] 25 | if t is not None: 26 | rquery(t, p, r, found) 27 | return found 28 | 29 | if __name__ == '__main__': 30 | import sys 31 | sys.path.append('../') 32 | from geom.point import * 33 | data1 = [ (2,2), (0,5), (8,0), (9,8), (7,14), 34 | (13,12), (14,13) ] 35 | points = [Point(d[0], d[1]) for d in data1] 36 | px = [p.x for p in points] 37 | py = [p.y for p in points] 38 | xmin = min(px) 39 | xmax = max(px) 40 | ymin = min(py) 41 | ymax = max(py) 42 | xylim = [ [xmin, xmax], [ymin, ymax] ] 43 | t = prkdtree(points, xylim) 44 | p = Point(5,5) 45 | print range_query(t, p, 5) 46 | -------------------------------------------------------------------------------- /prkdtree3.py: -------------------------------------------------------------------------------- 1 | from prkdtree1 import * 2 | from kdtree3 import * # use update_neighbors and INF 3 | 4 | prmaxdist = INF 5 | 6 | def prkdtree_nnquery(t, p, n, found, depth=0): 7 | global prmaxdist 8 | if t is None: 9 | return 10 | if t.is_leaf() and t.point is not None: #*@\label{prkdtree3:diff1} 11 | prmaxdist = update_neighbors(t.point, p, found, n) 12 | return 13 | axis,dir = prkdcompare(t, p, depth) 14 | if dir<0: 15 | nearer_tree, farther_tree = t.left, t.right 16 | else: 17 | nearer_tree, farther_tree = t.right, t.left 18 | prkdtree_nnquery(nearer_tree, p, n, found, depth+1) 19 | #prmaxdist = update_neighbors(t.point, p, found, n) #*@\label{prkdtree3:diff2} 20 | if (t.center-p[axis]) < prmaxdist: 21 | prkdtree_nnquery(farther_tree, p, n, found, depth+1) 22 | return 23 | 24 | def nearest_neighbor_query(t, p, n=1): 25 | nearest_neighbors = [] 26 | prkdtree_nnquery(t, p, n, nearest_neighbors) 27 | return nearest_neighbors[:n] 28 | 29 | if __name__ == '__main__': 30 | import sys 31 | sys.path.append('../') 32 | from geom.point import * 33 | data1 = [ (2,2), (0,5), (8,0), (9,8), (7,14), 34 | (13,12), (14,13) ] 35 | points = [Point(d[0], d[1]) for d in data1] 36 | px = [p.x for p in points] 37 | py = [p.y for p in points] 38 | xmin = min(px) 39 | xmax = max(px) 40 | ymin = min(py) 41 | ymax = max(py) 42 | xylim = [ [xmin, xmax], [ymin, ymax] ] 43 | t = prkdtree(points, xylim) 44 | n = 3 45 | p = Point(5,5) 46 | nearests = nearest_neighbor_query(t, p, n) 47 | print [x[0] for x in nearests[:n]] 48 | print [x[1] for x in nearests[:n]] 49 | print sorted([p.distance(x) for x in points])[:n] 50 | -------------------------------------------------------------------------------- /kdtree2a.py: -------------------------------------------------------------------------------- 1 | """ 2 | k-D trees, Part 2a. 3 | 4 | Rectangle range query of point k-D trees 5 | 6 | Contact: 7 | Ningchuan Xiao 8 | The Ohio State University 9 | Columbus, OH 10 | """ 11 | 12 | __author__ = "Ningchuan Xiao " 13 | 14 | import sys 15 | sys.path.append('..') 16 | from indexing.kdtree1 import * 17 | 18 | def range_query_orthogonal(t, rect, found, depth=0): 19 | """ 20 | Orthogonal (rectangular) range search for points 21 | 22 | Input 23 | t: node of a point k-D tree 24 | rect: 2D list defining a rectangle as [ [xmin, xmax], [ymin, ymax] ] 25 | found: a list to hold points found, declared outside 26 | 27 | Output 28 | This function does not return any values. However, all the points 29 | found during the query process will be appended to list found. 30 | """ 31 | if t is None: 32 | return 33 | k = len(t.point) 34 | axis = depth%k 35 | if t.point[axis] < rect[axis][0]: 36 | range_query_orthogonal(t.right, rect, found, depth+1) 37 | return 38 | if t.point[axis] > rect[axis][1]: 39 | range_query_orthogonal(t.left, rect, found, depth+1) 40 | return 41 | x, y = t.point.x, t.point.y 42 | if not (rect[0][0]>x or rect[0][1]y or rect[1][1]0: 35 | range_query_circular(t.right, p, r, found, depth+1) 36 | return 37 | if kdcompare(t, Point(p.x+r, p.y+r), depth)<0: 38 | range_query_circular(t.left, p, r, found, depth+1) 39 | return 40 | if p.distance(t.point) <= r: 41 | found.append(t.point) 42 | range_query_circular(t.left, p, r, found, depth+1) 43 | range_query_circular(t.right, p, r, found, depth+1) 44 | return 45 | 46 | def kdtree_range_query_circular(t, p, r): 47 | found = [] 48 | range_query_circular(t, p, r, found) 49 | return found 50 | 51 | def test(): 52 | data1 = [ (2,2), (0,5), (8,0), (9,8), (7,14), 53 | (13,12), (14,13) ] 54 | points = [Point(d[0], d[1]) for d in data1] 55 | p = Point(5,5) 56 | t1 = kdtree(points) 57 | found = [] 58 | range_query_circular(t1, p, 5, found) 59 | print(found) 60 | 61 | if __name__ == '__main__': 62 | test() 63 | -------------------------------------------------------------------------------- /pm1quadtree.py: -------------------------------------------------------------------------------- 1 | from pmquadtree import * 2 | 3 | def split_by_edges_pm1(edges, pmq): 4 | subedges = [] 5 | for e in edges: 6 | if is_intersect(pmq.extent, e): 7 | subedges.append(e) 8 | elif pmq.extent.contains(e.fr) and\ 9 | pmq.extent.contains(e.to): 10 | subedges.append(e) 11 | if len(subedges) == 0: 12 | pmq.type = WHITE 13 | return 14 | if pmq.vertex is not None: 15 | is_same_source = True 16 | for e in subedges: 17 | if not e.is_endpoint(pmq.vertex): 18 | is_same_source = False 19 | if is_same_source: 20 | for e in subedges: 21 | pmq.edges.append(e) 22 | pmq.type = BLACK 23 | return 24 | else: # pmq does not contain a vertex 25 | if len(subedges) == 1: 26 | pmq.type = BLACK 27 | pmq.edges.append(subedges[0]) 28 | return 29 | if pmq.extent.is_minimal(): 30 | for e in subedges: 31 | pmq.edges.append(e) 32 | pmq.type = BLACK 33 | return 34 | if pmq.is_leaf(): # now we split this if necessary: 35 | xmin = pmq.extent.xmin 36 | xmax = pmq.extent.xmax 37 | ymin = pmq.extent.ymin 38 | ymax = pmq.extent.ymax 39 | xmid = xmin + (xmax-xmin)/2.0 40 | ymid = ymin + (ymax-ymin)/2.0 41 | exts = [ Extent(xmin, xmid, ymid, ymax), # nw 42 | Extent(xmid, xmax, ymid, ymax), # ne 43 | Extent(xmid, xmax, ymin, ymid), # se 44 | Extent(xmin, xmid, ymin, ymid) # sw 45 | ] 46 | pmq.quads = [ PMQuadTreeNode(exts[i].getcenter(), 47 | exts[i]) 48 | for i in range(4) ] 49 | if pmq.vertex: 50 | for q in pmq.quads: 51 | if q.extent.contains(pmq.vertex): 52 | q.vertex = pmq.vertex 53 | pmq.vertex = None 54 | for i in range(4): 55 | split_by_edges_pm1(subedges, pmq.quads[i]) 56 | 57 | -------------------------------------------------------------------------------- /rtree1.py: -------------------------------------------------------------------------------- 1 | """ 2 | R-tree, part 1 3 | 4 | Contact: 5 | Ningchuan Xiao 6 | The Ohio State University 7 | Columbus, OH 8 | """ 9 | 10 | __author__ = "Ningchuan Xiao " 11 | 12 | from extent import * 13 | 14 | class Entry(): 15 | def __init__(self, extent=None, child=None, 16 | parent=None, node=None): 17 | self.MBR = extent 18 | self.child = child # a child node 19 | self.node = node # node containing this entry 20 | def __repr__(self): 21 | return str(self.MBR) 22 | 23 | class RTreeNode(): 24 | def __init__(self, M, parent=None): 25 | self.entries = [] 26 | self.M = M 27 | self.parent = parent # an entry in the parent node 28 | self.extent = None 29 | def __getitem__(self, i): 30 | if i>=self.M or i>=len(self.entries): 31 | return None 32 | return self.entries[i] 33 | def __repr__(self): 34 | return str(self.extent) 35 | def is_leaf(self): 36 | for e in self.entries: 37 | if e.child is not None: 38 | return False 39 | return True 40 | def is_root(self): 41 | return self.parent is None 42 | def update(self): 43 | if not len(self.entries): 44 | return 45 | if self.entries[0] is not None: 46 | self.extent = self.entries[0].MBR 47 | for e in self.entries[1:]: 48 | self.extent = union_extent(self.extent, e.MBR) 49 | def update_up(self): 50 | self.update() 51 | if self.is_root(): 52 | return 53 | self.parent.MBR = self.extent 54 | self.parent.node.update_up() 55 | def get_all_leaves(self, depth=0): 56 | if not self.is_leaf(): 57 | for e in self.entries: 58 | e.child.get_all_leaves(depth+1) 59 | else: 60 | print depth, "-", self, self.entries 61 | return 62 | 63 | def union_extent(e1, e2): 64 | xmin = min(e1.xmin, e2.xmin) 65 | xmax = max(e1.xmax, e2.xmax) 66 | ymin = min(e1.ymin, e2.ymin) 67 | ymax = max(e1.ymax, e2.ymax) 68 | return Extent(xmin, xmax, ymin, ymax) 69 | -------------------------------------------------------------------------------- /pointquadtree1.py: -------------------------------------------------------------------------------- 1 | """ 2 | Point quadtree. Part 1. 3 | 4 | History: 5 | 6 | November 12, 2016 7 | 8 | The search_pqtree function now returns None if the point is found and 9 | is_find_only is set to False so that points will not be duplicated 10 | in the tree. 11 | 12 | November 19, 2015 13 | 14 | changed the two conditions in search_pqtree to: 15 | if p.x>=q.point.x 16 | and 17 | if p.y>=q.point.y 18 | 19 | This forces the consistency in how the four quads are determined in 20 | functions search_pqtree and insert_pqtree 21 | (Thanks to Hui Kong for examining the code!) 22 | 23 | Contact: 24 | Ningchuan Xiao 25 | The Ohio State University 26 | Columbus, OH 27 | """ 28 | 29 | __author__ = "Ningchuan Xiao " 30 | 31 | class PQuadTreeNode(): 32 | def __init__(self,point,nw=None,ne=None,se=None,sw=None): 33 | self.point = point 34 | self.nw = nw 35 | self.ne = ne 36 | self.se = se 37 | self.sw = sw 38 | def __repr__(self): 39 | return str(self.point) 40 | def is_leaf(self): 41 | return self.nw==None and self.ne==None and \ 42 | self.se==None and self.sw==None 43 | 44 | def search_pqtree(q, p, is_find_only=True): 45 | if q is None: 46 | return 47 | if q.point == p: 48 | if is_find_only: 49 | return q 50 | else: 51 | return 52 | dx,dy = 0,0 53 | if p.x >= q.point.x: 54 | dx = 1 55 | if p.y >= q.point.y: 56 | dy = 1 57 | qnum = dx+dy*2 58 | child = [q.sw, q.se, q.nw, q.ne][qnum] 59 | if child is None and not is_find_only: 60 | return q 61 | return search_pqtree(child, p, is_find_only) 62 | 63 | def insert_pqtree(q, p): 64 | n = search_pqtree(q, p, False) 65 | node = PQuadTreeNode(point=p) 66 | if p.x < n.point.x and p.y < n.point.y: 67 | n.sw = node 68 | elif p.x < n.point.x and p.y >= n.point.y: 69 | n.nw = node 70 | elif p.x >= n.point.x and p.y < n.point.y: 71 | n.se = node 72 | else: 73 | n.ne = node 74 | 75 | def pointquadtree(data): 76 | root = PQuadTreeNode(point = data[0]) 77 | for p in data[1:]: 78 | insert_pqtree(root, p) 79 | return root 80 | -------------------------------------------------------------------------------- /extent.py: -------------------------------------------------------------------------------- 1 | """ 2 | Extent class 3 | 4 | Contact: 5 | Ningchuan Xiao 6 | The Ohio State University 7 | Columbus, OH 8 | """ 9 | 10 | __author__ = "Ningchuan Xiao " 11 | 12 | # import sys 13 | # sys.path.append('../geom') 14 | # from point import * 15 | # 16 | from math import sqrt 17 | 18 | class Extent(): 19 | def __init__(self, xmin=0, xmax=0, ymin=0, ymax=0): 20 | self.xmin = xmin 21 | self.xmax = xmax 22 | self.ymin = ymin 23 | self.ymax = ymax 24 | def __getitem__(self, i): 25 | if i==0: return self.xmin 26 | if i==1: return self.xmax 27 | if i==2: return self.ymin 28 | if i==3: return self.ymax 29 | return None 30 | def __repr__(self): 31 | return "[{0}, {1}, {2}, {3}]".format( 32 | self.xmin, self.xmax ,self.ymin, self.ymax) 33 | def __eq__(self, other): 34 | return self.xmin==other.xmin and\ 35 | self.xmax==other.xmax and \ 36 | self.ymin==other.ymin and \ 37 | self.ymax==other.ymax 38 | def touches(self, other): 39 | return not (self.xmin>other.xmax or\ 40 | self.xmaxother.ymax or\ 42 | self.ymaxpoint.x or\ 45 | self.xmaxpoint.y or\ 47 | self.ymaxymax: 38 | rquery(t.se, p, r, found) 39 | return 40 | elif x>xmax and y>ymax: 41 | rquery(t.sw, p, r, found) 42 | return 43 | elif x>xmax and y xmax: 56 | rquery(t.nw, p, r, found) # left points only 57 | rquery(t.sw, p, r, found) 58 | return 59 | if y > ymax: 60 | rquery(t.se, p, r, found) # below points only 61 | rquery(t.sw, p, r, found) 62 | return 63 | if p.distance(t.point) <= r: 64 | found.append(t.point) 65 | rquery(t.nw, p, r, found) 66 | rquery(t.ne, p, r, found) 67 | rquery(t.se, p, r, found) 68 | rquery(t.sw, p, r, found) 69 | return 70 | found = [] 71 | if t is not None: 72 | rquery(t, p, r, found) 73 | return found 74 | 75 | def test(): 76 | count = 0 77 | data = [ [i, j] for i in range(100) for j in range(100) ] 78 | points = [Point(d[0], d[1]) for d in data] 79 | q = pointquadtree(points) 80 | time1 = time.time() 81 | found = range_query(q, Point(50, 50), 2) 82 | time2 = time.time() 83 | print(count) 84 | print(found) 85 | print(time2-time1) 86 | 87 | if __name__ == "__main__": 88 | import sys 89 | sys.path.append('../geom') 90 | from point import * 91 | from pointquadtree1 import * 92 | import time 93 | test() 94 | -------------------------------------------------------------------------------- /pmquadtree.py: -------------------------------------------------------------------------------- 1 | # Used by all PM quadtrees 2 | import sys 3 | sys.path.append('../geom') 4 | from point import * 5 | from linesegment import Segment 6 | from intersection import test_intersect 7 | from extent import * 8 | 9 | BLACK = 2 # nodes with point or line 10 | WHITE = 1 # nodes with no point or line intersecing 11 | GREY = 0 # intermediate nodes 12 | 13 | class PMQuadTreeNode(): 14 | def __init__(self, point, extent, 15 | nw=None, ne=None, se=None, sw=None): 16 | self.point = point # center 17 | self.extent = extent 18 | self.quads = [nw, ne, se, sw] 19 | self.vertex = None 20 | self.edges = [] 21 | self.type = GREY 22 | def __repr__(self): 23 | return str(self.point) 24 | def __getitem__(self, i): 25 | if i<4: return self.quads[i] 26 | return None 27 | def is_leaf(self): 28 | return sum([ q is None for q in self.quads])==4 29 | 30 | def split_by_points(points, pmq): 31 | if len(points) == 1: 32 | pmq.vertex = points[0] 33 | pmq.type = BLACK 34 | return 35 | if len(points) ==0: 36 | pmq.type = WHITE 37 | return 38 | xmin = pmq.extent.xmin 39 | xmax = pmq.extent.xmax 40 | ymin = pmq.extent.ymin 41 | ymax = pmq.extent.ymax 42 | xmid = xmin + (xmax-xmin)/2.0 43 | ymid = ymin + (ymax-ymin)/2.0 44 | exts = [ Extent(xmin, xmid, ymid, ymax), # nw 45 | Extent(xmid, xmax, ymid, ymax), # ne 46 | Extent(xmid, xmax, ymin, ymid), # se 47 | Extent(xmin, xmid, ymin, ymid) # sw 48 | ] 49 | pmq.quads = [PMQuadTreeNode(exts[i].getcenter(),exts[i]) 50 | for i in range(4)] 51 | subpoints = [[], [], [], []] # four empty points lists 52 | for p in points: 53 | for i in range(4): 54 | if exts[i].contains(p): 55 | subpoints[i].append(p) 56 | for i in range(4): 57 | split_by_points(subpoints[i], pmq.quads[i]) 58 | 59 | def search_pmquadtree(pmq, x, y): 60 | if pmq.type is not GREY: 61 | return pmq 62 | for q in pmq.quads: 63 | if q.extent.contains(Point(x, y)): 64 | return search_pmquadtree(q, x, y) 65 | return None 66 | 67 | def is_intersect(extent, edge): 68 | if not extent.touches(edge.extent()): 69 | return False 70 | # four corners clockwise 71 | p1 = Point(extent.xmin, extent.ymin) 72 | p2 = Point(extent.xmin, extent.ymax) 73 | p3 = Point(extent.xmax, extent.ymax) 74 | p4 = Point(extent.xmax, extent.ymin) 75 | segs = [ Segment(0, p1, p2), Segment(1, p2, p3), 76 | Segment(2, p3, p4), Segment(3, p4, p1) ] 77 | s0 = Segment(4, edge.fr, edge.to) 78 | for s in segs: 79 | if test_intersect(s, s0): 80 | return True 81 | return False 82 | -------------------------------------------------------------------------------- /pm2quadtree.py: -------------------------------------------------------------------------------- 1 | from xdcel import * 2 | from pmquadtree import * 3 | import pickle 4 | 5 | def split_by_edges_pm2(edges, pmq): 6 | subedges = [] 7 | for e in edges: 8 | if is_intersect(pmq.extent, e): 9 | subedges.append(e) 10 | elif pmq.extent.contains(e.fr) and\ 11 | pmq.extent.contains(e.to): 12 | subedges.append(e) 13 | if len(subedges) == 0: 14 | pmq.type = WHITE 15 | return 16 | elif len(subedges) == 1: 17 | pmq.type = BLACK 18 | pmq.edges.append(subedges[0]) 19 | return 20 | else: 21 | p1,p2 = subedges[0].fr, subedges[0].to 22 | common_vertex = None 23 | if subedges[1].is_endpoint(p1): 24 | common_vertex = p1 25 | elif subedges[1].is_endpoint(p2): 26 | common_vertex = p2 27 | if common_vertex is not None: 28 | for e in subedges[2:]: 29 | if not e.is_endpoint(common_vertex): 30 | common_vertex = None 31 | break 32 | if common_vertex is not None: 33 | for e in subedges: 34 | pmq.edges.append(e) 35 | pmq.type = BLACK 36 | return 37 | if pmq.extent.is_minimal(): 38 | for e in subedges: 39 | pmq.edges.append(e) 40 | pmq.type = BLACK 41 | return 42 | if pmq.is_leaf(): 43 | xmin = pmq.extent.xmin 44 | xmax = pmq.extent.xmax 45 | ymin = pmq.extent.ymin 46 | ymax = pmq.extent.ymax 47 | xmid = xmin + (xmax-xmin)/2.0 48 | ymid = ymin + (ymax-ymin)/2.0 49 | exts = [ Extent(xmin, xmid, ymid, ymax), # nw 50 | Extent(xmid, xmax, ymid, ymax), # ne 51 | Extent(xmid, xmax, ymin, ymid), # se 52 | Extent(xmin, xmid, ymin, ymid) # sw 53 | ] 54 | pmq.quads = [ PMQuadTreeNode(exts[i].getcenter(), 55 | exts[i]) 56 | for i in range(4) ] 57 | if pmq.vertex: 58 | for q in pmq.quads: 59 | if q.extent.contains(pmq.vertex): 60 | q.vertex = pmq.vertex 61 | pmq.vertex = None 62 | for i in range(4): 63 | split_by_edges_pm2(subedges, pmq.quads[i]) 64 | 65 | def test(): 66 | D = pickle.load(open('../data/mydcel.pickle')) 67 | XD = Xdcel(D) 68 | 69 | X = [v.x for v in D.vertices] 70 | Y = [v.y for v in D.vertices] 71 | xmin,xmax,ymin,ymax = min(X)-1, max(X)+1,\ 72 | min(Y)-1, max(Y)+1 73 | maxmax = max(xmax,ymax) 74 | xmax=ymax=maxmax 75 | extent = Extent(xmin, xmax, ymin, ymax) 76 | 77 | pm2q = PMQuadTreeNode(extent.getcenter(), extent) 78 | split_by_points(XD.vertices, pm2q) 79 | split_by_edges_pm2(XD.edges, pm2q) 80 | print search_pmquadtree(pm2q, 10, 10) 81 | 82 | if __name__ == '__main__': 83 | test() 84 | 85 | -------------------------------------------------------------------------------- /prkdtree1.py: -------------------------------------------------------------------------------- 1 | from bisect import * 2 | 3 | class PRKDTreeNode(): 4 | def __init__(self, xyrange, center, point, left, right): 5 | self.xyrange = xyrange # ranges of xy 6 | self.center = center # center coordinate 7 | self.point = point # point 8 | self.left = left # left child subtree 9 | self.right = right # right child subtree 10 | def is_leaf(self): 11 | return (self.left == None and self.right == None) 12 | def __repr__(self): 13 | return str(self.center) 14 | 15 | # r-root node of a subtree, p-point, depth-current depth 16 | def prkdcompare(r, p, depth): 17 | k = len(p) 18 | dim = depth%k 19 | if p[dim] <= r.center: 20 | return dim,-1 # left 21 | else: 22 | return dim,1 # right 23 | 24 | def prkdtree(points, xylim, center=None, depth=0): 25 | if len(points)==1: 26 | return PRKDTreeNode(xyrange=xylim, 27 | center=center, 28 | point=points[0], 29 | left=None, 30 | right=None) 31 | if len(points)==0: 32 | return PRKDTreeNode(xyrange=xylim, 33 | center=center, 34 | point=None, 35 | left=None, 36 | right=None) 37 | k = len(points[0]) 38 | axis = depth % k 39 | pmid = (xylim[axis][1]+xylim[axis][0])/2.0 40 | points.sort(key=lambda points:points[axis]) 41 | P = [p[axis] for p in points] 42 | pivot = bisect(P, pmid) # includes all <= 43 | xmin,xmax=xylim[0][0], xylim[0][1] 44 | ymin,ymax=xylim[1][0], xylim[1][1] 45 | rangel = [ [xmin, xmax], [ymin, ymax] ] 46 | rangel[axis][1] = pmid 47 | ranger = [ [xmin, xmax], [ymin, ymax] ] 48 | ranger[axis][0] = pmid 49 | axis2 = (depth+1) % k 50 | pmidl = (rangel[axis2][0]+rangel[axis2][1])/2.0 51 | pmidr = (ranger[axis2][0]+ranger[axis2][1])/2.0 52 | return PRKDTreeNode(xyrange = xylim, 53 | center = pmid, 54 | point = None, 55 | left=prkdtree(points[:pivot], 56 | rangel,pmidl,depth+1), 57 | right=prkdtree(points[pivot:], 58 | ranger,pmidr,depth+1)) 59 | 60 | # query if point p is in t 61 | def query_prkdtree(t, p, depth=0): 62 | if t is None: 63 | return 64 | if t.point == p: 65 | return p 66 | if t.is_leaf(): 67 | return 68 | if prkdcompare(t, p, depth)[1] < 0: 69 | next = t.left 70 | else: 71 | next = t.right 72 | p0 = query_prkdtree(next, p, depth+1) 73 | if p0 is not None: 74 | return p0 75 | return 76 | 77 | if __name__ == '__main__': 78 | import sys 79 | sys.path.append('../') 80 | from geom.point import * 81 | data1 = [ (2,2), (0,5), (8,0), (9,8), (7,14), 82 | (13,12), (14,13) ] 83 | points = [Point(d[0], d[1]) for d in data1] 84 | px = [p.x for p in points] 85 | py = [p.y for p in points] 86 | xmin = min(px) 87 | xmax = max(px) 88 | ymin = min(py) 89 | ymax = max(py) 90 | xylim = [ [xmin, xmax], [ymin, ymax] ] 91 | t = prkdtree(points, xylim) 92 | print [query_prkdtree(t, p) for p in points] 93 | -------------------------------------------------------------------------------- /bst.py: -------------------------------------------------------------------------------- 1 | """ 2 | Binary search trees 3 | 4 | Contact: 5 | Ningchuan Xiao 6 | The Ohio State University 7 | Columbus, OH 8 | """ 9 | 10 | __author__ = "Ningchuan Xiao " 11 | 12 | class node(): 13 | def __init__(self, data, left, right): 14 | self.data = data 15 | self.left = left 16 | self.right = right 17 | def __repr__(self): 18 | return str(self.data) 19 | 20 | def search_bt(t, d, is_find_only=True): 21 | """ 22 | Input 23 | t: a node of a binary tree 24 | d: target data to be found in the tree 25 | is_find_only: True/False, specifying type of output 26 | 27 | Output 28 | the node that contans d or None if is_find_only is True, otherwise 29 | the node that should be the parent node of d 30 | """ 31 | if t is None: 32 | return 33 | if t.data == d: 34 | if is_find_only: 35 | return t 36 | else: 37 | return 38 | if d < t.data: 39 | next = t.left 40 | else: 41 | next = t.right 42 | if is_find_only==False and next is None: 43 | return t 44 | return search_bt(next, d, is_find_only) 45 | 46 | def insert(t, d): 47 | n = search_bt(t, d, False) 48 | if n is None: 49 | return 50 | n0 = node(d, left=None, right=None) 51 | if d < n.data: 52 | n.left = n0 53 | else: 54 | n.right = n0 55 | 56 | def bt(data): 57 | root = node(data=data[0], left=None, right=None) 58 | for d in data[1:]: 59 | insert(root, d) 60 | return root 61 | 62 | def search_bt_loop(t, d, is_find_only=True): 63 | """ 64 | similar to search_bt, but use a while loop instead of recursive 65 | """ 66 | while True: 67 | if t is None: 68 | return 69 | if t.data == d: 70 | if is_find_only: 71 | return t 72 | else: 73 | return 74 | if d < t.data: 75 | next = t.left 76 | else: 77 | next = t.right 78 | if not is_find_only and next is None: 79 | return t 80 | t = next 81 | 82 | def insert_loop(t, d): 83 | n = search_bt_loop(t, d, False) 84 | if n is None: 85 | return 86 | n0 = node(d, left=None, right=None) 87 | if d < n.data: 88 | n.left = n0 89 | else: 90 | n.right = n0 91 | 92 | def bt_loop(data): 93 | root = node(data=data[0], left=None, right=None) 94 | for d in data[1:]: 95 | insert_loop(root, d) 96 | return root 97 | 98 | def bt_print(t): 99 | if t.left: 100 | bt_print(t.left) 101 | print(t) 102 | if t.right: 103 | bt_print(t.right) 104 | 105 | def tree_print(t): 106 | """ 107 | This is adopted from the MIT OpenCourseWare at 108 | https://ocw.mit.edu/courses/6-006-introduction-to-algorithms-fall-2011/7f7ba1c1c85b1ec4bd58965bfe791489_bst.py 109 | 110 | The old link does not work: 111 | http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-006-introduction-to-algorithms-fall-2011/readings/binary-search-trees/bst.py 112 | 113 | Now supports Python 3 114 | """ 115 | def tree_print_helper(t): 116 | if t is None: 117 | return [], 0, 0 118 | # label = str(t.key) 119 | label = str(t) 120 | leftstr, leftpos, leftwidth = tree_print_helper(t.left) 121 | rightstr, rightpos, rightwidth = tree_print_helper(t.right) 122 | middle = max(rightpos+leftwidth - leftpos+1, len(label), 2) # length 123 | pos = leftpos + middle // 2 # pos of current node 124 | width = leftpos + middle + rightwidth - rightpos 125 | while len(leftstr)maxdist: 42 | maxdist = d 43 | maxi = i 44 | maxj = j 45 | e1 = tmpentries[maxi] 46 | e2 = tmpentries[maxj] 47 | allexts = [] # holds the rest of the MBRs 48 | for ext in tmpentries: 49 | if ext is not e1 and ext is not e2: 50 | allexts.append(ext) 51 | L1.entries.append(e1) 52 | L2.entries.append(e2) 53 | L1.update() 54 | L2.update() 55 | while len(allexts): 56 | numremained = len(allexts) 57 | gotonode = None 58 | if len(L1.entries) == m-numremained: 59 | gotonode = L1 60 | elif len(L2.entries) == m-numremained: 61 | gotonode = L2 62 | if gotonode is not None: 63 | while len(allexts): 64 | ext = allexts.pop() 65 | gotonode.entries.append(ext) 66 | else: 67 | minarea = union_extent(L1.extent,L2.extent).area() 68 | minext = -1 69 | gotonode = None 70 | for i in range(len(allexts)): 71 | tmpext1 = union_extent(L1.extent, 72 | allexts[i].MBR) 73 | tmparea1 = tmpext1.area() - L1.extent.area() 74 | tmpext2 = union_extent(L2.extent, 75 | allexts[i].MBR) 76 | tmparea2 = tmpext2.area() - L2.extent.area() 77 | if min(tmparea1, tmparea2) > minarea: 78 | continue 79 | minext = i 80 | if tmparea1 < tmparea2: 81 | if tmparea1 < minarea: 82 | tmpgotonode = L1 83 | minarea = tmparea1 84 | elif tmparea2 < tmparea1: 85 | if tmparea2 < minarea: 86 | tmpgotonode = L2 87 | minarea = tmparea2 88 | else: 89 | minarea = tmparea1 90 | if L1.extent.area() < L2.extent.area(): 91 | tmpgotonode = L1 92 | elif L2.extent.area() < L1.extent.area(): 93 | tmpgotonode = L2 94 | else: 95 | if len(L1.entries) < len(L2.entries): 96 | tmpgotonode = L1 97 | else: 98 | tmpgotonode = L2 99 | if minext <> -1 and tmpgotonode is not None: 100 | ext = allexts.pop(minext) 101 | gotonode = tmpgotonode 102 | gotonode.entries.append(ext) 103 | gotonode.update() 104 | for ent in L1.entries: 105 | ent.node = L1 106 | if ent.child is not None: 107 | ent.child.parent = ent 108 | for ent in L2.entries: 109 | ent.node = L2 110 | if ent.child is not None: 111 | ent.child.parent = ent 112 | split(node, L1, L2) 113 | L1.update_up() 114 | L2.update_up() 115 | return True 116 | 117 | def split(node, L1, L2): 118 | entry1 = Entry(L1.extent) 119 | entry2 = Entry(L2.extent) 120 | if node.is_root(): 121 | node.entries = [] 122 | entry1.node = node 123 | entry2.node = node 124 | entry1.child = L1 125 | entry2.child = L2 126 | node.entries.append(entry1) 127 | node.entries.append(entry2) 128 | L1.parent = entry1 129 | L2.parent = entry2 130 | return 131 | else: 132 | entry1.node = L1 133 | L1.parent = node.parent 134 | L1.parent.child = L1 135 | del node 136 | insert(L1.parent.node, L2.extent, L2) 137 | return 138 | 139 | def search_rtree_extent(node, e): 140 | if node.is_leaf(): 141 | return node 142 | best_entry = None 143 | intersect_area = -1 144 | for ent in node.entries: 145 | tmp_area = ent.MBR.intersect(e) 146 | if tmp_area > intersect_area: 147 | intersect_area = tmp_area 148 | best_entry = ent 149 | return search_rtree_extent(best_entry.child, e) 150 | 151 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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You may not convey a covered 525 | work if you are a party to an arrangement with a third party that is 526 | in the business of distributing software, under which you make payment 527 | to the third party based on the extent of your activity of conveying 528 | the work, and under which the third party grants, to any of the 529 | parties who would receive the covered work from you, a discriminatory 530 | patent license (a) in connection with copies of the covered work 531 | conveyed by you (or copies made from those copies), or (b) primarily 532 | for and in connection with specific products or compilations that 533 | contain the covered work, unless you entered into that arrangement, 534 | or that patent license was granted, prior to 28 March 2007. 535 | 536 | Nothing in this License shall be construed as excluding or limiting 537 | any implied license or other defenses to infringement that may 538 | otherwise be available to you under applicable patent law. 539 | 540 | 12. No Surrender of Others' Freedom. 541 | 542 | If conditions are imposed on you (whether by court order, agreement or 543 | otherwise) that contradict the conditions of this License, they do not 544 | excuse you from the conditions of this License. If you cannot convey a 545 | covered work so as to satisfy simultaneously your obligations under this 546 | License and any other pertinent obligations, then as a consequence you may 547 | not convey it at all. For example, if you agree to terms that obligate you 548 | to collect a royalty for further conveying from those to whom you convey 549 | the Program, the only way you could satisfy both those terms and this 550 | License would be to refrain entirely from conveying the Program. 551 | 552 | 13. Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | --------------------------------------------------------------------------------