├── LICENSE ├── README.md ├── SweepIntersectorLib ├── Point.py ├── PriorityQueue.py ├── Segment.py ├── SkipList.py ├── SortSeq.py ├── SweepIntersector.py └── __init__.py ├── demo.py └── misc └── logo.png /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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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 | 676 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # SweepIntersectorLib 2 | 3 | ![Logo](./misc/logo.png) 4 | 5 | _SweepIntersectorLib_ is an implementation in pure Python of a sweep line algorithm for line-segment intersection, based on the algorithm described in the paper: 6 | 7 | [Mehlhorn, K., Näher, S.(1994).
Implementation of a sweep line algorithm 8 | for the Straight Line Segment Intersection Problem (MPI-I-94-160). 9 | Saarbrücken: Max-Planck-Institut für Informatik.](https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_1834220) 10 | 11 | Given a list of line segments in 2D, the algorithm finds all their pairwise intersections. In contrast to the classical [Bentely-Ottmann](https://en.wikipedia.org/wiki/Bentley%E2%80%93Ottmann_algorithm) algorithm, segments are allowed to be vertical, several segments may intersect in the same point, endpoints of segments my lie on other segments or may be common with their endpoints. 12 | 13 | ## Demo 14 | The demo uses the _matplotlib_ library to visualize the results. 15 | Install it first: 16 | ``` 17 | pip install matplotlib 18 | ``` 19 | Then run the demo: 20 | ``` 21 | cd /path/to/sweep_intersector 22 | python demo.py 23 | ``` 24 | 25 | ## Usage 26 | The whole work is done by the method `findIntersections()` of the class `SweepIntersector`: 27 | 28 | ```Python 29 | intSector = SweepIntersector() 30 | isectDic = intSector.findIntersections(segList) 31 | ``` 32 | The segment list `segList` is a Python `list` of tuples `(vs,ve)`, where `vs` is the start point and `ve` the end point of a segment. The points `vs` and `ve` are given as tuples `(x,y)? where `x` and `y? are their coordinates in the 2D plane. 33 | 34 | The method returns a dictionary `isectDic` with items `seg:isects` for all segments that had intersections. The key of the dictionary, `seg`, is a tuple `(vs,ve)` identical to the one in the input list and the value `isects` is a list of all intersections of the segment `seg`. These are given as tuples `(x,y)`, where again `x` and `y` are their coordinates in the 2D plane. This list includes the start and end points `vs` and `ve` and is ordered from `vs` to `ve`. 35 | 36 | ### Usage example: 37 | ```Python 38 | from SweepIntersectorLib.SweepIntersector import SweepIntersector 39 | 40 | segList = [] 41 | segList.append( ((1.0,1.0),(5.0,6.0)) ) 42 | segList.append( ((1.0,4.0),(4.0,0.0)) ) 43 | segList.append( ((1.5,5.0),(3.0,1.0)) ) 44 | ... 45 | 46 | isector = SweepIntersector() 47 | isectDic = isector.findIntersections(segList) 48 | for seg,isects in isectDic.items(): 49 | for p in isects[1:-1]: # here without end points 50 | plotInterxectionPoint(p) 51 | ``` 52 | -------------------------------------------------------------------------------- /SweepIntersectorLib/Point.py: -------------------------------------------------------------------------------- 1 | # Implementation in pure Python of a sweep line algorithm for line-segment 2 | # intersection, based on the algorithmof described in the paper: 3 | # 4 | # Mehlhorn, K., Näher, S.(1994). Implementation of a sweep line algorithm 5 | # for the Straight Line Segment Intersection Problem (MPI-I-94-160). 6 | # Saarbrücken: Max-Planck-Institut für Informatik. 7 | # https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_1834220# 8 | # 9 | # Implementation of the class 10 | # 11 | 12 | class Point(): 13 | ID = 0 14 | EPS = 0.00001 15 | EPS2 = EPS*EPS 16 | def __init__(self,p): 17 | self.x = p[0] 18 | self.y = p[1] 19 | self.id = Point.ID 20 | Point.ID += 1 21 | 22 | def compare(self,other): 23 | if self is other: return 0 24 | dx = self.x - other.x 25 | if dx > Point.EPS2: return 1 26 | if dx < -Point.EPS2: return -1 27 | dy = self.y - other.y 28 | if dy > Point.EPS2: return 1 29 | if dy < -Point.EPS2: return -1 30 | return 0 31 | 32 | def __gt__(self,other): 33 | return self.compare(other) > 0 34 | 35 | def __lt__(self,other): 36 | return self.compare(other) < 0 37 | 38 | def __ge__(self,other): 39 | return self.compare(other) >= 0 40 | 41 | def __le__(self,other): 42 | return self.compare(other) <= 0 43 | 44 | def __eq__(self,other): 45 | if other is None: return False 46 | return self.compare(other) == 0 47 | 48 | def __iter__(self): 49 | # used to create tuples 50 | return iter([self.x,self.y]) 51 | 52 | def __repr__(self): 53 | return '(%d: %6.2f,%6.2f)'%(self.id,self.x,self.y) 54 | 55 | def plot(self,color='k',size=3): 56 | import matplotlib.pyplot as plt 57 | plt.plot(self.x,self.y,color+'o',markersize=size) 58 | plt.text(self.x,self.y,str(self.id)) 59 | -------------------------------------------------------------------------------- /SweepIntersectorLib/PriorityQueue.py: -------------------------------------------------------------------------------- 1 | # Implementation in pure Python of a sweep line algorithm for line-segment 2 | # intersection, based on the algorithmof described in the paper: 3 | # 4 | # Mehlhorn, K., Näher, S.(1994). Implementation of a sweep line algorithm 5 | # for the Straight Line Segment Intersection Problem (MPI-I-94-160). 6 | # Saarbrücken: Max-Planck-Institut für Informatik. 7 | # https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_1834220# 8 | # 9 | # Implementation of the class . 10 | # 11 | 12 | import heapq 13 | 14 | class QueueNode(): 15 | def __init__(self,key,inf): 16 | self.key = key 17 | self.inf = inf 18 | def __gt__(self,other): 19 | return self.key > other.key 20 | 21 | def __lt__(self,other): 22 | return self.key < other.key 23 | 24 | def __ge__(self,other): 25 | return self.key >= other.key 26 | 27 | def __le__(self,other): 28 | return self.key <= other.key 29 | 30 | def __eq__(self,other): 31 | return self.key == other.key 32 | 33 | class PriorityQueue(): 34 | def __init__(self): 35 | self.queue = [] 36 | 37 | @staticmethod 38 | def prio(node): 39 | """ 40 | Returns the priority of 41 | """ 42 | return node.key 43 | 44 | @staticmethod 45 | def inf(node): 46 | """ 47 | Returns the value of 48 | """ 49 | return node.inf 50 | 51 | def insert(self, key, value): 52 | """ 53 | Adds a new node to the structure and returns it. 54 | """ 55 | node = QueueNode(key,value) 56 | heapq.heappush(self.queue, node) 57 | return node 58 | 59 | return self.heapInsert(key, value) 60 | 61 | def min(self): # corresponds to find_min() in LEDA 62 | """ 63 | Returns the node with minimal priority 64 | None if structure is empty 65 | """ 66 | if self.queue: 67 | return self.queue[0] 68 | else: 69 | return None 70 | 71 | def delMin(self): 72 | """ 73 | Removes the node node=self.findMin() 74 | from structure and return its priority. 75 | Precondition: the structure is not empty. 76 | """ 77 | return heapq.heappop(self.queue) 78 | 79 | def size(self): 80 | """ 81 | Returns the size of the structure 82 | """ 83 | return len(self.queue) 84 | 85 | # returns True if the structure is empty 86 | # and False otherwise. 87 | def empty(self): 88 | """ 89 | Returns True if the structure is empty, 90 | else False. 91 | """ 92 | return not self.queue 93 | -------------------------------------------------------------------------------- /SweepIntersectorLib/Segment.py: -------------------------------------------------------------------------------- 1 | # Implementation in pure Python of a sweep line algorithm for line-segment 2 | # intersection, based on the algorithmof described in the paper: 3 | # 4 | # Mehlhorn, K., Näher, S.(1994). Implementation of a sweep line algorithm 5 | # for the Straight Line Segment Intersection Problem (MPI-I-94-160). 6 | # Saarbrücken: Max-Planck-Institut für Informatik. 7 | # https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_1834220# 8 | # 9 | # Implementation of the class 10 | # 11 | 12 | from math import inf 13 | from .Point import Point 14 | 15 | class Segment(): 16 | pSweep = None 17 | ID = 0 18 | def __init__(self, p1, p2): 19 | self.p1 = p1 20 | self.p2 = p2 21 | self.dx = self.p2.x - self.p1.x 22 | self.dy = self.p2.y - self.p1.y 23 | 24 | self.id = Segment.ID 25 | Segment.ID += 1 26 | 27 | if self.p2.x != self.p1.x: 28 | self.slope = self.dy / self.dx 29 | self.yShift = self.p1.y - self.slope * self.p1.x 30 | else: # vertical segment 31 | self.slope = inf 32 | self.yShift = -1. * inf 33 | 34 | def start(self): 35 | return self.p1 36 | 37 | def end(self): 38 | return self.p2 39 | 40 | def isTrivial(self): 41 | return self.dx == 0 and self.dy == 0 42 | 43 | @staticmethod 44 | def setpSweep(pSweep): 45 | Segment.pSweep = pSweep 46 | 47 | @staticmethod 48 | # see https://docs.python.org/3.0/whatsnew/3.0.html#ordering-comparisons 49 | # for comparison in Python >= 3.0 50 | def cmpVal(a, b): 51 | return (a > b)*1. - (a < b)*1. 52 | 53 | def compare(self,other): 54 | if self is other: 55 | return 0 56 | s = 0 57 | if Segment.pSweep is self.p1: 58 | s = Segment.orientation(other,Segment.pSweep) 59 | elif Segment.pSweep is other.p1: 60 | s = -Segment.orientation(self,Segment.pSweep) 61 | else: 62 | raise Exception('Compare error in Segment') 63 | 64 | if s or self.isTrivial() or other.isTrivial(): 65 | return s 66 | s = Segment.orientation(other,self.p2) 67 | # overlapping segments will be ordered by their id-numbers 68 | return s if s else self.id-other.id 69 | 70 | @staticmethod 71 | def orientation(s,point): 72 | orient = s.dy*(point.x-s.p1.x) - s.dx*(point.y-s.p1.y) 73 | return Segment.cmpVal( s.dy*(s.p1.x-point.x), s.dx*(s.p1.y-point.y) ) 74 | 75 | def intersectionOfLines(self,s): 76 | if self.slope == s.slope: return None 77 | if self.p1 == s.p1 or self.p1 == s.p2: 78 | return self.p1 79 | if self.p2 == s.p1 or self.p2 == s.p2: 80 | return self.p2 81 | if self.p1.x == self.p2.x: # is vertical 82 | cx = self.p1.x 83 | else: 84 | if s.p1.x == s.p2.x: # is vertical 85 | cx = s.p1.x 86 | else: 87 | cx = (s.yShift-self.yShift)/(self.slope-s.slope) 88 | if self.p1.x == self.p2.x: # is vertical 89 | cy = s.slope * cx + s.yShift 90 | else: 91 | cy = self.slope * cx + self.yShift 92 | return Point((cx,cy)) 93 | 94 | def __gt__(self,other): 95 | # return self.p1 > other.p1 96 | return self.compare(other) > 0 97 | 98 | def __lt__(self,other): 99 | # return self.p1 < other.p1 100 | return self.compare(other) < 0 101 | 102 | def __ge__(self,other): 103 | # return self.p1 >= other.p1 104 | return self.compare(other) >= 0 105 | 106 | def __le__(self,other): 107 | # return self.p1 <= other.p1 108 | return self.compare(other) <= 0 109 | 110 | def __eq__(self,other): 111 | if other is None: return False 112 | # return self.p1 == other.p1 113 | return self.compare(other) == 0 114 | 115 | def __hash__(self): 116 | return self.id 117 | 118 | def __repr__(self): 119 | return '[%d: %s -> %s]'%(self.id,str(self.p1),str(self.p2)) 120 | 121 | def plot(self,color='k'): 122 | import matplotlib.pyplot as plt 123 | self.start().plot('b') 124 | self.end().plot('r') 125 | v1 = self.start() 126 | v2 = self.end() 127 | plt.plot([v1.x,v2.x],[v1.y,v2.y],color) 128 | x = (v1.x+v2.x)/2 129 | y = (v1.y+v2.y)/2 130 | plt.text(x,y,str(self.id)) 131 | 132 | -------------------------------------------------------------------------------- /SweepIntersectorLib/SkipList.py: -------------------------------------------------------------------------------- 1 | # Implementation in pure Python of a sweep line algorithm for line-segment 2 | # intersection, based on the algorithmof described in the paper: 3 | # 4 | # Mehlhorn, K., Näher, S.(1994). Implementation of a sweep line algorithm 5 | # for the Straight Line Segment Intersection Problem (MPI-I-94-160). 6 | # Saarbrücken: Max-Planck-Institut für Informatik. 7 | # https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_1834220# 8 | # 9 | # Implementation of the class . 10 | # 11 | # Adapted and simplified from py-skiplist by Alexander Zhukov, 12 | # at https://github.com/ZhukovAlexander/py-skiplist 13 | # He published the code under the "Do What The F*ck You Want To Public License", 14 | # the easiest license out there. It gives the user permissions to do whatever 15 | # they want with your code. We say "thank you"! 16 | 17 | from itertools import chain, dropwhile, count, repeat 18 | import random 19 | 20 | def geometric(p): 21 | return (next(dropwhile(lambda _: random.randint(1, int(1. / p)) == 1, count())) for _ in repeat(1)) 22 | 23 | class NIL(object): 24 | """Sentinel object that always compares greater than another object""" 25 | __slots__ = () 26 | 27 | def __cmp__(self, other): 28 | # None is always greater than the other 29 | return 1 30 | 31 | def __lt__(self, other): 32 | return False 33 | 34 | def __le__(self, other): 35 | return False 36 | 37 | def __ge__(self, other): 38 | return True 39 | 40 | def __str__(self): 41 | return 'NIL' 42 | 43 | def __nonzero__(self): 44 | return False 45 | 46 | def __bool__(self): 47 | return False 48 | 49 | class SkipNode(): 50 | def __init__(self, key, data, succ, prev): 51 | self.key = key 52 | self.data = data 53 | self.succ = succ 54 | self.prev = prev 55 | 56 | for level in range(len(prev)): 57 | prev[level].succ[level] = self.succ[level].prev[level] = self 58 | 59 | class SkipList(): 60 | distribution = geometric(0.5) 61 | def __init__(self, **kwargs): 62 | 63 | self._tail = SkipNode(NIL(), None, [], []) 64 | self._head = SkipNode(None, 'HEAD', [self.tail], []) 65 | self._tail.prev.extend([self.head]) 66 | 67 | self._size = 0 68 | 69 | for k, v in kwargs.items(): 70 | self[k] = v 71 | 72 | @property 73 | def head(self): 74 | return self._head 75 | 76 | @property 77 | def tail(self): 78 | return self._tail 79 | 80 | def _height(self): 81 | return len(self.head.succ) 82 | 83 | def _level(self, start=None, level=0): 84 | node = start or self.head.succ[level] 85 | while node is not self.tail: 86 | yield node 87 | node = node.succ[level] 88 | 89 | def _scan(self, key): 90 | return_value = None 91 | height = len(self.head.succ) 92 | prevs = [self.head] * height 93 | node = self.head.succ[-1] 94 | for level in reversed(range(height)): 95 | node = next( 96 | dropwhile( 97 | lambda node_: node_.succ[level].key <= key, 98 | chain([self.head], self._level(node, level)) 99 | ) 100 | ) 101 | if node.key == key: 102 | return_value = node 103 | else: 104 | prevs[level] = node 105 | 106 | return return_value, prevs 107 | 108 | def _insert(self, key, data): 109 | # Inserts data into appropriate position. 110 | 111 | node, update = self._scan(key) 112 | 113 | if node: 114 | node.data = data 115 | return node 116 | 117 | node_height = next(self.distribution) + 1 118 | # because height should be positive non-zero 119 | # if node's height is greater than number of levels 120 | # then add new levels, if not do nothing 121 | height = len(self.head.succ) 122 | 123 | update.extend([self.head for _ in range(height, node_height)]) 124 | 125 | self.head.succ.extend([self.tail for _ in range(height, node_height)]) 126 | 127 | self.tail.prev.extend([self.head for _ in range(height, node_height)]) 128 | 129 | new_node = SkipNode(key, data, [update[l].succ[l] for l in range(node_height)], [update[l] for l in range(node_height)]) 130 | self._size += 1 131 | return new_node 132 | 133 | def _remove(self, key): 134 | # Removes node with given data. No operation if data is not in list. 135 | 136 | node, update = self._scan(key) 137 | if not node: 138 | return 139 | 140 | for level in range(len(node.succ)): 141 | update[level].succ[level] = node.succ[level] 142 | 143 | # trim not used head pointers 144 | for i in reversed(range(len(self.head.succ))): 145 | if self.head.succ[i] != self.tail: 146 | break 147 | elif i > 0: # at least one pointer 148 | head_node = self.head.succ.pop() 149 | del head_node 150 | 151 | del node 152 | self._size -= 1 153 | 154 | def __len__(self): 155 | return self._size 156 | 157 | def __repr__(self): 158 | return 'skiplist({{{}}})'.format( 159 | ', '.join('{key}: {value}'.format(key=node.key, value=node.data) for node in self._level()) 160 | ) 161 | 162 | def __getitem__(self, key): 163 | # Returns item with given index 164 | node, _ = self._scan(key) 165 | if node is None: 166 | return None 167 | return node.data 168 | 169 | def __setitem__(self, key, value): 170 | return self._insert(key, value) 171 | 172 | def __delitem__(self, key): 173 | self._remove(key) 174 | 175 | def __iter__(self): 176 | # Iterate over keys in sorted order 177 | return (node.key for node in self._level()) 178 | 179 | def iteritems(self): 180 | return ((node.key, node.data) for node in self._level()) 181 | 182 | def iterkeys(self): 183 | return (item[0] for item in self.iteritems()) 184 | 185 | def itervalues(self): 186 | return (item[1] for item in self.iteritems()) 187 | -------------------------------------------------------------------------------- /SweepIntersectorLib/SortSeq.py: -------------------------------------------------------------------------------- 1 | # Implementation in pure Python of a sweep line algorithm for line-segment 2 | # intersection, based on the algorithmof described in the paper: 3 | # 4 | # Mehlhorn, K., Näher, S.(1994). Implementation of a sweep line algorithm 5 | # for the Straight Line Segment Intersection Problem (MPI-I-94-160). 6 | # Saarbrücken: Max-Planck-Institut für Informatik. 7 | # https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_1834220# 8 | # 9 | # Implementation of the class . 10 | # This class emulates the LEDA class using our own code. 11 | # 12 | 13 | from .SkipList import SkipList, SkipNode 14 | 15 | class SortSeq(SkipList): 16 | def insert(self, key, inf): 17 | """ 18 | If there is a node in the structure, then inf is replaced by 19 | , otherwise a new node is added to the structure. 20 | In both cases the node is returned. 21 | """ 22 | from .Segment import Segment 23 | node, _ = self._scan(key) 24 | if node: 25 | node.data = inf 26 | return node 27 | else: 28 | node = self._insert(key, inf) 29 | return node 30 | 31 | def succ(self, node): 32 | """ 33 | Returns the successor node of in the sequence 34 | containing , None if there is no such node. 35 | """ 36 | node = node.succ[0] 37 | if node == self._tail: 38 | return None 39 | else: 40 | return node 41 | 42 | def pred(self, node): 43 | """ 44 | Returns the predecessor node of in the sequence 45 | containing , None if there is no such node. 46 | """ 47 | node = node.prev[0] 48 | if node == self._head: 49 | return None 50 | else: 51 | return node 52 | 53 | def changeInf(self, node, inf): 54 | """ 55 | Makes be the data of . 56 | """ 57 | from .Segment import Segment 58 | node.data = inf 59 | 60 | def lookup(self, key): 61 | """ 62 | Returns the node with key , None if there is no such item. 63 | """ 64 | node, _ = self._scan(key) 65 | return node 66 | 67 | def locate(self,key): 68 | """ 69 | Returns the node (key',inf) in SortSeq such that key' is minimal 70 | with key' >= key. None if no such node exists 71 | """ 72 | _, update = self._scan(key) 73 | return update[0].succ[0] 74 | 75 | @staticmethod 76 | def key(node): 77 | """ 78 | Returns the key of . 79 | Precondition: is a node in SortSeq 80 | """ 81 | return node.key 82 | 83 | @staticmethod 84 | def inf(node): 85 | """ 86 | Returns the element of . 87 | Precondition: is a node in SortSeq 88 | """ 89 | return node.data 90 | 91 | def delete(self,key): 92 | """ 93 | Removes the node with the key from SortSeq. 94 | No operation if no such key exists. 95 | """ 96 | self._remove(key) 97 | 98 | def empty(self): 99 | return len(self) == 0 100 | 101 | def min(self): 102 | if self.empty(): 103 | return None 104 | else: 105 | return self.head.succ[0] 106 | 107 | # ----------------------------------------------------------------------- 108 | # The following methods change the order of the structure so that it no 109 | # longer remains sorted. Therefore they are implemented here and 110 | # not in the base class . 111 | 112 | def insertAt(self, node, key, inf): 113 | """ 114 | Like insert(key,inf), the node gives the position of the 115 | node in the sequence. 116 | Precondition: is a node in SortSeq with either key(node) 117 | is maximal with key(node) <= or key(node) is minimal with 118 | key(node) >= . 119 | """ 120 | from .Segment import Segment 121 | if key == node.key: 122 | node.data = inf 123 | return node 124 | 125 | # Not often used, so we insert with the same height as 126 | prevNode = node if key > node.key else node.prev[0] 127 | succNode = prevNode.succ[0] 128 | newSucc = [s for s in prevNode.succ if s == succNode] 129 | newPrev = [s for s in succNode.prev if s == prevNode] 130 | new_node = SkipNode(key, inf, newSucc, newPrev) 131 | self._size += 1 132 | return new_node 133 | 134 | def delItem(self, node): 135 | """ 136 | Removes the from SortSeq containing it. 137 | Precondition: is a node in SortSeq. 138 | """ 139 | for level in range(len(node.succ)): 140 | node.prev[level].succ[level] = node.succ[level] 141 | node.succ[level].prev[level] = node.prev[level] 142 | # trim not used head pointers 143 | for i in reversed(range(len(self.head.succ))): 144 | if self.head.succ[i] != self.tail: 145 | break 146 | elif i > 0: # at least one pointer 147 | head_node = self.head.succ.pop() 148 | del head_node 149 | del node 150 | self._size -= 1 151 | 152 | def reverseItems(self, a, b): 153 | """ 154 | The subsequence of SortSeq from nodes to is reversed. 155 | Precondition: Node appears before in SortSeq. 156 | NOTE: This operation destroys the order in the SortSeq! 157 | """ 158 | while a != b: 159 | c = a 160 | a = a.succ[0] 161 | self.delItem(c) 162 | 163 | # insert c after b 164 | predNode = b 165 | succNode = b.succ[0] 166 | c.succ = [s for s in predNode.succ if s == succNode] 167 | c.prev = [s for s in succNode.prev if s == predNode] 168 | for level in range(len(c.prev)): 169 | c.prev[level].succ[level] = c.succ[level].prev[level] = c 170 | self._size += 1 171 | -------------------------------------------------------------------------------- /SweepIntersectorLib/SweepIntersector.py: -------------------------------------------------------------------------------- 1 | # Implementation in pure Python of a sweep line algorithm for line-segment 2 | # intersection, based on the algorithmof described in the paper: 3 | # 4 | # Mehlhorn, K., Näher, S.(1994). Implementation of a sweep line algorithm 5 | # for the Straight Line Segment Intersection Problem (MPI-I-94-160). 6 | # Saarbrücken: Max-Planck-Institut für Informatik. 7 | # https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_1834220# 8 | # 9 | # Implementation of the main class that implements the 10 | # sweep line algorithm for line-segment intersection. 11 | # 12 | 13 | from collections import defaultdict 14 | 15 | from .SortSeq import SortSeq 16 | from .PriorityQueue import PriorityQueue 17 | from .Segment import Segment 18 | from .Point import Point 19 | 20 | class SweepIntersector(): 21 | def __init__(self): 22 | self.X_structure = SortSeq() 23 | self.Y_structure = SortSeq() 24 | self.lastNode = dict() 25 | self.original = dict() 26 | self.assoc = dict() 27 | self.interDic = dict() 28 | self.segQueue = PriorityQueue() 29 | self.pSweep = None 30 | self.N = 0 31 | self.isectDict = defaultdict(list) 32 | self.intersectingSegments = defaultdict(list) 33 | 34 | def findIntersections(self,origSegList): 35 | """ 36 | Main method. Computes all intersections between a list of 37 | segments. 38 | : List of tuples (vs,ve) for segments, where vs is the start 39 | point and ve the end point. The points v1 and v2 are given 40 | as tuples (x,y) where x and y are their coordinates in the 41 | plane. 42 | Returns: A dictionary for all segments that had inter- 43 | sections. , the key of the dictionary, is a tuple 44 | (vs,ve) identical to the one in the input list and 45 | is the list of the intersections points. These points 46 | are given tuples (x,y) where again x and y are their 47 | coordinates in the plane. This list includes the start and 48 | end points vs and ve and is ordered from vs to ve. 49 | 50 | Usage example: 51 | 52 | from SweepIntersectorLib import SweepIntersector 53 | 54 | origSegList = [] 55 | origSegList.append( ((1.0,1.0),(5.0,6.0)) ) 56 | origSegList.append( ((1.0,4.0),(4.0,0.0)) ) 57 | origSegList.append( ((1.5,5.0),(3.0,1.0)) ) 58 | ... 59 | 60 | isector = SweepIntersector() 61 | isectDic = isector.findIntersections(origSegList) 62 | for seg,isects in isectDic.items(): 63 | ... 64 | 65 | """ 66 | self.initializeStructures(origSegList) 67 | 68 | # Main loop 69 | while not self.X_structure.empty(): 70 | # move to next event point. 71 | event = self.X_structure.min() 72 | Segment.pSweep = self.pSweep = self.X_structure.key(event) 73 | v = self.pSweep 74 | 75 | # self.G.append(self.pSweep); 76 | # print('GRAPH') 77 | # for elem in self.G: 78 | # print(elem) 79 | # print(self.Y_structure) 80 | # p = self.Y_structure.head 81 | # while p.succ[0].key: 82 | # node = p.succ[0] 83 | # if node.data: 84 | # print('*') 85 | # print('k--> ',node.key) 86 | # print('d--> ',node.data,type(node.data)) 87 | # print('dk---> ',node.data.key) 88 | # print('dd---> ',node.data.data,type(node.data.data)) 89 | # p = p.succ[0] 90 | # for key,val in self.interDic.items(): 91 | # print('dic',key, val.key) 92 | # self.plotAll() 93 | 94 | # If there is an item associated with , 95 | # key(sit) is either an ending or passing segment. 96 | # We use as an entry point to compute the bundle of 97 | # segments ending at or passing through . 98 | # In particular, we compute the first and last 99 | # item of this bundle and the successor 100 | # and predecessor items. 101 | sit = SortSeq.inf(event) 102 | 103 | if sit is None: 104 | # Here we do not know any segments ending or passing through 105 | # . However, could come to lie on a segment 106 | # inserted before. To check this we look up the zero length 107 | # segment (pSweep,pSweep). 108 | sit = self.Y_structure.lookup(Segment(self.pSweep,self.pSweep)) 109 | 110 | sitSucc = None 111 | sitPred = None 112 | sitFirst = None 113 | sitLast = None 114 | 115 | # A value of None for and after the 116 | # following computation indicates that there are no segments 117 | # ending at or passing through 118 | 119 | if sit: # key(sit) is an ending or passing segment 120 | # first walk up until 121 | while self.Y_structure.inf(sit) == event: 122 | sit = self.Y_structure.succ(sit) 123 | sitSucc = self.Y_structure.succ(sit) 124 | xit = self.Y_structure.inf(sit) 125 | if xit: 126 | s1 = self.Y_structure.key(sit) 127 | s2 = self.Y_structure.key(sitSucc) 128 | self.interDic[(s1.id,s2.id)] = xit 129 | 130 | # Walk down until , construct edges for all segments 131 | # in the bundle, assign information to continuing segments, 132 | # and delete ending segments from the Y_structure 133 | while True: 134 | s = self.Y_structure.key(sit) 135 | sr = self.assoc[s] 136 | 137 | self.lastNode[s] = v 138 | if self.pSweep is s.p2: # ending segment 139 | it = self.Y_structure.pred(sit) 140 | self.Y_structure.delItem(sit) 141 | sit = it; 142 | else: # passing segment 143 | self.Y_structure.changeInf(sit,None) 144 | sit = self.Y_structure.pred(sit) 145 | if (sr is not s) and (sr.p2 is self.pSweep): 146 | self.assoc[s] = s 147 | 148 | if self.Y_structure.inf(sit) != event: 149 | break # end of while True: 150 | 151 | sitPred = sit 152 | sitFirst = self.Y_structure.succ(sitPred) 153 | 154 | # reverse the bundle of continuing segments (if existing) 155 | if sitFirst != sitSucc: 156 | sitLast = self.Y_structure.pred(sitSucc) 157 | self.Y_structure.reverseItems(sitFirst,sitLast) 158 | 159 | # Insert all segments starting at 160 | while self.pSweep is self.nextSeg.start(): # identity 161 | # insert into the Y-structure and associate the 162 | # corresponding item with the right endpoint of in 163 | # the X-structure (already present) 164 | sit = self.Y_structure.locate(self.nextSeg) 165 | seg0 = self.Y_structure.key(sit) 166 | 167 | if self.nextSeg != seg0: 168 | # is not collinear with , insert it 169 | sit = self.Y_structure.insertAt(sit, self.nextSeg, None) 170 | self.X_structure.insert(self.nextSeg.end(),sit) 171 | self.lastNode[self.nextSeg] = v 172 | 173 | if sitSucc is None: 174 | # There are only starting segments, compute 175 | # and using the first inserted segment 176 | sitSucc = self.Y_structure.succ(sit) 177 | sitPred = self.Y_structure.pred(sit) 178 | sitFirst = sitSucc 179 | else: 180 | # and are collinear; if is 181 | # longer insert (seg0.end(),next_seg.end()) into 182 | p = seg0.end() 183 | q = self.nextSeg.end() 184 | self.assoc[seg0] = self.nextSeg 185 | if p < q: 186 | newSeg = Segment(p,q) 187 | self.assoc[newSeg] = newSeg 188 | self.original[newSeg] = self.original[self.nextSeg] 189 | self.segQueue.insert(p,newSeg) 190 | 191 | # delete minimum and assign new minimum to 192 | self.segQueue.delMin() 193 | self.nextSeg = self.segQueue.inf(self.segQueue.min()) 194 | 195 | # if still has the value , there were no ending, 196 | # passing or starting segments, i.e., is an isolated 197 | # point. In this case we are done, otherwise we delete the event 198 | # associated with from the X-structure and compute 199 | # possible intersections between new neighbors. 200 | if sitPred is not None: 201 | # is no longer adjacent to its former successor we 202 | # change its intersection event to None. 203 | xit = self.Y_structure.inf(sitPred) 204 | 205 | if xit is not None: 206 | s1 = self.Y_structure.key(sitPred) 207 | s2 = self.Y_structure.key(sitFirst) 208 | self.interDic[(s1.id,s2.id)] = xit 209 | self.Y_structure.changeInf(sitPred, None) 210 | 211 | # compute possible intersections between and its 212 | # successor and and its predecessor 213 | self.computeIntersection(sitPred) 214 | sit = self.Y_structure.pred(sitSucc) 215 | if sit != sitPred: 216 | self.computeIntersection(sit) 217 | self.X_structure.delItem(event) 218 | 219 | self.collectAndSortResult() 220 | return self.intersectingSegments 221 | 222 | def initializeStructures(self,origSegList): 223 | """ 224 | Initializes the class using the provided list of segments . 225 | A vertex is represented as a tuple (x,y). 226 | A segment is represented by a tuple of vertices (vs,ve), where is the 227 | starting point and the end point. is a list of segments . 228 | """ 229 | infinity = 1 230 | for segIndex, seg in enumerate(origSegList): 231 | v1, v2 = seg 232 | 233 | # Compute an upper bound |Infinity| for the input coordinates 234 | while abs(v1[0]) >= infinity or abs(v1[1]) >= infinity or \ 235 | abs(v2[0]) >= infinity or abs(v2[1]) >= infinity: 236 | infinity *= 2; 237 | 238 | it1 = self.X_structure.insert(Point(seg[0]),None) 239 | it2 = self.X_structure.insert(Point(seg[1]),None) 240 | if it1 == it2: continue # Ignore zero-length segments 241 | 242 | # Insert operations into the X-structure leave previously 243 | # inserted points unchanged to achieve that any pair of 244 | # endpoints and with p1 == p2 are identical. 245 | p1 = SortSeq.key(it1) 246 | p2 = SortSeq.key(it2) 247 | s = Segment(p1,p2) if p1 < p2 else Segment(p2,p1) 248 | 249 | # use maps to associate with every segment its original 250 | self.original[s] = (seg,segIndex) 251 | self.assoc[s] = s 252 | 253 | # for every created segment (p1,p2) insert the pair (p1,(p1,p2)) 254 | # into priority queue 255 | self.segQueue.insert(s.start(),s) 256 | 257 | # insert a lower and an upper sentinel segment to avoid special 258 | # cases when traversing the Y-structure 259 | lowerSentinel = Segment( Point((-infinity,-infinity)), Point((infinity,-infinity))) 260 | upperSentinel = Segment( Point((-infinity, infinity)), Point((infinity, infinity))) 261 | 262 | # the sweep begins at the lower left corner 263 | Segment.pSweep = self.pSweep = lowerSentinel.start() 264 | self.Y_structure.insert(upperSentinel,None); 265 | self.Y_structure.insert(lowerSentinel,None); 266 | 267 | # insert a stopper into and initialize |next_seg| with 268 | # the first segment in the queue. 269 | pStop = Point((infinity,infinity)) 270 | sStop = Segment(pStop,pStop) 271 | self.segQueue.insert(pStop,sStop) 272 | self.nextSeg = self.segQueue.inf(self.segQueue.min()) 273 | self.N = sStop.id 274 | 275 | def computeIntersection(self,sit0): 276 | # Given an item in the Y-structure compute the point of 277 | # intersection with its successor and (if existing) insert it into 278 | # the event queue and do all necessary updates. 279 | sit1 = self.Y_structure.succ(sit0) 280 | s0 = self.Y_structure.key(sit0) 281 | s1 = self.Y_structure.key(sit1) 282 | 283 | # is the successor of in the Y-structure, hence, 284 | # and intersect right or above of the sweep line 285 | # if (s0.start(),s0.end(),s1.end() is not a left turn and 286 | # (s1.start(),s1.end(),s0.end() is not a right turn. 287 | # In this case we intersect the underlying lines 288 | if Segment.orientation(s0,s1.end()) <= 0 and Segment.orientation(s1,s0.end()) >= 0: 289 | it = self.interDic.get((s0.id,s1.id),None) 290 | if it is not None: 291 | self.Y_structure.changeInf(sit0,it) 292 | del self.interDic[(s0.id,s1.id)] 293 | else: 294 | q = s0.intersectionOfLines(s1) 295 | if q: 296 | self.Y_structure.changeInf(sit0, self.X_structure.insert(q,sit0)) 297 | 298 | # insert intersection point into result dictionary 299 | if s0.p1 != q and s0.p2 != q: 300 | self.isectDict[self.original[s0]].append((q.x,q.y)) 301 | if s1.p1 != q and s1.p2 != q: 302 | self.isectDict[self.original[s1]].append((q.x,q.y)) 303 | 304 | @staticmethod 305 | def inorderExtend(segment, v1, v2, points): 306 | # Extend a segment by that are on 307 | # between the points v1, v2 308 | k, r = None, False 309 | if v1[0] < v2[0]: k, r = lambda i: i[0], True 310 | elif v1[0] > v2[0]: k, r = lambda i: i[0], False 311 | elif v1[1] < v2[1]: k, r = lambda i: i[1], True 312 | else: k, r = lambda i: i[1], False 313 | l = [ p for p in sorted(points, key=k, reverse=r) ] 314 | i = next((i for i, p in enumerate(segment) if p == v2), -1) 315 | assert(i>=0) 316 | for e in l: 317 | # a vertex can appear only once in a segment 318 | if not e in segment: 319 | segment.insert(i, e) 320 | return segment 321 | 322 | def collectAndSortResult(self): 323 | for seg,isects in self.isectDict.items(): 324 | v1,v2 = seg[0] 325 | segment = self.inorderExtend([v1,v2],v1,v2,isects) 326 | self.intersectingSegments[seg[0]] = segment 327 | 328 | def plotY(self): 329 | import matplotlib.pyplot as plt 330 | for node in self.Y_structure._level(): 331 | node.key.plot() 332 | if node.data: 333 | node.data.plot('m') 334 | plt.gca().axis('equal') 335 | plt.show() 336 | 337 | def plotResult(self): 338 | import matplotlib.pyplot as plt 339 | plt.close() 340 | for key,value in self.original.items(): 341 | v1,v2 = key.p1,key.p2 342 | plt.plot([v1.x,v2.x],[v1.y,v2.y],'k:') 343 | plt.plot(v1.x,v1.y,'k.') 344 | plt.plot(v2.x,v2.y,'k.') 345 | # plt.text(v1.x,v1.y,str(v1.id)) 346 | # for isect in self.isects: 347 | # plt.plot(isect.x,isect.y,'ro',markersize=3,zorder=10) 348 | # plt.gca().axis('equal') 349 | # plt.show() 350 | 351 | def plotAll(self): 352 | import matplotlib.pyplot as plt 353 | plt.subplot(2,2,1) 354 | for isect in self.isects: 355 | plt.plot(isect.x,isect.y,'rx',markersize=12) 356 | count = 0 357 | for key,value in self.original.items(): 358 | v1,v2 = key.p1,key.p2 359 | plt.plot([v1.x,v2.x],[v1.y,v2.y],'k') 360 | plt.text(v1.x,v1.y,str(v1.id)) 361 | count += 1 362 | plt.gca().axis('equal') 363 | plt.gca().set_title('Original Segs') 364 | plt.subplot(2,2,2) 365 | for s in self.original.keys(): 366 | v1,v2 = s.p1, s.p2 367 | plt.plot([v1.x,v2.x],[v1.y,v2.y],'k') 368 | x = (v1.x+v2.x)/2 369 | y = (v1.y+v2.y)/2 370 | plt.text(x,y,str(s.id)) 371 | plt.gca().axis('equal') 372 | plt.gca().set_title('Segments') 373 | plt.subplot(2,2,3) 374 | for node in self.X_structure._level(): 375 | node.key.plot() 376 | if node.data: 377 | node.data.key.plot() 378 | plt.plot(self.pSweep.x,self.pSweep.y,'co',markersize=8) 379 | plt.gca().axis('equal') 380 | plt.gca().set_title('X-Structure') 381 | plt.subplot(2,2,4) 382 | for node in self.Y_structure._level(): 383 | node.key.plot() 384 | if node.data: 385 | if isinstance(node.data.key,Segment): 386 | node.data.key.plot('m') 387 | else: 388 | node.data.key.plot('m',10) 389 | plt.plot(self.pSweep.x,self.pSweep.y,'co',markersize=8) 390 | for isect in self.isects: 391 | plt.plot(isect.x,isect.y,'rx',markersize=3) 392 | plt.gca().axis('equal') 393 | plt.gca().set_title('Y-Structure') 394 | plt.show() 395 | -------------------------------------------------------------------------------- /SweepIntersectorLib/__init__.py: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/prochitecture/sweep_intersector/d8f540e4d9ecbde77bfef3499d91a72d30587532/SweepIntersectorLib/__init__.py -------------------------------------------------------------------------------- /demo.py: -------------------------------------------------------------------------------- 1 | import random 2 | import matplotlib.pyplot as plt 3 | from SweepIntersectorLib.SweepIntersector import SweepIntersector 4 | 5 | segList = [] 6 | 7 | # create some random segments 8 | for i in range(50): 9 | vs = (random.uniform(-1,1),random.uniform(-1,1)) 10 | ve = (random.uniform(-1,1),random.uniform(-1,1)) 11 | segList.append( (vs,ve) ) 12 | 13 | # add some vertical segments 14 | for i in range(5): 15 | vs = (random.uniform(-1,1),random.uniform(-1,1)) 16 | ve = (vs[0],random.uniform(-1,1)) 17 | segList.append( (vs,ve) ) 18 | 19 | # compute intersections 20 | isector = SweepIntersector() 21 | isecDic = isector.findIntersections(segList) 22 | 23 | # plot original segments 24 | for seg in segList: 25 | vs,ve = seg 26 | plt.plot([vs[0],ve[0]],[vs[1],ve[1]],'k:') 27 | 28 | # plot intersection points 29 | for seg,isects in isecDic.items(): 30 | for p in isects[1:-1]: 31 | plt.plot(p[0],p[1],'r.') 32 | 33 | plt.gca().axis('equal') 34 | plt.show() 35 | -------------------------------------------------------------------------------- /misc/logo.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/prochitecture/sweep_intersector/d8f540e4d9ecbde77bfef3499d91a72d30587532/misc/logo.png --------------------------------------------------------------------------------