lineintersect.py

import numpy as np

def doBoundingBoxesIntersect(a, b, c, d):
    '''
    Check if bounding boxes do intersect. If one bounding box touches
    the other, they do intersect.
    First segment is of points a and b, second of c and d.
    '''
    ll1_x = min(a[0],b[0]); ll2_x = min(c[0],d[0])
    ll1_y = min(a[1],b[1]); ll2_y = min(c[1],d[1])
    ur1_x = max(a[0],b[0]); ur2_x = max(c[0],d[0])
    ur1_y = max(a[1],b[1]); ur2_y = max(c[1],d[1])

    return ll1_x <= ur2_x and \
           ur1_x >= ll2_x and \
           ll1_y <= ur2_y and \
           ur1_y >= ll2_y

def isPointOnLine(a,b,c):
    '''
    Check if a point a is on a line b-c.
    '''
    # move to origin
    aTmp = (0,0)
    bTmp = (b[0] - a[0], b[1] - a[1])
    cTmp = (c[0] - a[0], c[1] - a[1])
    r = np.cross(bTmp, cTmp)
    return np.abs(r) < 0.0000000001

def isPointRightOfLine(a,b,c):
    '''
    Check if a point (c) is right of a line (a-b).
    If (c) is on the line, it is not right it.
    '''
    # move to origin
    aTmp = (0,0)
    bTmp = (b[0] - a[0], b[1] - a[1])
    cTmp = (c[0] - a[0], c[1] - a[1])
    return np.cross(bTmp, cTmp) < 0

def lineSegmentTouchesOrCrossesLine(a,b,c,d):
    '''
    Check if line segment (a-b) touches or crosses
    line segment (c-d).
    '''
    return isPointOnLine(a,b,c) or \
           isPointOnLine(a,b,d) or \
          (isPointRightOfLine(a,b,c) ^
           isPointRightOfLine(a,b,d))

def doLinesIntersect(a,b,c,d):
    '''
    Check if line segments (a-b) and (c-d) intersect.
    '''
    #print(type(a), a,b,c,d)
    return doBoundingBoxesIntersect(a,b,c,d) and \
           lineSegmentTouchesOrCrossesLine(a,b,c,d) and \
           lineSegmentTouchesOrCrossesLine(c,d,a,b)


##############################
## Tests
##############################

def test_doBoundingBoxesIntersect():
    A=(1,1); B=(2,2); C=(3,1); D=(4,2)
    assert doBoundingBoxesIntersect(A,B,C,D) == False
    A=(1,2); B=(3,4); C=(2,1); D=(4,3)
    assert doBoundingBoxesIntersect(A,B,C,D) == True

def test_isPointOnLine():
    A=(1,1); B=(3,3); C=(2,2)
    assert isPointOnLine(A,B,C) == True
    A=(1,1); B=(3,3); C=(3,2)
    assert isPointOnLine(A,B,C) == False


def test_isPointRightOfLine():
    A=(1,1); B=(3,3); C=(2,2)
    assert isPointRightOfLine(A,B,C) == False
    A=(1,1); B=(3,3); C=(3,2)
    assert isPointRightOfLine(A,B,C) == True
    A=(1,1); B=(3,3); C=(1,2)
    assert isPointRightOfLine(A,B,C) == False

# a lot of testcases to be tested with the final function

def tcase(name):
    if name == 'F1':
        return (0,0), (7,7), (3,4), (4,5), False
    elif name == 'F2':
        return (-4,4), (-2,1), (-2,3), (0,0), False
    elif name == 'F3':
        return (0,0), (0,1), (2,2), (2,3), False
    elif name == 'F4':
        return (0,0), (0,1), (2,2), (3,2), False
    elif name == 'F5':
        return (-1,-1), (2,2), (3,3), (5,5), False
    elif name == 'F6':
        return (0,0), (1,1), (2,0), (0.5,2), False
    elif name == 'F7':
        return (1,1), (4,1), (2,2), (3,2), False
    elif name == 'F8':
        return (0,5), (6,0), (2,1), (2,2), False
    elif name == 'T1':
        return (0,-2), (0,2), (-2,0), (2,0), True
    elif name == 'T2':
        return (5,5), (0,0), (1,1), (8,2), True
    elif name == 'T3':
        return (-1,0), (0,0), (-1,-1), (-1,1), True
    elif name == 'T4':
        return (0,2), (2,2), (2,0), (2,4), True
    elif name == 'T5':
        return (0,0), (5,5), (1,1), (3,3), True
    elif name == 'T6':
        return (0,0), (3,3), (0,0), (3,3), True

cases = ['F1', 'F2', 'F3', 'F4', 'F5', 'F6', 'F7', 'F8',
         'T1', 'T2', 'T3', 'T4', 'T5', 'T6']

def check_intersection(name):
    A,B,C,D, result = tcase(name)
    assert doLinesIntersect(A,B,C,D) == result

def test_doLinesIntersect():
    for case in cases:
        yield check_intersection, case