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class Line(object): |
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# Line class. mainly used for intersection check. |
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def __init__(self, point1, point2): |
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self.point1 = point1 |
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self.point2 = point2 |
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def intersect_with(self, another_line): |
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"""Check another_line intersect with itself or not. |
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Args: |
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another_line (Line): another line |
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Returns: |
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bool: return true when intersects |
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""" |
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# Find the four orientations needed for general and special cases |
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o1 = self.orientation(self.point1, self.point2, another_line.point1) |
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o2 = self.orientation(self.point1, self.point2, another_line.point2) |
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o3 = self.orientation(another_line.point1, another_line.point2, |
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self.point1) |
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o4 = self.orientation(another_line.point1, another_line.point2, |
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self.point2) |
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# General case |
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if o1 != o2 and o3 != o4: |
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return True |
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# Special Cases |
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# p1, q1 and p2 are colinear and p2 lies on segment p1q1 |
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if o1 == 0 and self.on_segment(self.point1, |
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another_line.point1, |
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self.point2): |
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return True |
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# p1, q1 and p2 are colinear and q2 lies on segment p1q1 |
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if o2 == 0 and self.on_segment(self.point1, |
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another_line.point2, |
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self.point2): |
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return True |
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# p2, q2 and p1 are colinear and p1 lies on segment p2q2 |
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if o3 == 0 and self.on_segment(another_line.point1, |
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self.point1, |
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another_line.point2): |
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return True |
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# p2, q2 and q1 are colinear and q1 lies on segment p2q2 |
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if o4 == 0 and self.on_segment(another_line.point1, |
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self.point2, |
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another_line.point2): |
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return True |
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# Doesn't fall in any of the above cases |
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return False |
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def on_segment(self, point1, point2, point3): |
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"""Check point q lies on line pr or not. |
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Given three colinear points p, q, r |
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the function checks if point q lies on line segment 'pr'. |
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Args: |
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point1 (Point): p |
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point2 (Point): q |
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point3 (Point): r |
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Returns: |
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bool: true when they are on segment |
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""" |
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if (point2.x <= max(point1.x, point3.x) |
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and point2.x >= min(point1.x, point3.x) |
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and point2.y <= max(point1.y, point3.y) |
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and point2.y >= min(point1.y, point3.y)): |
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return True |
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else: |
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return False |
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def orientation(self, point1, point2, point3): |
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"""To find orientation of ordered triplet (p, q, r). |
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Args: |
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point1 (Point): p |
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point2 (Point): q |
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point3 (Point): r |
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Returns: |
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int: 0 --> p, q and r are colinear, |
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1 --> Clockwise |
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2 --> Counterclockwise |
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""" |
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val = (point2.y - point1.y) * (point3.x - point2.x) - \ |
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(point2.x - point1.x) * (point3.y - point2.y) |
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if val == 0: |
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return 0 |
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elif val > 0: |
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return 1 |
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else: |
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return 2 |
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def double_length(self): |
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"""Double the length of current line from point1 to point2. |
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110
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Returns: |
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tuple: new end point coordinations |
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""" |
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return (self.point1.x + 2 * (self.point2.x - self.point1.x), |
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self.point1.y + 2 * (self.point2.y - self.point1.y)) |
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117
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118
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class Point(object): |
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# class for point, mainly used in Line class |
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121
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def __init__(self, x, y): |
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self.x = x |
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self.y = y |
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125
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126
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def is_inside(polygon, point): |
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line2 = Line(Point(point[0], point[1]), Point(100, point[1])) |
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intersections = 0 |
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point_pairs = [ |
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i for i in zip(polygon, polygon[1:])] + [(polygon[-1], polygon[0])] |
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while point_pairs: |
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# we draw polygon reversely |
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i = point_pairs.pop() |
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q1 = Point(i[0][0], i[0][1]) |
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p1 = Point(i[1][0], i[1][1]) |
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line1 = Line(p1, q1) |
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if line1.intersect_with(line2): |
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# double the length when find a intersection |
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if point_pairs: |
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point_pairs[-1] = (point_pairs[-1][0], |
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line1.double_length()) |
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if line1.orientation(p1, Point(*point), q1) == 0: |
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return line1.on_segment(p1, Point(*point), q1) |
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intersections += 1 |
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if intersections % 2: |
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return True |
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else: |
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return False |
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149
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150
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151
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if __name__ == '__main__': # pragma: no cover |
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assert is_inside(((1, 1), (1, 3), (3, 3), (3, 1)), |
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(2, 2)) is True, "First" |
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assert is_inside(((1, 1), (1, 3), (3, 3), (3, 1)), |
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(4, 2)) is False, "Second" |
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156
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assert is_inside(((1, 1), (4, 1), (2, 3)), |
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(3, 2)) is True, "Third" |
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assert is_inside(((1, 1), (4, 1), (1, 3)), |
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(3, 3)) is False, "Fourth" |
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assert is_inside(((2, 1), (4, 1), (5, 3), (3, 4), (1, 3)), |
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(4, 3)) is True, "Fifth" |
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assert is_inside(((2, 1), (4, 1), (3, 2), (3, 4), (1, 3)), |
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(4, 3)) is False, "Sixth" |
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assert is_inside(((1, 1), (3, 2), (5, 1), (4, 3), (5, 5), |
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(3, 4), (1, 5), (2, 3)), |
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(3, 3)) is True, "Seventh" |
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167
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assert is_inside(((1, 1), (1, 5), (5, 5), (5, 4), (2, 4), |
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(2, 2), (5, 2), (5, 1)), |
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(4, 3)) is False, "Eighth" |
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KenMercusLai /
checkio
