Point inside line and plane

Point vs line

To check if a point is on a line/segement.

1. PointInLine(P0,P,L)

It serves to check if P0 falls in the line (P,L).
P0 = np.array([0.5,0.5,0.5])
P = np.array([0,0,0])
L = np.array([1.1,1.1,1.1])               # slope
PointInLine(P0,P,L)
>>>  True
_images/pointXline1.png

2. PointInSegment(P0,P1,P2)

It serves to check if P0 falls in the segment (P1,P2).
P0 = np.array([0.5,0.5,0.5])
P1 = np.array([0,0,0])
P2 = np.array([0.4,0.4,0.4])
PointInLine(P0,P1,P2)
>>>  False
_images/pointXline2.png

Point vs plane

The point might be single or multiple.)

3. PointInPolygon(P0, polygon)

It serves to check if P0 falls in the polygon.
Point =  np.array([0.5,0.5,0.5])
vertices = [(0,0,0),(1,0,0),(1,1,1),(0,1,1)]
polygon = np.array(vertices)
PointInPolygon(Point, polygon)
>>>  True

4. PointsInPolygon2D(P0s, polygon)

It serves to check if multiple points P0s fall in the 2D polygon.
Points = np.array([(0,0),(0.5,0),(1,0),(1.5,0),(2,0)])
polygon = np.arraynp.array([(1,-1),(1,3),(2,1),(1.75,0)])
ret = PointsInPolygon2D(Points, polygon)
>>>  array([False, False, True, True, False])
For the case of a matrix of points, it returns a matrix of the same sizes holding boolean values.
Points = np.array([[(0,0),(0.5,0)],[(1,0),(1.5,0)],[(2,0),(2.5,0]])
polygon = np.arraynp.array([(1,-1),(1,3),(2,1),(1.75,0)])
ret = PointsInPolygon2D(Points, polygon)
>>>  array([[False, False], [True,  True], [False,False]])
_images/pointsandpolygon.png

5. PointsInPolygon(P0s, polygon)

It serves to check if multiple points P0s fall in the 3D polygon.
Points = np.array([(0,0,0),(0.5,0,0),(1,0,0),(1.5,0,0),(2,0,0)])
polygon = np.arraynp.array([(1,-1,0),(1,3,0),(2,1,0),(1.75,0,0)])
ret = PointsInPolygon(Points, polygon)
>>>  array([False, False,  True,  True, False])

6. Flow chart for their algorithm

_images/PointEdge.png _images/PointInPolygon.png