Line against line, plane and polygon¶
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
>>> ret = PointInLine(P0,P,L)

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])
>>> ret = PointInLine(P0,P1,P2)

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)
>>> ret = PointInPolygon(Point, polygon)
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)
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)

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)
6. Flow chart for their algorithm

