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63 lines
1.8 KiB
Python
63 lines
1.8 KiB
Python
import math
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import numpy as np
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import numpy.linalg as npla
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def rotation_matrix_to_euler(R : np.ndarray) -> np.ndarray:
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sy = math.sqrt(R[0,0] * R[0,0] + R[1,0] * R[1,0])
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singular = sy < 1e-6
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if not singular :
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x = math.atan2(R[2,1] , R[2,2])
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y = math.atan2(-R[2,0], sy)
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z = math.atan2(R[1,0], R[0,0])
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else :
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x = math.atan2(-R[1,2], R[1,1])
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y = math.atan2(-R[2,0], sy)
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z = 0
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return np.array([x, y, z])
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def segment_length(p1 : np.ndarray, p2 : np.ndarray):
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"""
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p1 (2,)
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p2 (2,)
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"""
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return npla.norm(p2-p1)
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def segment_to_vector(p1 : np.ndarray, p2 : np.ndarray):
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"""
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p1 (2,)
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p2 (2,)
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"""
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x = p2-p1
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x /= npla.norm(x)
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return x
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def intersect_two_line(a1, a2, b1, b2) -> np.ndarray:
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"""
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Returns the point of intersection of the lines (not segments) passing through a2,a1 and b2,b1.
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a1: [x, y] a point on the first line
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a2: [x, y] another point on the first line
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b1: [x, y] a point on the second line
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b2: [x, y] another point on the second line
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"""
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s = np.vstack([a1,a2,b1,b2]) # s for stacked
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h = np.hstack((s, np.ones((4, 1)))) # h for homogeneous
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l1 = np.cross(h[0], h[1]) # get first line
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l2 = np.cross(h[2], h[3]) # get second line
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x, y, z = np.cross(l1, l2) # point of intersection
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if z == 0: # lines are parallel
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return (float('inf'), float('inf'))
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return np.array( [x/z, y/z], np.float32 )
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def polygon_area(poly : np.ndarray) -> float:
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"""
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calculate area of n-vertices polygon with non intersecting edges
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poly np.ndarray (n,2)
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"""
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return float( np.abs(np.sum( poly[:,0] * np.roll( poly[:,1], -1 ) - poly[:,1] * np.roll( poly[:,0], -1 ) ) / 2) )
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