获取旋转线的坐标

Question

I have 2 lines (A and B) defined by P1 and P2 (xyz) coordinates.

p1_A = [5, 10, 3]
p2_A = [15, 13, 3]

p1_B = [6, 20, 3]
p2_B = [9, 22, 5]

and the corresponding rotation matrix R to rotate line A to B:

R = array([[ 0.8468851 , -0.29080408, -0.44521748],
       [ 0.22027131,  0.95385981, -0.20403924],
       [ 0.48401051,  0.07472916,  0.87186546]])

Then, I calculated the dot product to rotate the vector R.dot(vecA) . I don't know how to continue from here. I need the (xyz) coordinates of the rotated line A.

EDIT:

I tried hippozhipos's solution (red dashed line) to rotate line A. I would expect the dashed line to rotate at the midpoint (see green dot) and to be parallel to the blue (reference line).

import matplotlib.pyplot as plt

p1_A = [5, 10, 3]
p2_A = [15, 13, 3]

p1_B = [6, 20, 3]
p2_B = [9, 22, 5]

mid_point = np.array([10. , 11.5,  3. ])

p1_A_rot = multVecMatrix(p1_A, R)
p2_A_rot = multVecMatrix(p2_A, R)

fig = plt.figure()
ax = fig.add_subplot(111)
ax.set_aspect('equal')
ax.set_xlim([0,23])
ax.set_ylim([0,23])
ax.plot([p1_A[0],p2_A[0]], [p1_A[1],p2_A[1]], 'r')
ax.plot(t0_cent[0], t0_cent[1], 'go')
# Reference
ax.plot([p1_B[0],p2_B[0]], [p1_B[1],p2_B[1]], 'b')

# Rotated
ax.plot([p1_A_rot[0],p2_A_rot[0]], [p1_A_rot[1],p2_A_rot[1]], 'r')

Plot

Answer 1

You have 2 points for line A and a rotation matrix. So to obtain the rotation, simply multiply the vectors representing the 2 points with the rotation matrix. Here is the function to do just that:

def multVecMatrix(vec3, mat3):
    x = vec3[0] * mat3[0][0] + vec3[1] * mat3[1][0] + vec3[2] * mat3[2][0]
    y = vec3[0] * mat3[0][1] + vec3[1] * mat3[1][1] + vec3[2] * mat3[2][1]
    z = vec3[0] * mat3[0][2] + vec3[1] * mat3[1][2] + vec3[2] * mat3[2][2]

So to get the rotated vector for line A:

rotatedP1_A = multVecMatrix(P1_A, R)
rotatedP2_A = multVecMatrix(P2_A, R)

Working example:

p1_A = [5, 10, 3]
p2_A = [15, 13, 3]

R = [[ 0.8468851 , -0.29080408, -0.44521748],
       [ 0.22027131,  0.95385981, -0.20403924],
       [ 0.48401051,  0.07472916,  0.87186546]]

def multVecMatrix(vec3, mat3):
    x = vec3[0] * mat3[0][0] + vec3[1] * mat3[1][0] + vec3[2] * mat3[2][0]
    y = vec3[0] * mat3[0][1] + vec3[1] * mat3[1][1] + vec3[2] * mat3[2][1]
    z = vec3[0] * mat3[0][2] + vec3[1] * mat3[1][2] + vec3[2] * mat3[2][2]
    return [x, y, z]

rotatedP1_A = multVecMatrix(p1_A, R)
rotatedP2_A = multVecMatrix(p2_A, R)

print(rotatedP1_A, rotatedP2_A)

Answer 2

To make a line parallel to B , you don't need rotation matrix.

Calculate direction vector of B line and add it to the middle of A