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utils.py
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import numpy as np
import matplotlib.pyplot as plt
from scipy.spatial.transform import Rotation
import pdb
def get_transform_matrix(V, T, normal = np.array([0, 0, 1])):
# 计算旋转轴
rotation_axis = np.cross(normal, V)
# 计算旋转角度
cos_theta = np.dot(normal, V)
sin_theta = np.linalg.norm(rotation_axis)
theta = np.arctan2(sin_theta, cos_theta)
# 使用旋转轴和旋转角度构建旋转矩阵
rotation_matrix = Rotation.from_rotvec(theta * rotation_axis).as_matrix()
transform_matrix = np.eye(4) # 创建一个4x4的单位矩阵
transform_matrix[:3, :3] = rotation_matrix # 将旋转矩阵放入变换矩阵的左上角
transform_matrix[:3, 3] = T # 将平移向量放入变换矩阵的右上角
return transform_matrix
def get_rotation_matrix(V, normal = np.array([0, 0, 1])):
# 计算旋转轴
rotation_axis = np.cross(normal, V)
# 计算旋转角度
cos_theta = np.dot(normal, V)
sin_theta = np.linalg.norm(rotation_axis)
theta = np.arctan2(sin_theta, cos_theta)
# 使用旋转轴和旋转角度构建旋转矩阵
rotation_matrix = Rotation.from_rotvec(theta * rotation_axis).as_matrix()
return rotation_matrix
def _get_circle_points(r, theta_start = 0, theta_end = 2*np.pi, sample_num = 100):
# Generate angles
theta = np.linspace(theta_start, theta_end, sample_num)
# Generate points on the circle
x = r * np.cos(theta)
y = r * np.sin(theta)
z = np.zeros_like(x)
points = np.column_stack([x, y, z])
return points
def get_transformed_circle(r, V, T, theta_start = 0, theta_end = 2*np.pi, sample_num = 100):
_circle_points = _get_circle_points(r, theta_start, theta_end, sample_num)
# 将坐标点扩展为齐次坐标，添加额外的维度为1
homogeneous_points = np.column_stack((_circle_points, np.ones((sample_num, 1))))
transforme_matrix = get_transform_matrix(V, T)
transformed_circle = np.dot(transforme_matrix, homogeneous_points.T).T
return transformed_circle[:, :3]
def get_transformed_circle_1(r, V, T, theta_start = 0, theta_end = 2*np.pi, sample_num = 100):
circle_points = _get_circle_points(r, theta_start, theta_end, sample_num)
# 将坐标点扩展为齐次坐标，添加额外的维度为1
# homogeneous_points = np.column_stack((_circle_points, np.ones((sample_num, 1))))
rotation_matrix = get_rotation_matrix(V)
rotation_circle = np.dot(rotation_matrix, circle_points.T).T
# pdb.set_trace()
# a = rotation_circle[0, :]
# b = rotation_circle[49, :]
# c = rotation_circle[99, :]
# d = np.cross(b - a, c - b)
# e = d / np.linalg.norm(d)
# # print(e)
# pdb.set_trace()
transformed_circle = rotation_circle + T
# a = transformed_circle[0, :]
# b = transformed_circle[49, :]
# c = transformed_circle[99, :]
# d = np.cross(b - a, c - b)
# e = d / np.linalg.norm(d)
# # print(e)
return transformed_circle
def scatter_points(ax, points, color='r'):
# ax.set_box_aspect([1, 1, 1]) # 设置三个坐标轴尺度一致
ax.scatter(points[:, 0], points[:, 1], points[:, 2], color=color)
def plot_points(ax, points, color='r'):
# ax.set_box_aspect([1, 1, 1]) # 设置三个坐标轴尺度一致
ax.plot(points[:, 0], points[:, 1], points[:, 2], color=color)
def get_guided_L_cord(r=1):
# 引导灯坐标
p1 = np.array([ 0, np.sqrt(3) * r / 3, 0])
p2 = np.array([-r / 2.0, -np.sqrt(3) * r / 6, 0])
p3 = np.array([ r / 2.0, -np.sqrt(3) * r / 6, 0])
return p1, p2, p3
def cords2insc(A, B, C, T):
TA = T + A
TB = T + B
TC = T + C
alpha = cords2inc(TA, TB)
beta = cords2inc(TB, TC)
gamma = cords2inc(TC, TA)
return TA, TB, TC, alpha, beta, gamma
def cords2inc(vec0, vec1):
# vec0 = vec0 * vec_expansion
# vec1 = vec1 * vec_expansion
dot_product = np.dot(vec0, vec1)
mag0 = np.linalg.norm(vec0)
mag1 = np.linalg.norm(vec1)
inc_rad = np.arccos(dot_product / (mag0 * mag1))
return inc_rad
def T_points2circle_r(TA, TB, circle_angle):
l = np.linalg.norm(TB-TA)
cc_r = l / 2 / np.tan(circle_angle)
r = l / 2 / np.sin(circle_angle)
return cc_r, r
if __name__ == '__main__':
r = 1
V = np.array([1, 0, 0])
T = np.array([2, 0, 0])
# T = np.array([ 0.,-0.28867513, 2. ])
circle_points = get_transformed_circle_1(r, V, T)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
scatter_points(ax, circle_points, 'g')
plt.show()