[英]How do you convert Euler angles to the Axis Angle representation in Python?
我正在尝试将欧拉角转换为 Python 中的轴角表示。 我已经在这个网站上复制了 function: https://www.euclideanspace.com/maths/geometry/rotations/conversions/eulerToAngle/并翻译成 ZA7F5F7F35426B62821B52821B 但是,他们这里使用的欧拉顺序是 yzx,而我的是 zxy,所以这会导致错误的转换。
是否有任何 Python 包可以使用 zxy 的欧拉顺序进行此转换,或者有人可以为我提供此转换的伪代码吗?
我的代码目前看起来像这样(所以我想制作一个名为“euler_zxy_to_axis_angle”的 function 而不是我现在拥有的那个)。
def euler_yzx_to_axis_angle(y_euler, z_euler, x_euler, normalize=True):
# Assuming the angles are in radians.
c1 = math.cos(y_euler/2)
s1 = math.sin(y_euler/2)
c2 = math.cos(z_euler/2)
s2 = math.sin(z_euler/2)
c3 = math.cos(x_euler/2)
s3 = math.sin(x_euler/2)
c1c2 = c1*c2
s1s2 = s1*s2
w = c1c2*c3 - s1s2*s3
x = c1c2*s3 + s1s2*c3
y = s1*c2*c3 + c1*s2*s3
z = c1*s2*c3 - s1*c2*s3
angle = 2 * math.acos(w)
if normalize:
norm = x*x+y*y+z*z
if norm < 0.001:
# when all euler angles are zero angle =0 so
# we can set axis to anything to avoid divide by zero
x = 1
y = 0
z = 0
else:
norm = math.sqrt(norm)
x /= norm
y /= norm
z /= norm
return x, y, z, angle
因此,我想要做的一个例子是将欧拉角转换为 zxy 阶,其中z=1.2, x=1.5, y=1.0
为正确的角轴表示,在这种情况下axis = [ 0.3150331, 0.6684339, 0.6737583], angle = 2.4361774
。 (根据https://www.andre-gaschler.com/rotationconverter/ )。
目前我的 function 正在返回axis=[ 0.7371612, 0.6684339, 0.098942 ] angle = 2.4361774
,因为它将欧拉角解释为具有 yzx 顺序。
因此,在弄乱了数字之后,我重新分配了方程式中的值并得到了
import math
def euler_yzx_to_axis_angle(z_e, x_e, y_e, normalize=True):
# Assuming the angles are in radians.
c1 = math.cos(z_e/2)
s1 = math.sin(z_e/2)
c2 = math.cos(x_e/2)
s2 = math.sin(x_e/2)
c3 = math.cos(y_e/2)
s3 = math.sin(y_e/2)
c1c2 = c1*c2
s1s2 = s1*s2
w = c1c2*c3 - s1s2*s3
x = c1c2*s3 + s1s2*c3
y = s1*c2*c3 + c1*s2*s3
z = c1*s2*c3 - s1*c2*s3
angle = 2 * math.acos(w)
if normalize:
norm = x*x+y*y+z*z
if norm < 0.001:
# when all euler angles are zero angle =0 so
# we can set axis to anything to avoid divide by zero
x = 1
y = 0
z = 0
else:
norm = math.sqrt(norm)
x /= norm
y /= norm
z /= norm
return z, x, y, angle
print(euler_yzx_to_axis_angle(1.2, 1.5, 1.0))
其中的 output 是
(0.31503310585743804, 0.668433885385261, 0.6737583269114973, 2.4361774412758335)
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