[英]Python: Rotate plane (set of points) to match new normal vector using scipy.spatial.transform.Rotation
So I'm currently trying to take slices on a plane orthogonal to a spline.所以我目前正在尝试在与样条正交的平面上进行切片。 Direction doesn't really matter too much since I'm using the points to interpolate 3D scans方向并不重要,因为我使用这些点来插入 3D 扫描
I'm mainly unsure about the rotmat method (this is a stripped down version of my class, technically a NURBS-Python surface derived class), where I'm rotating the plane mesh from a flat x/y plane (all z=0) to match the new normal vector (tangent of the spline, stored in the der variable).我主要不确定 rotmat 方法(这是我的 class 的精简版本,技术上是 NURBS-Python 表面派生类),其中我从平面 x/y 平面旋转平面网格(所有 z=0 ) 以匹配新的法线向量(样条的切线,存储在 der 变量中)。
Anyone have an idea how to rotate a set of points to go from one normal vector to another?任何人都知道如何将一组点从一个法向量旋转到 go 到另一个? The angle around the axis of the new vector doesn't matter than much to me.围绕新向量的轴的角度对我来说并不重要。
(sorry for vg, kind of an obscure library but somewhat convenient actually): (对不起 vg,一种不起眼的库,但实际上有点方便):
from scipy.interpolate import splprep, splev
import numpy as np
import vg
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from scipy.spatial.transform import Rotation as R
class SplineTube():
_points = np.array(
[[0, 0, 0],
[0, 1, 0],
[1, 1, 0],
[1, 0, 0]],
) - np.array([0.5, 0.5, 0])
_normal = np.array([0, 0, 1])
def __init__(self, x, y, z, n = 3, degree=2, **kwargs):
assert n >= 3
tck, u = splprep([x, y, z], s=0, k=2)
evalpts = np.linspace(0, 1, n)
pts = np.array(splev(evalpts, tck))
der = np.array(splev(evalpts, tck, der=1))
points = []
for i in range(n):
points_slice = self.rotmat(der[:, i], self._points)
points_slice = points_slice + pts[:, i]
points.append(points_slice)
points = np.stack(points)
return points
def rotmat(self, vector, points):
perpen = vg.perpendicular(self._normal, vector)
r = R.from_rotvec(perpen)
rotmat = r.apply(points)
return rotmat
Here's an example where I used a meshgrid instead of the _points, but is very similar:这是我使用网格而不是 _points 的示例,但非常相似:
Planes following spline跟随样条的平面
x = [0, 1, 2, 3, 6]
y = [0, 2, 5, 6, 2]
z = [0, 3, 5, 7, 10]
tck, u = splprep([x, y, z], s=0, k=2)
evalpts = np.linspace(0, 1, 10)
pts = splev(evalpts, tck)
der = splev(evalpts, tck, der=1)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot(pts[0], pts[1], pts[2])
ax.quiver(*pts, *der, length=0.05)
ax.scatter(x, y, z)
planes = SplineTube(x, y, z, n=10)
ax.scatter(planes[:, :, 0], planes[:, :, 1], planes[:, :, 2])
I think I ended up producing something that seems to work in the end:我想我最终产生了一些似乎最终有效的东西:
import numpy as np
import vg
from pytransform3d.rotations import matrix_from_axis_angle
def _rotmat(self, vector, points):
"""
Rotates a 3xn array of 3D coordinates from the +z normal to an
arbitrary new normal vector.
"""
vector = vg.normalize(vector)
axis = vg.perpendicular(vg.basis.z, vector)
angle = vg.angle(vg.basis.z, vector, units='rad')
a = np.hstack((axis, (angle,)))
R = matrix_from_axis_angle(a)
r = Rot.from_matrix(R)
rotmat = r.apply(points)
return rotmat
Not too insanely complicated, just start with a plane of points aligned with the xy plane (assuming you're using xy as your horizontal like me here apparently, please don't hate me), then it'll rotate it along the vector and not really care about rotation about the axis.不太复杂,只需从与 xy 平面对齐的点平面开始(假设您显然像我一样在这里使用 xy 作为水平线,请不要讨厌我),然后它会沿着向量旋转它并不太关心绕轴旋转。 Seems to work ok.似乎工作正常。
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