Matplotlib旋转3d磁盘

Question

我有一条线和一些点，它们在3D空间的这条线上。我知道点有一定的误差，但误差只垂直于直线。为了观察这一点，我想要有一个误差半径的圆盘，在直线上居中，与直线的方向正交。我找到了这个solution，但是我不能让它正常工作。

如果我运行代码和状态，我希望输出垂直于'z‘轴，得到我期望的结果。在直线上具有给定半径并在z轴上定向的圆盘。

pathpatch_2d_to_3d(p, z=z,normal='z')

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我想把磁盘旋转一下。为了找到那个点的井向量，我使用了一个闭合的点，通过使用那个向量。这是我放在normal=(vx,vy,vz)上的向量，但当我这样做的时候，磁盘甚至不在图表上。我不确定我错在哪里。有人有什么建议吗？

这是我的代码。

import matplotlib.pyplot as plt
from matplotlib.patches import Circle, PathPatch
from mpl_toolkits.mplot3d import Axes3D
import mpl_toolkits.mplot3d.art3d as art3d
import numpy as np
from scipy.interpolate import interp1d

md,wellz,wellx,welly=np.genfromtxt("./well.csv",delimiter=",",unpack=True)

# Building interpolation function that map a measured depth to its repsective x,y,z coordinates
fz = interp1d(md,wellz)
fx = interp1d(md,wellx)
fy = interp1d(md,welly)

pointDepth = np.array([15790,15554,15215,14911,14274,13927,13625,13284,12983,12640,12345,12004,11704,11361,11061,10717,10418,10080,9771])


def rotation_matrix(d):
    """
Calculates a rotation matrix given a vector d. The direction of d
corresponds to the rotation axis. The length of d corresponds to 
the sin of the angle of rotation.

Variant of: http://mail.scipy.org/pipermail/numpy-discussion/2009-March/040806.html
    """
    sin_angle = np.linalg.norm(d)

    if sin_angle == 0:
    return np.identity(3)

    d = d/sin_angle

    eye = np.eye(3)
    ddt = np.outer(d, d)
    skew = np.array([[    0,  d[2],  -d[1]],
                  [-d[2],     0,  d[0]],
                  [d[1], -d[0],    0]], dtype=np.float64)

    M = ddt + np.sqrt(1 - sin_angle**2) * (eye - ddt) + sin_angle * skew
    return M

def pathpatch_2d_to_3d(pathpatch, z = 0, normal = 'z'):
    """
    Transforms a 2D Patch to a 3D patch using the given normal vector.

    The patch is projected into they XY plane, rotated about the origin
    and finally translated by z.
    """
    if type(normal) is str: #Translate strings to normal vectors
        index = "xyz".index(normal)
        normal = np.roll((1,0,0), index)

    normal = normal/np.linalg.norm(normal) #Make sure the vector is normalised

    path = pathpatch.get_path() #Get the path and the associated transform
    trans = pathpatch.get_patch_transform()

    path = trans.transform_path(path) #Apply the transform
    pathpatch.__class__ = art3d.PathPatch3D #Change the class
    pathpatch._code3d = path.codes #Copy the codes
    pathpatch._facecolor3d = pathpatch.get_facecolor #Get the face color    

    verts = path.vertices #Get the vertices in 2D

    d = np.cross(normal, (0, 0, 1)) #Obtain the rotation vector   
    M = rotation_matrix(d) #Get the rotation matrix
    pathpatch._segment3d = np.array([np.dot(M, (x, y, 0)) + (0, 0, z) for x, y in verts])

def pathpatch_translate(pathpatch, delta):
    """
    Translates the 3D pathpatch by the amount delta.
    """
    pathpatch._segment3d += delta


fig = plt.figure() 
ax = fig.add_subplot(111, projection='3d') 
ax.plot(wellx,welly,wellz,c='k') 

for n,pd in enumerate(pointDepth): 
    x,y,z = fx(pd),fy(pd),fz(pd) 

    # figure out a vector from the point
    vx,vy,vz = (fx(pd-10)-x),(fy(pd-10)-y),(fz(pd-10)-z) 

    #Draw Circle
    p = Circle((x,y), 100) 
    ax.add_patch(p) 
    pathpatch_2d_to_3d(p, z=z,normal=(vx,vy,vz))
    pathpatch_translate(p,(0,0,0))

ax.set_xlim3d(np.min(wellx),np.max(wellx)) 
ax.set_ylim3d(np.min(welly), np.max(welly)) 
ax.set_zlim3d(np.min(wellz), np.max(wellz))
plt.show()

Answer 1

这是我想出的解决方案。我决定取点在直线上的位置和p.._segment3d中第一个点的位置之间的差异。这给出了我的圆离我想要的地方有多远，然后我简单地平移了面片的距离减去圆的半径，这样它就会居中。

我添加了一些随机数作为一些“错误”，下面是最终的代码和生成的图像

import matplotlib.pyplot as plt
from matplotlib.patches import Circle, PathPatch
from mpl_toolkits.mplot3d import Axes3D
import mpl_toolkits.mplot3d.art3d as art3d
import numpy as np
from scipy.interpolate import interp1d

md,wellz,wellx,welly=np.genfromtxt("./well.csv",delimiter=",",unpack=True)

# Building interpolation function that map a measured depth to its repsective x,y,z coordinates
fz = interp1d(md,wellz)
fx = interp1d(md,wellx)
fy = interp1d(md,welly)

pointDepth = np.array([15790,15554,15215,14911,14274,13927,13625,13284,12983,12640,12345,12004,11704,11361,11061,10717,10418,10080,9771])

# Some random radii
dist = [random.random()*100 for x in pointDepth]

def rotation_matrix(d):
    """
Calculates a rotation matrix given a vector d. The direction of d
corresponds to the rotation axis. The length of d corresponds to 
the sin of the angle of rotation.

Variant of: http://mail.scipy.org/pipermail/numpy-discussion/2009-March/040806.html
    """
    sin_angle = np.linalg.norm(d)

    if sin_angle == 0:
    return np.identity(3)

    d = d/sin_angle

    eye = np.eye(3)
    ddt = np.outer(d, d)
    skew = np.array([[    0,  d[2],  -d[1]],
                  [-d[2],     0,  d[0]],
                  [d[1], -d[0],    0]], dtype=np.float64)

    M = ddt + np.sqrt(1 - sin_angle**2) * (eye - ddt) + sin_angle * skew
    return M

def pathpatch_2d_to_3d(pathpatch, z = 0, normal = 'z'):
    """
    Transforms a 2D Patch to a 3D patch using the given normal vector.

    The patch is projected into they XY plane, rotated about the origin
    and finally translated by z.
    """
    if type(normal) is str: #Translate strings to normal vectors
        index = "xyz".index(normal)
        normal = np.roll((1,0,0), index)

    normal = normal/np.linalg.norm(normal) #Make sure the vector is normalised

    path = pathpatch.get_path() #Get the path and the associated transform
    trans = pathpatch.get_patch_transform()

    path = trans.transform_path(path) #Apply the transform
    pathpatch.__class__ = art3d.PathPatch3D #Change the class
    pathpatch._code3d = path.codes #Copy the codes
    pathpatch._facecolor3d = pathpatch.get_facecolor #Get the face color    

    verts = path.vertices #Get the vertices in 2D

    d = np.cross(normal, (0, 0, 1)) #Obtain the rotation vector   
    M = rotation_matrix(d) #Get the rotation matrix
    pathpatch._segment3d = np.array([np.dot(M, (x, y, 0)) + (0, 0, z) for x, y in verts])

def pathpatch_translate(pathpatch, delta):
    """
    Translates the 3D pathpatch by the amount delta.
    """
    pathpatch._segment3d += delta


fig = plt.figure() 
ax = fig.add_subplot(111, projection='3d') 
ax.plot(wellx,welly,wellz,c='k') 

for n,pd in enumerate(pointDepth): 
    x,y,z = fx(pd),fy(pd),fz(pd) 

    r = dist[n]

    # figure out a vector from the point
    vx,vy,vz = (fx(pd-10)-x),(fy(pd-10)-y),(fz(pd-10)-z) 

    #Draw Circle
    p = Circle((x,y), r) 
    ax.add_patch(p) 
    pathpatch_2d_to_3d(p, z=z,normal=(vx,vy,vz))
    difs = (x,y,z)-p._segment3d[0]
    pathpatch_translate(p,(difs[0]-r/2,difs[1]-r/2,difs[2]-r/2))


ax.set_xlim3d(np.min(wellx),np.max(wellx)) 
ax.set_ylim3d(np.min(welly), np.max(welly)) 
ax.set_zlim3d(np.min(wellz), np.max(wellz))
plt.show()

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