Matplotlib旋轉3d磁盤

Question

我有一條線和一些點在3D空間的那條線上。我知道這個點有一定的誤差，但是誤差只是垂直於線。要查看此信息，我希望磁盤的半徑爲錯誤半徑，並且與線的方向正交。我發現這solution，但我不能得到它的工作。

如果我跑我想將「Z」輸出正常的代碼和狀態軸我得到啥子我woudl期待。具有給定半徑的磁盤並且在z軸上定向。

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

我想旋轉的磁盤。爲了在那一點找到井向量，我使用了一個使用該向量的點。這是我作爲normal=(vx,vy,vz)放置的矢量，但是當我這樣做時，磁盤甚至不在圖表上。我不確定我要出錯的地方。有人有建議嗎？

這是我的代碼。

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

這是我想出的解決方案。我決定採取點在線的位置和第一點在p.._segment3d的第一點之間的區別。這給了我離我想要的距離多遠的距離，然後我簡單地將該距離減去圓的半徑，以便它將居中。

我已經在一些隨機數作爲一些「錯誤」加入，這裏是最後的代碼和生成的圖像

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()