基于法线向量和Matlab或matplotlib中的点绘制平面

5 回答

• 5

  对于所有的复制/粘贴，这里是使用matplotlib的Python的类似代码：

  import numpy as np
  import matplotlib.pyplot as plt
  from mpl_toolkits.mplot3d import Axes3D
  
  point  = np.array([1, 2, 3])
  normal = np.array([1, 1, 2])
  
  # a plane is a*x+b*y+c*z+d=0
  # [a,b,c] is the normal. Thus, we have to calculate
  # d and we're set
  d = -point.dot(normal)
  
  # create x,y
  xx, yy = np.meshgrid(range(10), range(10))
  
  # calculate corresponding z
  z = (-normal[0] * xx - normal[1] * yy - d) * 1. /normal[2]
  
  # plot the surface
  plt3d = plt.figure().gca(projection='3d')
  plt3d.plot_surface(xx, yy, z)
  plt.show()
  

  

  回复于 2024-05-03T04:15:42+08:00
• 28

  以上答案都足够好了 . 有一点需要注意的是，他们使用相同的方法来计算给定（x，y）的z值 . 回退是因为它们使平面网格化并且空间中的平面可能变化（仅保持其投影相同） . 例如，你无法在3D空间中获得一个正方形（但是一个扭曲的正方形） .

  为避免这种情况，使用旋转有不同的方法 . 如果你首先在x-y平面上生成数据（可以是任何形状），然后将它旋转相等的数量（[0 0 1]到你的向量），那么你将得到你想要的 . 只需在代码下方运行以供参考 .

  point = [1,2,3];
  normal = [1,2,2];
  t=(0:10:360)';
  circle0=[cosd(t) sind(t) zeros(length(t),1)];
  r=vrrotvec2mat(vrrotvec([0 0 1],normal));
  circle=circle0*r'+repmat(point,length(circle0),1);
  patch(circle(:,1),circle(:,2),circle(:,3),.5);
  axis square; grid on;
  %add line
  line=[point;point+normr(normal)]
  hold on;plot3(line(:,1),line(:,2),line(:,3),'LineWidth',5)
  

  它得到一个3D圆：
  

  回复于 2024-05-03T04:15:42+08:00
• 1

  对于想在表面上使用渐变的复制贴纸：

  from mpl_toolkits.mplot3d import Axes3D
  from matplotlib import cm
  import numpy as np
  import matplotlib.pyplot as plt
  
  point = np.array([1, 2, 3])
  normal = np.array([1, 1, 2])
  
  # a plane is a*x+b*y+c*z+d=0
  # [a,b,c] is the normal. Thus, we have to calculate
  # d and we're set
  d = -point.dot(normal)
  
  # create x,y
  xx, yy = np.meshgrid(range(10), range(10))
  
  # calculate corresponding z
  z = (-normal[0] * xx - normal[1] * yy - d) * 1. / normal[2]
  
  # plot the surface
  plt3d = plt.figure().gca(projection='3d')
  
  Gx, Gy = np.gradient(xx * yy)  # gradients with respect to x and y
  G = (Gx ** 2 + Gy ** 2) ** .5  # gradient magnitude
  N = G / G.max()  # normalize 0..1
  
  plt3d.plot_surface(xx, yy, z, rstride=1, cstride=1,
                     facecolors=cm.jet(N),
                     linewidth=0, antialiased=False, shade=False
  )
  plt.show()
  

  

  回复于 2024-05-03T04:15:42+08:00
• 49

  对于Matlab：

  point = [1,2,3];
  normal = [1,1,2];
  
  %# a plane is a*x+b*y+c*z+d=0
  %# [a,b,c] is the normal. Thus, we have to calculate
  %# d and we're set
  d = -point*normal'; %'# dot product for less typing
  
  %# create x,y
  [xx,yy]=ndgrid(1:10,1:10);
  
  %# calculate corresponding z
  z = (-normal(1)*xx - normal(2)*yy - d)/normal(3);
  
  %# plot the surface
  figure
  surf(xx,yy,z)
  

  

  注意：此解决方案仅在法线（3）不为0时才有效 . 如果平面与z轴平行，则可以旋转尺寸以保持相同的方法：

  z = (-normal(3)*xx - normal(1)*yy - d)/normal(2); %% assuming normal(3)==0 and normal(2)~=0
  
  %% plot the surface
  figure
  surf(xx,yy,z)
  
  %% label the axis to avoid confusion
  xlabel('z')
  ylabel('x')
  zlabel('y')
  

  回复于 2024-05-03T04:15:42+08:00
• 5

  一个更干净的Python示例，也适用于棘手的$ z，y，z $情况，

  from mpl_toolkits.mplot3d import axes3d
  from matplotlib.patches import Circle, PathPatch
  import matplotlib.pyplot as plt
  from matplotlib.transforms import Affine2D
  from mpl_toolkits.mplot3d import art3d
  import numpy as np
  
  def plot_vector(fig, orig, v, color='blue'):
     ax = fig.gca(projection='3d')
     orig = np.array(orig); v=np.array(v)
     ax.quiver(orig[0], orig[1], orig[2], v[0], v[1], v[2],color=color)
     ax.set_xlim(0,10);ax.set_ylim(0,10);ax.set_zlim(0,10)
     ax = fig.gca(projection='3d')  
     return fig
  
  def rotation_matrix(d):
      sin_angle = np.linalg.norm(d)
      if sin_angle == 0:return np.identity(3)
      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, normal):
      if type(normal) is str: #Translate strings to normal vectors
          index = "xyz".index(normal)
          normal = np.roll((1.0,0,0), index)
  
      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):
      pathpatch._segment3d += delta
  
  def plot_plane(ax, point, normal, size=10, color='y'):    
      p = Circle((0, 0), size, facecolor = color, alpha = .2)
      ax.add_patch(p)
      pathpatch_2d_to_3d(p, z=0, normal=normal)
      pathpatch_translate(p, (point[0], point[1], point[2]))
  
  
  o = np.array([5,5,5])
  v = np.array([3,3,3])
  n = [0.5, 0.5, 0.5]
  
  from mpl_toolkits.mplot3d import Axes3D
  fig = plt.figure()
  ax = fig.gca(projection='3d')  
  plot_plane(ax, o, n, size=3)    
  ax.set_xlim(0,10);ax.set_ylim(0,10);ax.set_zlim(0,10)
  plt.show()
  

  

  回复于 2024-05-03T04:15:42+08:00