如何围绕x，y和z轴将3d数组（nxnxn）旋转x度？

Question

我有一个用numpy创建的3d数组，我想知道如何将其旋转自定义角度，而不仅仅是rot90numpy 的功能。有人可以帮忙吗？

3d矩阵表示图像（例如立方体或其他形状），即

0:
1 1 1
1   1
1 1 1

1:
1   1

1   1

2:
1 1 1
1   1
1 1 1

编辑：移动解决方案来回答

Answer 1

看一下scipy.ndimage.interpolation.rotate函数。

之所以用科学而不是用麻木，是因为只需改变数组的索引就可以将图像旋转90度。但是，如果要将图像旋转任意角度，则必须处理插值，这将为问题增加新的一层。这是因为当您将旋转图像旋转90度时，原始图像中的所有像素都与旋转图像中的像素“完全对齐”。通常，旋转图像时不是这种情况。

Answer 2

经过一番尝试和错误后，我想出了一些用于我的目的的代码（0 表示数组中为空，另一个数字表示填充的体素。

def rotate(self, deg_angle, axis):
        d = len(self.matrix)
        h = len(self.matrix[0])
        w = len(self.matrix[0][0])
        min_new_x = 0
        max_new_x = 0
        min_new_y = 0
        max_new_y = 0
        min_new_z = 0
        max_new_z = 0
        new_coords = []
        angle = radians(deg_angle)

        for z in range(d):
            for y in range(h):
                for x in range(w):

                    new_x = None
                    new_y = None
                    new_z = None

                    if axis == "x":
                        new_x = int(round(x))
                        new_y = int(round(y*cos(angle) - z*sin(angle)))
                        new_z = int(round(y*sin(angle) + z*cos(angle)))
                    elif axis == "y":
                        new_x = int(round(z*sin(angle) + x*cos(angle)))
                        new_y = int(round(y))
                        new_z = int(round(z*cos(angle) - x*sin(angle)))
                    elif axis == "z":
                        new_x = int(round(x*cos(angle) - y*sin(angle)))
                        new_y = int(round(x*sin(angle) + y*cos(angle)))
                        new_z = int(round(z))

                    val = self.matrix.item((z, y, x))
                    new_coords.append((val, new_x, new_y, new_z))
                    if new_x < min_new_x: min_new_x = new_x
                    if new_x > max_new_x: max_new_x = new_x
                    if new_y < min_new_y: min_new_y = new_y
                    if new_y > max_new_y: max_new_y = new_y
                    if new_z < min_new_z: min_new_z = new_z
                    if new_z > max_new_z: max_new_z = new_z

        new_x_offset = abs(min_new_x)
        new_y_offset = abs(min_new_y)
        new_z_offset = abs(min_new_z)

        new_width = abs(min_new_x - max_new_x)
        new_height = abs(min_new_y - max_new_y)
        new_depth = abs(min_new_z - max_new_z)

        rotated = np.empty((new_depth + 1, new_height + 1, new_width + 1))
        rotated.fill(0)
        for coord in new_coords:
            val = coord[0]
            x = coord[1]
            y = coord[2]
            z = coord[3]

            if rotated[new_z_offset + z][new_y_offset + y][new_x_offset + x] == 0:
                rotated[new_z_offset + z][new_y_offset + y][new_x_offset + x] = val

        self.matrix = rotated

我使用上面代码的方式是：

cube = Rect_Prism(20, 20, 20) # creates a 3d array similar to above example, just bigger
cube.rotate(20, "x")
cube.rotate(60, "y")

Rect_Prism 创建一个 MxNxD 矩阵，但在本例中为 NxNxN。

以及打印时的结果：

                            # # # # # # # # # # # #          
                      # # #     #         # #       #        
                  # #           #   # # #           #        
              # #               # #                 #        
        # # #               # # # #                   #      
    # #               # # #       #                   #      
# # # # # # # # # # #             #                   #      
#                   #               #                   #    
  #                 #               #                   #    
  #                 #               #                   #    
  #                 #                 #                   #  
    #                 #               #                   #  
    #                 #               #                   #  
    #                 #                 #                 #  
      #                 #               #                 #  
      #                 #               # #               # #
      #                   #               #                 #
      #                   #               # # # # # # # # # #
      #                   #           # #                 #  
        #                   #   # # #               # # #    
        #                   # # #             # # #          
        #             # # # #             # #                
          #       # #         #     # # #                    
          #   # #             # # #                          
          # # # # # # # # # # # #