python draw parallelepiped

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庸人自扰
庸人自扰 2021-02-08 05:25

I am trying to draw a parallelepiped. Actually I started from the python script drawing a cube as:

import numpy as np
from mpl_toolkits.mplot3d import Axes3D
imp         


        
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  • 2021-02-08 05:45

    Given that the title of this question is 'python draw 3D cube', this is the article I found when I googled that question.

    For the purpose of those who do the same as me, who simply want to draw a cube, I have created the following function which takes four points of a cube, a corner first, and then the three adjacent points to that corner.

    It then plots the cube.

    The function is below:

    import numpy as np
    import matplotlib.pyplot as plt
    from mpl_toolkits.mplot3d import Axes3D
    from mpl_toolkits.mplot3d.art3d import Poly3DCollection, Line3DCollection
    
    def plot_cube(cube_definition):
        cube_definition_array = [
            np.array(list(item))
            for item in cube_definition
        ]
    
        points = []
        points += cube_definition_array
        vectors = [
            cube_definition_array[1] - cube_definition_array[0],
            cube_definition_array[2] - cube_definition_array[0],
            cube_definition_array[3] - cube_definition_array[0]
        ]
    
        points += [cube_definition_array[0] + vectors[0] + vectors[1]]
        points += [cube_definition_array[0] + vectors[0] + vectors[2]]
        points += [cube_definition_array[0] + vectors[1] + vectors[2]]
        points += [cube_definition_array[0] + vectors[0] + vectors[1] + vectors[2]]
    
        points = np.array(points)
    
        edges = [
            [points[0], points[3], points[5], points[1]],
            [points[1], points[5], points[7], points[4]],
            [points[4], points[2], points[6], points[7]],
            [points[2], points[6], points[3], points[0]],
            [points[0], points[2], points[4], points[1]],
            [points[3], points[6], points[7], points[5]]
        ]
    
        fig = plt.figure()
        ax = fig.add_subplot(111, projection='3d')
    
        faces = Poly3DCollection(edges, linewidths=1, edgecolors='k')
        faces.set_facecolor((0,0,1,0.1))
    
        ax.add_collection3d(faces)
    
        # Plot the points themselves to force the scaling of the axes
        ax.scatter(points[:,0], points[:,1], points[:,2], s=0)
    
        ax.set_aspect('equal')
    
    
    cube_definition = [
        (0,0,0), (0,1,0), (1,0,0), (0,0,1)
    ]
    plot_cube(cube_definition)
    

    Giving the result:

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  • 2021-02-08 05:55

    Done using matplotlib and coordinate geometry

    import matplotlib.pyplot as plt
    from mpl_toolkits.mplot3d import Axes3D
    import numpy as np
    
    
    def cube_coordinates(edge_len,step_size):
        X = np.arange(0,edge_len+step_size,step_size)
        Y = np.arange(0,edge_len+step_size,step_size)
        Z = np.arange(0,edge_len+step_size,step_size)
        temp=list()
        for i in range(len(X)):
            temp.append((X[i],0,0))
            temp.append((0,Y[i],0))
            temp.append((0,0,Z[i]))
            temp.append((X[i],edge_len,0))
            temp.append((edge_len,Y[i],0))
            temp.append((0,edge_len,Z[i]))
            temp.append((X[i],edge_len,edge_len))
            temp.append((edge_len,Y[i],edge_len))
            temp.append((edge_len,edge_len,Z[i]))
            temp.append((edge_len,0,Z[i]))
            temp.append((X[i],0,edge_len))
            temp.append((0,Y[i],edge_len))
        return temp
    
    
    edge_len = 10
    
    
    A=cube_coordinates(edge_len,0.01)
    A=list(set(A))
    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')
    A=zip(*A)
    X,Y,Z=list(A[0]),list(A[1]),list(A[2])
    ax.scatter(X,Y,Z,c='g')
    
    plt.show()
    
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  • 2021-02-08 06:00

    See my other answer (https://stackoverflow.com/a/49766400/3912576) for a simpler solution.

    Here is a more complicated set of functions which make matplotlib scale better and always forces the input to be a cube.

    The first parameter passed to cubify_cube_definition is the starting point, the second parameter is the second point, cube length is defined from this point, the third is a rotation point, it will be moved to match the length of the first and second.

    import numpy as np
    import matplotlib.pyplot as plt
    from mpl_toolkits.mplot3d import Axes3D
    from mpl_toolkits.mplot3d.art3d import Poly3DCollection, Line3DCollection
    
    def cubify_cube_definition(cube_definition):
        cube_definition_array = [
            np.array(list(item))
            for item in cube_definition
        ]
        start = cube_definition_array[0]
        length_decider_vector = cube_definition_array[1] - cube_definition_array[0]   
        length = np.linalg.norm(length_decider_vector)
    
        rotation_decider_vector = (cube_definition_array[2] - cube_definition_array[0])
        rotation_decider_vector = rotation_decider_vector / np.linalg.norm(rotation_decider_vector) * length
    
        orthogonal_vector = np.cross(length_decider_vector, rotation_decider_vector)
        orthogonal_vector = orthogonal_vector / np.linalg.norm(orthogonal_vector) * length
    
        orthogonal_length_decider_vector = np.cross(rotation_decider_vector, orthogonal_vector)
        orthogonal_length_decider_vector = (
            orthogonal_length_decider_vector / np.linalg.norm(orthogonal_length_decider_vector) * length)
    
        final_points = [
            tuple(start),
            tuple(start + orthogonal_length_decider_vector),
            tuple(start + rotation_decider_vector),
            tuple(start + orthogonal_vector)        
        ]
    
        return final_points
    
    
    def cube_vertices(cube_definition):
        cube_definition_array = [
            np.array(list(item))
            for item in cube_definition
        ]
    
        points = []
        points += cube_definition_array
        vectors = [
            cube_definition_array[1] - cube_definition_array[0],
            cube_definition_array[2] - cube_definition_array[0],
            cube_definition_array[3] - cube_definition_array[0]
        ]
    
        points += [cube_definition_array[0] + vectors[0] + vectors[1]]
        points += [cube_definition_array[0] + vectors[0] + vectors[2]]
        points += [cube_definition_array[0] + vectors[1] + vectors[2]]
        points += [cube_definition_array[0] + vectors[0] + vectors[1] + vectors[2]]
    
        points = np.array(points)
    
        return points
    
    
    def get_bounding_box(points): 
        x_min = np.min(points[:,0])
        x_max = np.max(points[:,0])
        y_min = np.min(points[:,1])
        y_max = np.max(points[:,1])
        z_min = np.min(points[:,2])
        z_max = np.max(points[:,2])
    
        max_range = np.array(
            [x_max-x_min, y_max-y_min, z_max-z_min]).max() / 2.0
    
        mid_x = (x_max+x_min) * 0.5
        mid_y = (y_max+y_min) * 0.5
        mid_z = (z_max+z_min) * 0.5
    
        return [
            [mid_x - max_range, mid_x + max_range],
            [mid_y - max_range, mid_y + max_range],
            [mid_z - max_range, mid_z + max_range]
        ]
    
    
    def plot_cube(cube_definition):
        points = cube_vertices(cube_definition)
    
        edges = [
            [points[0], points[3], points[5], points[1]],
            [points[1], points[5], points[7], points[4]],
            [points[4], points[2], points[6], points[7]],
            [points[2], points[6], points[3], points[0]],
            [points[0], points[2], points[4], points[1]],
            [points[3], points[6], points[7], points[5]]
        ]
    
        fig = plt.figure()
        ax = fig.add_subplot(111, projection='3d')
    
        faces = Poly3DCollection(edges, linewidths=1, edgecolors='k')
        faces.set_facecolor((0,0,1,0.1))
    
        ax.add_collection3d(faces)
    
        bounding_box = get_bounding_box(points)
    
        ax.set_xlim(bounding_box[0])
        ax.set_ylim(bounding_box[1])
        ax.set_zlim(bounding_box[2])
    
        ax.set_xlabel('x')
        ax.set_ylabel('y')
        ax.set_zlabel('z')
        ax.set_aspect('equal')
    
    
    cube_definition = cubify_cube_definition([(0,0,0), (0,3,0), (1,1,0.3)])
    plot_cube(cube_definition)
    

    Which produces the following result:

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  • 2021-02-08 06:00

    Plot surfaces with 3D PolyCollection (example)

    import numpy as np
    from mpl_toolkits.mplot3d import Axes3D
    from mpl_toolkits.mplot3d.art3d import Poly3DCollection, Line3DCollection
    import matplotlib.pyplot as plt
    
    points = np.array([[-1, -1, -1],
                      [1, -1, -1 ],
                      [1, 1, -1],
                      [-1, 1, -1],
                      [-1, -1, 1],
                      [1, -1, 1 ],
                      [1, 1, 1],
                      [-1, 1, 1]])
    
    P = [[2.06498904e-01 , -6.30755443e-07 ,  1.07477548e-03],
     [1.61535574e-06 ,  1.18897198e-01 ,  7.85307721e-06],
     [7.08353661e-02 ,  4.48415767e-06 ,  2.05395893e-01]]
    
    Z = np.zeros((8,3))
    for i in range(8): Z[i,:] = np.dot(points[i,:],P)
    Z = 10.0*Z
    
    fig = plt.figure()
    ax = fig.add_subplot(111, projection='3d')
    
    r = [-1,1]
    
    X, Y = np.meshgrid(r, r)
    # plot vertices
    ax.scatter3D(Z[:, 0], Z[:, 1], Z[:, 2])
    
    # list of sides' polygons of figure
    verts = [[Z[0],Z[1],Z[2],Z[3]],
     [Z[4],Z[5],Z[6],Z[7]], 
     [Z[0],Z[1],Z[5],Z[4]], 
     [Z[2],Z[3],Z[7],Z[6]], 
     [Z[1],Z[2],Z[6],Z[5]],
     [Z[4],Z[7],Z[3],Z[0]]]
    
    # plot sides
    ax.add_collection3d(Poly3DCollection(verts, 
     facecolors='cyan', linewidths=1, edgecolors='r', alpha=.25))
    
    ax.set_xlabel('X')
    ax.set_ylabel('Y')
    ax.set_zlabel('Z')
    
    plt.show()
    

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