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前のコードに追加を行った。

回転行列をかけるということで座標変換を行う。

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

from mpl_toolkits.mplot3d import proj3d
def orthogonal_proj(zfront, zback):
    width = zfront - zback;
    a = 1 / width
    b = - a * (zfront + zback) / 2
    return np.array([[1,0,0,0],
                     [0,1,0,0],
                     [0,0,a,b],
                     [0,0,0,zback]])
proj3d.persp_transformation = orthogonal_proj

def rotX(X):
    theta = X / 180.0 * np.pi;
    Rx = np.array([[1,0,0,0],
                   [0,np.cos(theta),np.sin(theta),0],
                   [0,-np.sin(theta),np.cos(theta),0],
                   [0,0,0,1]]);
    return Rx;

def rotY(Y):
    theta = Y / 180.0 * np.pi;
    Ry = np.array([[np.cos(theta),0,-np.sin(theta),0],
                   [0,1,0,0],
                   [np.sin(theta),0,np.cos(theta),0],
                   [0,0,0,1]]);
    return Ry;

def rotZ(Z):
    theta = Z / 180.0 * np.pi;
    Rz = np.array([[np.cos(theta),np.sin(theta),0,0],
                   [-np.sin(theta),np.cos(theta),0,0],
                   [0,0,1,0],
                   [0,0,0,1]]);
    return Rz;

def trans(x):
    Tr = np.array([[1,0,0,x[0]],
                   [0,1,0,x[1]],
                   [0,0,1,x[2]],
                   [0,0,0,1]]);
    return Tr;

def main():

    r = 50.0;
    theta = np.arange(0.0, 360.0, 30.0);
    x = np.array([]);
    y = np.array([]);
    z = np.array([]);

    for i in range(10):
        x_ = r * np.cos(theta / 180.0 * np.pi);
        y_ = r * np.sin(theta / 180.0 * np.pi);
        z_ = 10.0 * i * np.ones(x_.shape[0]);
        
        x = np.append(x, x_);
        y = np.append(y, y_);
        z = np.append(z, z_);
    
    X = np.array([x, y, z, np.ones(x.shape[0])]);
    X = np.dot(rotX(45.0), X);
    X = np.dot(rotY(45.0), X);
    X = np.dot(rotZ(10.0), X);
    X = np.dot(trans([10, 10, -10]), X);
    
    fig = plt.figure()
    ax = fig.gca(projection='3d')
    ax.scatter3D(X[0], X[1], X[2]);
    ax.set_aspect('equal')
    plt.grid()
    plt.savefig('plot201803.svg');
    plt.show();

if __name__ == '__main__':
    main()