Python 中的等角投影遇到麻烦

Question

我正在尝试从形状 I 生成形状 II，并且我创建了以下代码。

import pygame
from pygame.locals import *
from OpenGL.GL import *
from OpenGL.GLU import *
import numpy as np

vertices = np.array([
    [0, 0, 0, 1],
    [0.707, -0.408, 0, 1],
    [0, -0.816, 0, 1],
    [-0.707, -0.408, 0, 1],
    [-0.707, 0.408, 0, 1],
    [0, 0.816, 0, 1],
    [0.707, 0.408, 0, 1],
    [0, 0, 0, 1]
], dtype=np.float64)

edges = [
    (0, 1),
    (1, 2),
    (2, 3),
    (3, 4),
    (4, 5),
    (5, 6),
    (6, 7),
    (3, 0),
    (4, 7),
    (7, 2),
    (6, 1),
    (0, 5)
]

axis_vertices = np.array([
    [0, 0, 0, 1],
    [4, 0, 0, 1],
    [0, 4, 0, 1],
    [0, 0, 4, 1]
], dtype=np.float64)

axis_edges = [
    (0, 1),
    (0, 2),
    (0, 3)
]

def multiply_matrix_vector(matrix, vector):

    result = np.zeros(matrix.shape[0])

    for i in range(matrix.shape[0]):
        temp_result = np.dot(matrix[i, :], vector)
        
        list(result)[i] = temp_result
  

    return result


def draw_cube():
    glBegin(GL_LINES)
    glColor3f(1, 1, 1)
    for edge in edges:
        for vertex in edge:
            glVertex3fv(vertices[vertex][:3])
    glEnd()

def draw_axes():
    glBegin(GL_LINES)
    glColor3f(1, 0, 0)
    glVertex3fv(axis_vertices[0][:3])
    glVertex3fv(axis_vertices[1][:3])
    glColor3f(0, 1, 0)
    glVertex3fv(axis_vertices[0][:3])
    glVertex3fv(axis_vertices[2][:3])
    glColor3f(0, 0, 1)
    glVertex3fv(axis_vertices[0][:3])
    glVertex3fv(axis_vertices[3][:3])
    glEnd()

def set_perspective_matrix(fov, aspect, near, far):
    f = 1.0 / np.tan(np.radians(fov) / 2.0)
    perspective_matrix = np.array([
        [f / aspect, 0, 0, 0],
        [0, f, 0, 0],
        [0, 0, (far + near) / (near - far), (2 * far * near) / (near - far)],
        [0, 0, -1, 0]
    ])
    glLoadMatrixd(perspective_matrix.transpose())

def main():
    pygame.init()
    display = (800, 600)
    pygame.display.set_mode(display, DOUBLEBUF | OPENGL)
    
    set_perspective_matrix(45, (display[0] / display[1]), 0.1, 50.0)

    glTranslatef(0.0, 0.0, -5)
    draw_cube()
    pygame.display.flip()

    while True:
        for event in pygame.event.get():
            if event.type == pygame.QUIT:
                pygame.quit()
                quit()

        glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT)
        
        glPushMatrix()

        # Translate along the x-axis
        translation_matrix = np.array([
            [1, 0, 0, 1.5],
            [0, 1, 0, 0],
            [0, 0, 1, 0],
            [0, 0, 0, 1]
        ])
        global vertices
        vertices = np.dot(vertices, translation_matrix.T)

        # Perform isometric projection
        isometric_matrix = np.array([
            [0.707, -0.408, 0.577, 0],
            [0, 0.816, 0.577, 0],
            [-0.707, -0.408, 0.577, 0],
            [0, 0, 0, 1]
        ])
        vertices = multiply_matrix_vector(isometric_matrix, vertices.T).T

        draw_axes()
        glPopMatrix()

        draw_cube()
        pygame.display.flip()
        pygame.time.wait(10)

if __name__ == "__main__":
    main()

但是，我在调整时遇到了错误：

49号线

result[i] = temp_result
~~~~~~^^^

ValueError：用序列设置数组元素。当我进行以下修改时：

list(result)[i] = temp_result

我收到一个新错误： 64 号线，

glVertex3fv(vertices[vertex][:3])

          

IndexError：标量变量的索引无效。

你能帮我吗？

Answer 1

创建通过矩阵变换数组中所有顶点的函数：

def multiply_matrix_vector(matrix, vector):
    result = np.zeros(vector.shape)
    for i in range(vector.shape[0]):
        result[i] = vector[i] @ matrix
    return result

不变换原始顶点，而是变换

draw_cube

函数的参数：

def draw_cube(vertices, edges):
    glBegin(GL_LINES)
    glColor3f(1, 1, 1)
    for edge in edges:
        for vertex in edge:
            glVertex3fv(vertices[vertex][:3])
    glEnd()

如果要绘制立方体，请将顶点和边传递给函数：

draw_cube(vertices, edges)

如果你想变换立方体，复制顶点，变换顶点的副本，最后将变换后的顶点低音到

draw_cube

：

v = np.copy(vertices)

# Translate along the x-axis
translation_matrix = np.array([
    [1, 0, 0, 1.5],
    [0, 1, 0, 0],
    [0, 0, 1, 0],
    [0, 0, 0, 1]
])
v = multiply_matrix_vector(translation_matrix.T, v)

# Perform isometric projection
isometric_matrix = np.array([
    [0.707, -0.408, 0.577, 0],
    [0, 0.816, 0.577, 0],
    [-0.707, -0.408, 0.577, 0],
    [0, 0, 0, 1]
])
v = multiply_matrix_vector(isometric_matrix.T, v)

draw_cube(v, edges)