如何在python-opengl中连接“内部多维数据集”和“外部多维数据集”（4维对象）的顶点？

Question

I was trying to make a model of tesseract (4D object) in python using OpenGL and Pygame tools. Fortunately, I got the outlook (having a cube inside a cube) but couldn't join the vertices of inner cube with the outer one. This is my code, below.

import pygame
from pygame.locals import *
from OpenGL.GL import *
from OpenGL.GLU import *

vertices = ((1,-1,-1),(1,1,-1),(-1,1,-1),(-1,-1,-1),(1,-1,1),(1,1,1),(-1,-1,1),(-1,1,1))
vertices1 = ((2,-2,-2),(2,2,-2),(-2,2,-2),(-2,-2,-2),(2,-2,2),(2,2,2),(-2,-2,2),(-2,2,2))

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

def cube(edges,vertices):
    glBegin(GL_LINES)
    for edge in edges:
        for vertex in edge:
            glVertex3fv(vertices[vertex]) 
    glEnd()

def display_cube():
    pygame.init()
    display_window = (800,600)
    pygame.display.set_mode(display_window,DOUBLEBUF | OPENGL)
    gluPerspective(45,(display_window[0]/display_window[1]),0.1,50.0)
    glTranslatef(0.0,0.0,-10)
    while True:
        for event in pygame.event.get():
            if event.type == pygame.QUIT:
            pygame.quit()
            quit()

        glRotate(1,3,10,10) # (angle,x,y,z)
        glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT)

        cube(edges,vertices1) # large cube
        cube(edges,vertices) # small cube

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

display_cube()

I could easily get the inner cube (smaller one) surrounded by the outer cube (larger one). But not able to join the vertices of both.

Please help me sharing your valuable answers...

This is the image which I wanted to get

Thanks in advance.

Answer 1

Group points from both lists zip(vertices1, vertices2) and you have lines to draw.

def lines(vertices1, vertices2):
    for v1, v2 in zip(vertices1, vertices2):
        glBegin(GL_LINES)
        glVertex3fv(v1) 
        glVertex3fv(v2) 
        glEnd()


lines(vertices, vertices1)

And you get

Full code

import pygame
from pygame.locals import *
from OpenGL.GL import *
from OpenGL.GLU import *


vertices = ((1,-1,-1),(1,1,-1),(-1,1,-1),(-1,-1,-1),(1,-1,1),(1,1,1),(-1,-1,1),(-1,1,1))
vertices1 = ((2,-2,-2),(2,2,-2),(-2,2,-2),(-2,-2,-2),(2,-2,2),(2,2,2),(-2,-2,2),(-2,2,2))

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

def cube(edges,vertices):
    glBegin(GL_LINES)
    for edge in edges:
        for vertex in edge:
            glVertex3fv(vertices[vertex]) 
    glEnd()

def lines(vertices1, vertices2):
    for v1, v2 in zip(vertices1, vertices2):
        glBegin(GL_LINES)
        glVertex3fv(v1) 
        glVertex3fv(v2) 
        glEnd()

def display_cube():
    pygame.init()
    display_window = (800,600)
    pygame.display.set_mode(display_window,DOUBLEBUF | OPENGL)
    gluPerspective(45,(display_window[0]/display_window[1]),0.1,50.0)
    glTranslatef(0.0,0.0,-10)
    while True:
        for event in pygame.event.get():
            if event.type == pygame.QUIT:
                pygame.quit()
                quit()

        glRotate(1,3,10,10) # (angle,x,y,z)
        glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT)

        cube(edges,vertices1) # large cube
        cube(edges,vertices) # small cube
        lines(vertices1, vertices)

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

display_cube()

Answer 2

You can prepare 3 VAOs . 1st containing vertices for inner cube. 2nd containing vertices for outer cube. 3rd create VAO of pair wise vertices. For example

Lets say that ABCD are vertices of face of outer cube and abcd are vertices of face of inner cube. Now you want to draw line between A to a, B to b, C to c and D to d. So prepare VBO as (A ,a ,B ,b ,C ,c ,D ,d ). After this to draw this VBO use GL_LINE primitive.

I hope this is clear .