In the last tutorial we saw how to make a simple 3D simulation. In this tutorial we will build from the theory and code from the last tutorial and make a rotating 3D wireframe cube. See below a video of the simulation in action.

## The Idea

A cube is composed of 8 vertices and 6 faces. Each face is composed of 4 vertices, and each vertex can be shared by 3 faces. We will define a vertex list with 8 points, and define a list of faces. A face will be defined as list of 4 indices that are pointers to the vertex list.

To simulate a rotating wireframe cube, we will rotate the 8 vertices, project them, and save them in a new list. Then, we will draw the edges of each face using the face list to find the vertices of each face.

## The Code

""" Wireframe 3D cube simulation. Developed by Leonel Machava <[email protected]> http://codeNtronix.com """ import sys, math, pygame class Point3D: def __init__(self, x = 0, y = 0, z = 0): self.x, self.y, self.z = float(x), float(y), float(z) def rotateX(self, angle): """ Rotates the point around the X axis by the given angle in degrees. """ rad = angle * math.pi / 180 cosa = math.cos(rad) sina = math.sin(rad) y = self.y * cosa - self.z * sina z = self.y * sina + self.z * cosa return Point3D(self.x, y, z) def rotateY(self, angle): """ Rotates the point around the Y axis by the given angle in degrees. """ rad = angle * math.pi / 180 cosa = math.cos(rad) sina = math.sin(rad) z = self.z * cosa - self.x * sina x = self.z * sina + self.x * cosa return Point3D(x, self.y, z) def rotateZ(self, angle): """ Rotates the point around the Z axis by the given angle in degrees. """ rad = angle * math.pi / 180 cosa = math.cos(rad) sina = math.sin(rad) x = self.x * cosa - self.y * sina y = self.x * sina + self.y * cosa return Point3D(x, y, self.z) def project(self, win_width, win_height, fov, viewer_distance): """ Transforms this 3D point to 2D using a perspective projection. """ factor = fov / (viewer_distance + self.z) x = self.x * factor + win_width / 2 y = -self.y * factor + win_height / 2 return Point3D(x, y, 1)

This class remains pretty much the same. We use it to represent points in 3D space.

class Simulation: def __init__(self, win_width = 640, win_height = 480): pygame.init() self.screen = pygame.display.set_mode((win_width, win_height)) pygame.display.set_caption("3D Wireframe Cube Simulation (http://codeNtronix.com)") self.clock = pygame.time.Clock() self.vertices = [ Point3D(-1,1,-1), Point3D(1,1,-1), Point3D(1,-1,-1), Point3D(-1,-1,-1), Point3D(-1,1,1), Point3D(1,1,1), Point3D(1,-1,1), Point3D(-1,-1,1) ] # Define the vertices that compose each of the 6 faces. These numbers are # indices to the vertices list defined above. self.faces = [(0,1,2,3),(1,5,6,2),(5,4,7,6),(4,0,3,7),(0,4,5,1),(3,2,6,7)] self.angleX, self.angleY, self.angleZ = 0, 0, 0 def run(self): """ Main Loop """ while 1: for event in pygame.event.get(): if event.type == pygame.QUIT: sys.exit() self.clock.tick(50) self.screen.fill((0,0,0)) # Will hold transformed vertices. t = [] for v in self.vertices: # Rotate the point around X axis, then around Y axis, and finally around Z axis. r = v.rotateX(self.angleX).rotateY(self.angleY).rotateZ(self.angleZ) # Transform the point from 3D to 2D p = r.project(self.screen.get_width(), self.screen.get_height(), 256, 4) # Put the point in the list of transformed vertices t.append(p) for f in self.faces: pygame.draw.line(self.screen, (255,255,255), (t[f[0]].x, t[f[0]].y), (t[f[1]].x, t[f[1]].y)) pygame.draw.line(self.screen, (255,255,255), (t[f[1]].x, t[f[1]].y), (t[f[2]].x, t[f[2]].y)) pygame.draw.line(self.screen, (255,255,255), (t[f[2]].x, t[f[2]].y), (t[f[3]].x, t[f[3]].y)) pygame.draw.line(self.screen, (255,255,255), (t[f[3]].x, t[f[3]].y), (t[f[0]].x, t[f[0]].y)) self.angleX += 1 self.angleY += 1 self.angleZ += 1 pygame.display.flip() if __name__ == "__main__": Simulation().run()

First, on line 23, we define a list of faces. For each face, we set the indices of the vertices that compose it. In the *run()* function, we transform the vertices and store them in the *t* list. Then, we draw the edges of each face. Everything else remains pretty much the same.

Click here to download the full source code.

## Conclusion

That’s is everything for now. In a future tutorial, I will show you how to make a rotating solid cube.

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Nice work!

I am currently learning python & pygame.

Thanks for sharing your knowledge.

Keep it up!!!

Hello Mahesh. Thank you very much

its very good

Thank you.

Hi, this has helped me out loads Thank you for taking the time to put this tutorial together

Hey Man, great writing!

I’m working on gyroscope script, and this code will be ideal to visualize it’s measurements. I hope you don’t have anything against using it ?

Hello Marcin. Thank you.

You can freely use the code. I will be glad if you give me some credits though