Ejemplos de figuras 3D
El día de hoy vimos en clase como realizar figuras en 3D, tomando de ejemplo las figuras que se encuentran en el blog de Eduardo un compañero de generaciones anteriores.
Para poder trabajar debemos tener instaladas las siguientes librerías:
MATPLOTLIB
PyOpenGL
1. En este primer programa observaremos un cubo en 3D básico
import pygame
from pygame.locals import *
from OpenGL.GL import *
from OpenGL.GLU import *
verticies = (
(1, -1, -1),
(1, 1, -1),
(-1, 1, -1),
(-1, -1, -1),
(1, -1, 1),
(1, 1, 1),
(-1, -1, 1),
(-1, 1, 1)
)
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():
glBegin(GL_LINES)
for edge in edges:
for vertex in edge:
glVertex3fv(verticies[vertex])
glEnd()
def main():
pygame.init()
display = (800,600) #coordenadas de la ventana pygame
pygame.display.set_mode(display, DOUBLEBUF|OPENGL) #desplegar la ventana
gluPerspective(45, (display[0]/display[1]), 0.1, 50.0)
glTranslatef(0.0,0.0, -5)
while True:
for event in pygame.event.get():
if event.type == pygame.QUIT:
pygame.quit()
quit()
glRotatef(1, 3, 1, 1) #la rotacion sobre un punto
glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT)
Cube()
pygame.display.flip()
pygame.time.wait(10) #la velocidad del cubo
main()
Resultado
Código
import pygame
from pygame.locals import *
from OpenGL.GL import *
from OpenGL.GLU import *
verticies = (
(1, -1, -1),
(1, 1, -1),
(-1, 1, -1),
(-1, -1, -1),
(0,0,1)
)
edges = (
(4,0),
(4,1),
(4,2),
(4,3),
(0,1),
(0,3),
(2,1),
(2,3)
)
def Cube():
glBegin(GL_LINES)
for edge in edges:
for vertex in edge:
glVertex3fv(verticies[vertex])
glEnd()
def main():
pygame.init()
display = (800,600)
pygame.display.set_mode(display, DOUBLEBUF|OPENGL)
gluPerspective(45, (display[0]/display[1]), 0.1, 50.0)
glTranslatef(0.0,0.0, -5)
while True:
for event in pygame.event.get():
if event.type == pygame.QUIT:
pygame.quit()
quit()
glRotatef(1, 3, 1, 1)
glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT)
Cube()
pygame.display.flip()
pygame.time.wait(10)
main()
Resultado:
3. En el tercer programa visualizaremos un cubo en 3D con color
Código
#cubocolorespython
import sys, math, pygame
from operator import itemgetter
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, self.z)
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("Figura de cubo 3D en python")
self.clock = pygame.time.Clock()
self.vertices = [
Point3D(1, -1, -1),
Point3D(1, 1, -1),
Point3D(-1, 1, -1),
Point3D(-1, -1, -1),
Point3D(0, 0, 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), (0,1,4), (1,2,4), (2,3,4), (3,0,4)]
# Define colors for each face
self.colors = [(255, 0, 100), (100, 0, 0), (0, 25, 0), (0, 0, 255), (0, 255, 155)]
self.angle = 0
def run(self):
""" Main Loop """
while 1:
for event in pygame.event.get():
if event.type == pygame.QUIT:
pygame.quit()
sys.exit()
self.clock.tick(50)
self.screen.fill((0, 32, 0))
# It 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.angle).rotateY(self.angle).rotateZ(self.angle)
# 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)
# Calculate the average Z values of each face.
avg_z = []
i = 0
for f in self.faces:
z = (t[f[0]].z + t[f[1]].z + t[f[2]].z + t[f[3]].z) / 4.0
avg_z.append([i, z])
i = i + 1
# Draw the faces using the Painter's algorithm: # Distant faces are drawn before the closer ones.
for tmp in sorted(avg_z, key=itemgetter(1), reverse=True):
face_index = tmp[0]
f = self.faces[face_index]
pointlist = [(t[f[0]].x, t[f[0]].y), (t[f[1]].x, t[f[1]].y),
(t[f[1]].x, t[f[1]].y), (t[f[2]].x, t[f[2]].y),
(t[f[2]].x, t[f[2]].y), (t[f[3]].x, t[f[3]].y),
(t[f[3]].x, t[f[3]].y), (t[f[0]].x, t[f[0]].y)]
pygame.draw.polygon(self.screen, self.colors[face_index], pointlist)
self.angle += 1
pygame.display.flip()
if __name__ == "__main__":
Simulation().run()
Resultado
4. En este cuarto programa visualizaremos una gráfica sencilla en 3D
Código
# matplotlib que nos permiten graficar y visualizar datos en tercera dimensión. from mpl_toolkits.mplot3d import Axes3D import matplotlib.pyplot as plt # Creamos la figura fig = plt.figure() # Agrrgamos un plano 3D ax1 = fig.add_subplot(111, projection='3d') # Datos en array bi-dimensional xpos = [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] ypos = [10,1,1,1,1,6,2,1,7,2,3,5,1,3,2] num_elements = len(xpos) zpos = [1,0,0,0,0,0,0,0,0,0,0,0,0,0,0] dx = ldy = ldz = [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] # plot_wireframe nos permite agregar los datos x, y, z. Por ello 3D # Es necesario que los datos esten contenidos en un array bi-dimensiona ax1.bar3d(xpos,ypos, zpos, dx, ldy, ldz, color='red') # Mostramos el gráfico plt.show()
Resultado
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