I ported over the .cpp version of spinningcube found there to python for a better understanding of opengl and to create something new. While I get the same result as the compiled version from the book source code from both 6th and 7ed as the program is the same from the two editions, the program in its current state displays a green screen only. The book of OpenGl Superbible 7th ed. on page 177 shows a spinning colored cube is supposed to fly around. Any assistance would be greatly appreciated.
Update - June 24, 2019 - I have updated the code so that the cube appears, spins, and moves per the excellent code from Rabbid76. Thank You.
#!/usr/bin/python3
import sys
import time
import math
fullscreen = True
# sys.path.append("../shared")
# from math3d import m3dDegToRad, m3dRotationMatrix44, M3DMatrix44f, m3dLoadIdentity44, \
# m3dTranslateMatrix44, m3dScaleMatrix44, \
# m3dMatrixMultiply44, m3dTransposeMatrix44, \
# m3dRadToDeg
import numpy.matlib
import numpy as np
try:
from OpenGL.GLUT import *
from OpenGL.GL import *
from OpenGL.GLU import *
from OpenGL.raw.GL.ARB.vertex_array_object import glGenVertexArrays, \
glBindVertexArray
except:
print ('''
ERROR: PyOpenGL not installed properly.
''')
sys.exit()
from math import cos, sin
from array import array
M3D_PI = 3.14159265358979323846
M3D_PI_DIV_180 = M3D_PI / 180.0
M3D_INV_PI_DIV_180 = 57.2957795130823229
# Translate matrix. Only 4x4 matrices supported
def m3dTranslateMatrix44(m, x, y, z):
m[12] += x
m[13] += y
m[14] += z
def m3dDegToRad(num):
return (num * M3D_PI_DIV_180)
def m3dRadToDeg(num):
return (num * M3D_INV_PI_DIV_180)
def m3dOrtho(l, r, t, b, n, f):
return (GLfloat * 16)(
2/(r-l), 0, 0, 0,
0, 2/(t-b), 0, 0,
0, 0, -2/(f-n), 0,
-(r+l)/(r-l), -(t+b)/(t-b), -(f+n)/(f-n), 1)
def m3dPerspective(fov_y, aspect, n, f):
a = aspect
ta = math.tan( fov_y / 2 )
return (GLfloat * 16)(
1/(ta*a), 0, 0, 0,
0, 1/ta, 0, 0,
0, 0, -(f+n)/(f-n), -1,
0, 0, -2*f*n/(f-n), 0)
# Creates a 4x4 rotation matrix, takes radians NOT degrees
def m3dRotationMatrix44(m, angle, x, y, z):
s = sin(angle)
c = cos(angle)
mag = float((x * x + y * y + z * z) ** 0.5)
if mag == 0.0:
m3dLoadIdentity(m)
return
x /= mag
y /= mag
z /= mag
xx = x * x
yy = y * y
zz = z * z
xy = x * y
yz = y * z
zx = z * x
xs = x * s
ys = y * s
zs = z * s
one_c = 1.0 - c
m[0] = (one_c * xx) + c
m[1] = (one_c * xy) - zs
m[2] = (one_c * zx) + ys
m[3] = 0.0
m[4] = (one_c * xy) + zs
m[5] = (one_c * yy) + c
m[6] = (one_c * yz) - xs
m[7] = 0.0
m[8] = (one_c * zx) - ys
m[9] = (one_c * yz) + xs
m[10] = (one_c * zz) + c
m[11] = 0.0
m[12] = 0.0
m[13] = 0.0
m[14] = 0.0
m[15] = 1.0
def m3dMultiply(A, B):
C = (GLfloat * 16)(*identityMatrix)
for k in range(0, 4):
for j in range(0, 4):
C[k*4+j] = A[0*4+j] * B[k*4+0] + A[1*4+j] * B[k*4+1] + \
A[2*4+j] * B[k*4+2] + A[3*4+j] * B[k*4+3]
return C
def translate(tx, ty, tz):
"""creates the matrix equivalent of glTranslate"""
return np.array([1.0, 0.0, 0.0, 0.0,
0.0, 1.0, 0.0, 0.0,
0.0, 0.0, 1.0, 0.0,
tx, ty, tz, 1.0], np.float32)
def rotation_matrix(axis, theta):
"""
Return the rotation matrix associated with counterclockwise rotation about
the given axis by theta radians.
"""
axis = np.asarray(axis)
axis = axis / math.sqrt(np.dot(axis, axis))
a = math.cos(theta / 2.0)
b, c, d = -axis * math.sin(theta / 2.0)
aa, bb, cc, dd = a * a, b * b, c * c, d * d
bc, ad, ac, ab, bd, cd = b * c, a * d, a * c, a * b, b * d, c * d
return np.array([[aa + bb - cc - dd, 2 * (bc + ad), 2 * (bd - ac), 0],
[2 * (bc - ad), aa + cc - bb - dd, 2 * (cd + ab), 0],
[2 * (bd + ac), 2 * (cd - ab), aa + dd - bb - cc, 0],
[0,0,0,1]])
identityMatrix = [1,0,0,0, 0,1,0,0, 0,0,1,0, 0,0,0,1]
mv_location = (GLfloat * 16)(*identityMatrix)
proj_location = (GLfloat * 16)(*identityMatrix)
proj_matrix = (GLfloat * 16)(*identityMatrix)
many_cubes = False
# Vertex program
vs_source = '''
#version 410 core
in vec4 position;
out VS_OUT
{
vec4 color;
} vs_out;
uniform mat4 mv_matrix;
uniform mat4 proj_matrix;
void main(void)
{
gl_Position = proj_matrix * mv_matrix * position;
vs_out.color = position * 2.0 + vec4(0.5, 0.5, 0.5, 0.0);
}
'''
# Fragment program
fs_source = '''
#version 410 core
out vec4 color;
in VS_OUT
{
vec4 color;
} fs_in;
void main(void)
{
color = fs_in.color;
}
'''
def compile_program(vertex_source, fragment_source):
global mv_location
global proj_location
vertex_shader = None
fragment_shader = None
if vertex_source:
vertex_shader = glCreateShader(GL_VERTEX_SHADER)
glShaderSource(vertex_shader, vertex_source)
glCompileShader(vertex_shader)
if not glGetShaderiv(vertex_shader, GL_COMPILE_STATUS):
raise Exception('failed to compile shader "%s":\n%s' %
('vertex_shader', glGetShaderInfoLog(vertex_shader)))
if fragment_source:
fragment_shader = glCreateShader(GL_FRAGMENT_SHADER)
glShaderSource(fragment_shader, fragment_source)
glCompileShader(fragment_shader)
if not glGetShaderiv(fragment_shader, GL_COMPILE_STATUS):
raise Exception('failed to compile shader "%s":\n%s' %
('fragment_shader', glGetShaderInfoLog(fragment_shader)))
program = glCreateProgram()
glAttachShader(program, vertex_shader)
glAttachShader(program, fragment_shader)
glLinkProgram(program)
mv_location = glGetUniformLocation(program, "mv_matrix");
proj_location = glGetUniformLocation(program, "proj_matrix");
vao = GLuint(0)
glGenVertexArrays(1, vao);
glBindVertexArray(vao);
vertex_positions = [
-0.25, 0.25, -0.25,
-0.25, -0.25, -0.25,
0.25, -0.25, -0.25,
0.25, -0.25, -0.25,
0.25, 0.25, -0.25,
-0.25, 0.25, -0.25,
0.25, -0.25, -0.25,
0.25, -0.25, 0.25,
0.25, 0.25, -0.25,
0.25, -0.25, 0.25,
0.25, 0.25, 0.25,
0.25, 0.25, -0.25,
0.25, -0.25, 0.25,
-0.25, -0.25, 0.25,
0.25, 0.25, 0.25,
-0.25, -0.25, 0.25,
-0.25, 0.25, 0.25,
0.25, 0.25, 0.25,
-0.25, -0.25, 0.25,
-0.25, -0.25, -0.25,
-0.25, 0.25, 0.25,
-0.25, -0.25, -0.25,
-0.25, 0.25, -0.25,
-0.25, 0.25, 0.25,
-0.25, -0.25, 0.25,
0.25, -0.25, 0.25,
0.25, -0.25, -0.25,
0.25, -0.25, -0.25,
-0.25, -0.25, -0.25,
-0.25, -0.25, 0.25,
-0.25, 0.25, -0.25,
0.25, 0.25, -0.25,
0.25, 0.25, 0.25,
0.25, 0.25, 0.25,
-0.25, 0.25, 0.25,
-0.25, 0.25, -0.25 ]
buffer = GLuint(0)
glGenBuffers(1, buffer);
glBindBuffer(GL_ARRAY_BUFFER, buffer);
#ar=numpy.array(vertex_positions, dtype='float32')
ar=array("f",vertex_positions)
glBufferData(GL_ARRAY_BUFFER, ar.tostring(), GL_STATIC_DRAW)
glVertexAttribPointer(0, 3, GL_FLOAT, GL_FALSE, 0, None);
glEnableVertexAttribArray(0);
glEnable(GL_CULL_FACE);
glFrontFace(GL_CW);
glEnable(GL_DEPTH_TEST);
glDepthFunc(GL_LEQUAL);
return program
class Scene:
def __init__(self, width, height):
self.width = width
self.height = height
def display(self):
global mv_location
global proj_location
global proj_matrix
global many_cubes
currentTime = time.time()
green = [ 0.0, 0.25, 0.0, 1.0 ]
one = 1.0;
glViewport(0, 0, int((1360/2)-(512/2)), int((768/2)-(512/2)))
glClearBufferfv(GL_COLOR, 0, green);
glClearBufferfv(GL_DEPTH, 0, one);
glUseProgram(compile_program(vs_source, fs_source))
#proj_matrix = m3dOrtho(-1, 1, -1, 1, -10, 10)
#proj_matrix = m3dPerspective(50.0*math.pi/180.0, 512/512, 0.1, 1000.0)
#proj_matrix = m3dPerspective(m3dDegToRad(50.0), float(self.width) / float(self.height), 0.1, 1000.0);
glUniformMatrix4fv(proj_location, 1, GL_FALSE, proj_matrix)
if (many_cubes == True):
for i in range(0, 24):
f = i + currentTime * 0.3;
mv_matrix = (GLfloat * 16)(*identityMatrix)
T = (GLfloat * 16)(*identityMatrix)
m3dTranslateMatrix44(T, 0, 0, -4)
W = (GLfloat * 16)(*identityMatrix)
m3dTranslateMatrix44(W, sin(2.1 * f) * 0.5, cos(1.7 * f) * 0.5, sin(1.3 * f) * cos(1.5 * f) * 2.0)
RX = (GLfloat * 16)(*identityMatrix)
m3dRotationMatrix44(RX, currentTime * m3dDegToRad(45.0), 0.0, 1.0, 0.0)
RY = (GLfloat * 16)(*identityMatrix)
m3dRotationMatrix44(RY, currentTime * m3dDegToRad(81.0), 1.0, 0.0, 0.0)
mv_matrix = m3dMultiply(W, m3dMultiply(T, m3dMultiply(RY, RX)))
# or can multiply with numpy
#R = np.matmul(np.array(W).reshape(4,4) , np.matmul(np.array(RX).reshape(4,4), np.array(RY).reshape(4,4)))
#mv_matrix = np.matmul(R, np.array(T).reshape(4,4))
# third way this could be done
# T = np.matrix(translate(0.0, 0.0, -4.0)).reshape(4,4)
# W = np.matrix(translate(sin(2.1 * f) * 0.5, cos(1.7 * f) * 0.5, sin(1.3 * f) * cos(1.5 * f) * 2.0)).reshape(4,4)
# RX = np.matrix(rotation_matrix( [1.0, 0.0, 0.0], currentTime * m3dDegToRad(17.0)))
# RY = np.matrix(rotation_matrix( [0.0, 1.0, 0.0], currentTime * m3dDegToRad(13.0)))
# mv_matrix = RX * RY * T * W
glUniformMatrix4fv(mv_location, 1, GL_FALSE, mv_matrix)
glDrawArrays(GL_TRIANGLES, 0, 36)
else:
f = currentTime * 0.3;
mv_matrix = (GLfloat * 16)(*identityMatrix)
T = (GLfloat * 16)(*identityMatrix)
m3dTranslateMatrix44(T, 0, 0, -4)
W = (GLfloat * 16)(*identityMatrix)
m3dTranslateMatrix44(W, sin(2.1 * f) * 0.5, cos(1.7 * f) * 0.5, sin(1.3 * f) * cos(1.5 * f) * 2.0)
RX = (GLfloat * 16)(*identityMatrix)
m3dRotationMatrix44(RX, currentTime * m3dDegToRad(45.0), 0.0, 1.0, 0.0)
RY = (GLfloat * 16)(*identityMatrix)
m3dRotationMatrix44(RY, currentTime * m3dDegToRad(81.0), 1.0, 0.0, 0.0)
mv_matrix = m3dMultiply(W, m3dMultiply(T, m3dMultiply(RY, RX)))
# second way to that can multiply with numpy
#R = np.matmul(np.array(W).reshape(4,4) , np.matmul(np.array(RX).reshape(4,4), np.array(RY).reshape(4,4)))
#mv_matrix = np.matmul(R, np.array(T).reshape(4,4))
# third way this could be done
# T = np.matrix(translate(0.0, 0.0, -4.0)).reshape(4,4)
# W = np.matrix(translate(sin(2.1 * f) * 0.5, cos(1.7 * f) * 0.5, sin(1.3 * f) * cos(1.5 * f) * 2.0)).reshape(4,4)
# RX = np.matrix(rotation_matrix( [1.0, 0.0, 0.0], currentTime * m3dDegToRad(17.0)))
# RY = np.matrix(rotation_matrix( [0.0, 1.0, 0.0], currentTime * m3dDegToRad(13.0)))
# mv_matrix = RX * RY * T * W
glUniformMatrix4fv(mv_location, 1, GL_FALSE, mv_matrix)
glDrawArrays(GL_TRIANGLES, 0, 36)
glutSwapBuffers()
def reshape(self, width, height):
global proj_matrix
proj_matrix = m3dPerspective(m3dDegToRad(50.0), float(self.width) / float(self.height), 0.1, 1000.0);
self.width = width
self.height = height
def keyboard(self, key, x, y ):
global fullscreen
global many_cubes
print ('key:' , key)
if key == b'\x1b': # ESC
sys.exit()
elif key == b'f' or key == b'F': #fullscreen toggle
if (fullscreen == True):
glutReshapeWindow(512, 512)
glutPositionWindow(int((1360/2)-(512/2)), int((768/2)-(512/2)))
fullscreen = False
else:
glutFullScreen()
fullscreen = True
elif key == b'm' or key == b'M':
if (many_cubes == True):
many_cubes = False
else:
many_cubes = True
print('done')
def init(self):
pass
def timer(self, blah):
glutPostRedisplay()
glutTimerFunc( int(1/60), self.timer, 0)
time.sleep(1/60.0)
if __name__ == '__main__':
start = time.time()
glutInit()
glutInitDisplayMode(GLUT_RGBA | GLUT_DOUBLE | GLUT_DEPTH)
glutInitWindowSize(512, 512)
w1 = glutCreateWindow('OpenGL SuperBible - Spinny Cube')
glutInitWindowPosition(int((1360/2)-(512/2)), int((768/2)-(512/2)))
fullscreen = False
many_cubes = False
#glutFullScreen()
scene = Scene(512,512)
glutReshapeFunc(scene.reshape)
glutDisplayFunc(scene.display)
glutKeyboardFunc(scene.keyboard)
glutIdleFunc(scene.display)
#glutTimerFunc( int(1/60), scene.timer, 0)
scene.init()
glutMainLoop()
Matrices have to be initialized by the Identity Matrix and ech matrix need its "own" array of data:
identityMatrix = [1,0,0,0, 0,1,0,0, 0,0,1,0, 0,0,0,1]
mv_matrix = (GLfloat * 16)(*identityMatrix)
proj_matrix = (GLfloat * 16)(*identityMatrix)
If the projection matrix is the identity matrix, then the geometry has to be in normalized device space. The normalized device space is in range from (-1, -1, -1) to (1, 1, 1) and form a perfect cube volume. Your geometry is clipped by the far plane of the view volume, because you've set a z translation of -4.0.
Set up an Orthographic Projection Matrix, which "increase" the view volume:
r = right, l = left, b = bottom, t = top, n = near, f = far
X: 2/(r-l) 0 0 0
y: 0 2/(t-b) 0 0
z: 0 0 -2/(f-n) 0
t: -(r+l)/(r-l) -(t+b)/(t-b) -(f+n)/(f-n) 1
def m3dOrtho(l, r, t, b, n, f):
return (GLfloat * 16)(
2/(r-l), 0, 0, 0,
0, 2/(t-b), 0, 0,
0, 0, -2/(f-n), 0,
-(r+l)/(r-l), -(t+b)/(t-b), -(f+n)/(f-n), 1)
proj_matrix = m3dOrtho(-1, 1, -1, 1, -10, 10)
glUniformMatrix4fv(proj_location, 1, GL_FALSE, proj_matrix)
mv_matrix = (GLfloat * 16)(*identityMatrix)
m3dTranslateMatrix44(mv_matrix, 0.0, 0.0, -4.0)
m3dTranslateMatrix44(mv_matrix, sin(2.1 * f) * 0.5,
cos(1.7 * f) * 0.5,
sin(1.3 * f) * cos(1.5 * f) * 2.0)
Further note, that operations like glRotatef and gluPerspective change the current matrix of the deprecated fixed fucntion pipeline and make no sens at all if you use a shader with your own matrix uniforms.
Note, matrix operations can also be performed by libraries like PyGLM or NumPy.
For 3D objects I recommend to use Perspective Projection:
x: 1/(ta*a) 0 0 0
y: 0 1/ta 0 0
z: 0 0 -(f+n)/(f-n) -1
t: 0 0 -2*f*n/(f-n) 0
where:
a = w / h
ta = tan( fov_y / 2 );
2 * n / (r-l) = 1 / (ta * a)
2 * n / (t-b) = 1 / ta
e.g.
import math
def m3dPerspective(fov_y, aspect, n, f):
a = aspect
ta = math.tan( fov_y / 2 )
return (GLfloat * 16)(
1/(ta*a), 0, 0, 0,
0, 1/ta, 0, 0,
0, 0, -(f+n)/(f-n), -1,
0, 0, -2*f*n/(f-n), 0)
proj_matrix = m3dPerspective(50.0*math.pi/180.0, 512/512, 0.1, 1000.0)
glUniformMatrix4fv(proj_location, 1, GL_FALSE, proj_matrix)