# Drawing a rotated 3D cube#

```import math
import numpy as np

from vispy import app
from vispy.gloo import gl

def checkerboard(grid_num=8, grid_size=32):
row_even = grid_num // 2 * [0, 1]
row_odd = grid_num // 2 * [1, 0]
Z = np.row_stack(grid_num // 2 * (row_even, row_odd)).astype(np.uint8)
return 255 * Z.repeat(grid_size, axis=0).repeat(grid_size, axis=1)

def rotate(M, angle, x, y, z, point=None):
angle = math.pi * angle / 180
c, s = math.cos(angle), math.sin(angle)
n = math.sqrt(x * x + y * y + z * z)
x /= n
y /= n
z /= n
cx, cy, cz = (1 - c) * x, (1 - c) * y, (1 - c) * z
R = np.array([[cx * x + c, cy * x - z * s, cz * x + y * s, 0],
[cx * y + z * s, cy * y + c, cz * y - x * s, 0],
[cx * z - y * s, cy * z + x * s, cz * z + c, 0],
[0, 0, 0, 1]], dtype=M.dtype).T
M[...] = np.dot(M, R)
return M

def translate(M, x, y=None, z=None):
y = x if y is None else y
z = x if z is None else z
T = np.array([[1.0, 0.0, 0.0, x],
[0.0, 1.0, 0.0, y],
[0.0, 0.0, 1.0, z],
[0.0, 0.0, 0.0, 1.0]], dtype=M.dtype).T
M[...] = np.dot(M, T)
return M

def frustum(left, right, bottom, top, znear, zfar):
M = np.zeros((4, 4), dtype=np.float32)
M[0, 0] = +2.0 * znear / (right - left)
M[2, 0] = (right + left) / (right - left)
M[1, 1] = +2.0 * znear / (top - bottom)
M[3, 1] = (top + bottom) / (top - bottom)
M[2, 2] = -(zfar + znear) / (zfar - znear)
M[3, 2] = -2.0 * znear * zfar / (zfar - znear)
M[2, 3] = -1.0
return M

def perspective(fovy, aspect, znear, zfar):
h = math.tan(fovy / 360.0 * math.pi) * znear
w = h * aspect
return frustum(-w, w, -h, h, znear, zfar)

def makecube():
""" Generate vertices & indices for a filled cube """

vtype = [('a_position', np.float32, 3),
('a_texcoord', np.float32, 2)]
itype = np.uint32

# Vertices positions
p = np.array([[1, 1, 1], [-1, 1, 1], [-1, -1, 1], [1, -1, 1],
[1, -1, -1], [1, 1, -1], [-1, 1, -1], [-1, -1, -1]])

# Texture coords
t = np.array([[0, 0], [0, 1], [1, 1], [1, 0]])

faces_p = [0, 1, 2, 3, 0, 3, 4, 5, 0, 5, 6,
1, 1, 6, 7, 2, 7, 4, 3, 2, 4, 7, 6, 5]
faces_t = [0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2,
3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3]

vertices = np.zeros(24, vtype)
vertices['a_position'] = p[faces_p]
vertices['a_texcoord'] = t[faces_t]

indices = np.resize(
np.array([0, 1, 2, 0, 2, 3], dtype=itype), 6 * (2 * 3))
indices += np.repeat(4 * np.arange(6), 6).astype(np.uint32)

return vertices, indices

cube_vertex = """
uniform mat4 u_model;
uniform mat4 u_view;
uniform mat4 u_projection;
attribute vec3 a_position;
attribute vec2 a_texcoord;
varying vec2 v_texcoord;
void main()
{
gl_Position = u_projection * u_view * u_model * vec4(a_position,1.0);
v_texcoord = a_texcoord;
}
"""

cube_fragment = """
uniform sampler2D u_texture;
varying vec2 v_texcoord;
void main()
{
gl_FragColor = texture2D(u_texture, v_texcoord);
}
"""

class Canvas(app.Canvas):
def __init__(self):
app.Canvas.__init__(self, size=(512, 512),
title='Rotating cube (GL version)',
keys='interactive')

def on_initialize(self, event):
# Build & activate cube program
self.cube = gl.glCreateProgram()
gl.glUseProgram(self.cube)

# Get data & build cube buffers
vcube_data, self.icube_data = makecube()
vcube = gl.glCreateBuffer()
gl.glBindBuffer(gl.GL_ARRAY_BUFFER, vcube)
gl.glBufferData(gl.GL_ARRAY_BUFFER, vcube_data, gl.GL_STATIC_DRAW)
icube = gl.glCreateBuffer()
gl.glBindBuffer(gl.GL_ELEMENT_ARRAY_BUFFER, icube)
gl.glBufferData(gl.GL_ELEMENT_ARRAY_BUFFER,
self.icube_data, gl.GL_STATIC_DRAW)

# Bind cube attributes
stride = vcube_data.strides[0]
offset = 0
loc = gl.glGetAttribLocation(self.cube, "a_position")
gl.glEnableVertexAttribArray(loc)
gl.glVertexAttribPointer(loc, 3, gl.GL_FLOAT, False, stride, offset)

offset = vcube_data.dtype["a_position"].itemsize
loc = gl.glGetAttribLocation(self.cube, "a_texcoord")
gl.glEnableVertexAttribArray(loc)
gl.glVertexAttribPointer(loc, 2, gl.GL_FLOAT, False, stride, offset)

# Create & bind cube texture
crate = checkerboard()
texture = gl.glCreateTexture()
gl.glTexParameterf(gl.GL_TEXTURE_2D, gl.GL_TEXTURE_MIN_FILTER,
gl.GL_LINEAR)
gl.glTexParameterf(gl.GL_TEXTURE_2D, gl.GL_TEXTURE_MAG_FILTER,
gl.GL_LINEAR)
gl.glTexParameterf(gl.GL_TEXTURE_2D, gl.GL_TEXTURE_WRAP_S,
gl.GL_CLAMP_TO_EDGE)
gl.glTexParameterf(gl.GL_TEXTURE_2D, gl.GL_TEXTURE_WRAP_T,
gl.GL_CLAMP_TO_EDGE)
gl.glTexImage2D(gl.GL_TEXTURE_2D, 0, gl.GL_LUMINANCE, gl.GL_LUMINANCE,
gl.GL_UNSIGNED_BYTE, crate.shape[:2])
gl.glTexSubImage2D(gl.GL_TEXTURE_2D, 0, 0, 0, gl.GL_LUMINANCE,
gl.GL_UNSIGNED_BYTE, crate)
loc = gl.glGetUniformLocation(self.cube, "u_texture")
gl.glUniform1i(loc, texture)
gl.glBindTexture(gl.GL_TEXTURE_2D, 0)

# Create & bind cube matrices
view = np.eye(4, dtype=np.float32)
model = np.eye(4, dtype=np.float32)
projection = np.eye(4, dtype=np.float32)
translate(view, 0, 0, -7)
self.phi, self.theta = 60, 20
rotate(model, self.theta, 0, 0, 1)
rotate(model, self.phi, 0, 1, 0)
loc = gl.glGetUniformLocation(self.cube, "u_model")
gl.glUniformMatrix4fv(loc, 1, False, model)
loc = gl.glGetUniformLocation(self.cube, "u_view")
gl.glUniformMatrix4fv(loc, 1, False, view)
loc = gl.glGetUniformLocation(self.cube, "u_projection")
gl.glUniformMatrix4fv(loc, 1, False, projection)

# OpenGL initalization
gl.glClearColor(0.30, 0.30, 0.35, 1.00)
gl.glEnable(gl.GL_DEPTH_TEST)
self._resize(*(self.size + self.physical_size))
self.timer = app.Timer('auto', self.on_timer, start=True)

def on_draw(self, event):
gl.glClear(gl.GL_COLOR_BUFFER_BIT | gl.GL_DEPTH_BUFFER_BIT)
gl.glDrawElements(gl.GL_TRIANGLES, self.icube_data.size,
gl.GL_UNSIGNED_INT, None)

def on_resize(self, event):
self._resize(*(event.size + event.physical_size))

def _resize(self, width, height, physical_width, physical_height):
gl.glViewport(0, 0, physical_width, physical_height)
projection = perspective(35.0, width / float(height), 2.0, 10.0)
loc = gl.glGetUniformLocation(self.cube, "u_projection")
gl.glUniformMatrix4fv(loc, 1, False, projection)

def on_timer(self, event):
self.theta += .5
self.phi += .5
model = np.eye(4, dtype=np.float32)
rotate(model, self.theta, 0, 0, 1)
rotate(model, self.phi, 0, 1, 0)
loc = gl.glGetUniformLocation(self.cube, "u_model")
gl.glUniformMatrix4fv(loc, 1, False, model)
self.update()

if __name__ == '__main__':
c = Canvas()
c.show()
app.run()
```

Total running time of the script: (0 minutes 0.130 seconds)

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