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prototype-script.py
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"""
____ __ __ ____
/\ _`\ /'__`\ /\ \ /\ _`\
\ \ \/\ \ _ __ __ __ __ __ __ /\_\L\ \ \_\ \ \ \ \L\ \ ___ __ _
\ \ \ \ \/\`'__\/'__`\ /\ \/\ \/\ \ /'__`\ \/_/_\_<_ /'_` \ \ \ _ <' / __`\/\ \/'\
\ \ \_\ \ \ \//\ \L\.\_\ \ \_/ \_/ \ /\ \L\.\_ /\ \L\ \/\ \L\ \ \ \ \L\ \/\ \L\ \/> </
\ \____/\ \_\\ \__/.\_\\ \___x___/' \ \__/.\_\ \ \____/\ \___,_\ \ \____/\ \____//\_/\_\
\/___/ \/_/ \/__/\/_/ \/__//__/ \/__/\/_/ \/___/ \/__,_ / \/___/ \/___/ \//\/_/
.+------+ +------+ +------+ +------+ +------+.
.' | .'| /| /| | | |\ |\ |`. | `.
+---+--+' | +-+----+ | +------+ | +----+-+ | `+--+---+
| | | | | | | | | | | | | | | | | |
| ,+--+---+ | +----+-+ +------+ +-+----+ | +---+--+ |
|.' | .' |/ |/ | | \| \| `. | `. |
+------+' +------+ +------+ +------+ `+------+
+------+. +------+ +------+ +------+ .+------+
|`. | `. |\ |\ | | /| /| .' | .'|
| `+--+---+ | +----+-+ +------+ +-+----+ | +---+--+' |
| | | | | | | | | | | | | | | | | |
+---+--+. | +-+----+ | +------+ | +----+-+ | .+--+---+
`. | `.| \| \| | | |/ |/ |.' | .'
`+------+ +------+ +------+ +------+ +------+
"""
import numpy as np
import matplotlib.pyplot as plt
def _return_sin_and_cos(theta):
d = np.radians(theta)
c = np.cos(d)
s = np.sin(d)
return c, s
def rotx(theta):
c, s = _return_sin_and_cos(theta)
return np.array([
[1, 0, 0],
[0, c, -s],
[0, s, c]]
)
def roty(theta):
c, s = _return_sin_and_cos(theta)
return np.array([
[c, 0, s],
[0, 1, 0],
[-s, 0, c],
])
def rotz(theta):
c, s = _return_sin_and_cos(theta)
return np.array([
[c, -s, 0],
[s, c, 0],
[0, 0, 1],
])
def rotxyz(euler_vec):
rx = rotx(euler_vec.x)
ry = roty(euler_vec.y)
rz = rotz(euler_vec.z)
rxy = np.matmul(rx, ry)
rxyz = np.matmul(rxy, rz)
return rxyz
class Vector:
def __init__(self, x, y, z, name=None, alias=None):
self.x, self.y, self.z = x, y, z
self.name = name
self.alias = alias
def get_transformed_point(self, transform_matrix):
p = np.array([self.x, self.y, self.z, 1])
p = np.matmul(transform_matrix, p)
return Vector(p[0], p[1], p[2], self.name, self.alias)
def __repr__(self):
return f"Vector(x={self.x}, y={self.y}, z={self.z}, {self.name})"
def t_matrix(translation):
return [[1, 0, 0, translation.x],
[0, 1, 0, translation.y],
[0, 0, 1, translation.z],
[0, 0, 0, 1]]
def s_matrix(scale):
return [[scale, 0, 0, 0],
[ 0, scale, 0, 0],
[ 0, 0, scale, 0],
[ 0, 0, 0, 1]]
"""
E------F y
|`. | `. |
| `A--+---B *----- x
| | | | \
G---+--H | \
`. | `. | z
`C------D
"""
class NormalUnitCube:
CENTER = Vector(0, 0, 0, "cube-center")
POINTS = [
Vector(-1, +1, +1, "front-top-left", "A"),
Vector(+1, +1, +1, "front-top-right", "B"),
Vector(-1, -1, +1, "front-bottom-left", "C"),
Vector(+1, -1, +1, "front-bottom-right", "D"),
Vector(-1, +1, -1, "back-top-left", "E"),
Vector(+1, +1, -1, "back-top-right", "F"),
Vector(-1, -1, -1, "back-bottom-left", "G"),
Vector(+1, -1, -1, "back-bottom-right", "H"),
]
def __init__(self):
pass
class Cube:
UNIT_CUBE = NormalUnitCube()
def __init__(
self,
euler_vec=Vector(0, 0, 0),
scale=1,
translate_vec=Vector(0, 0, 0)
):
self.rotate_matrix = rotxyz(euler_vec)
self.euler_vec = euler_vec
self.scale = scale
self.translate_vec = translate_vec
r = self.rotate_matrix
s = self.scale
t = self.translate_vec
r_matrix = [
[r[0][0], r[0][1], r[0][2], 0],
[r[1][0], r[1][1], r[1][2], 0],
[r[2][0], r[2][1], r[2][2], 0],
[0, 0, 0, 1],
]
self.wrt_world_matrix = np.matmul(t_matrix(t), np.matmul(s_matrix(s), r_matrix))
self.points = Cube.UNIT_CUBE.POINTS
def get_world_wrt_camera_matrix(
translate_vec=Vector(0, 0, 0),
euler_vec=Vector(0, 0, 0)
):
Rmatrix = rotxyz(euler_vec)
t = translate_vec
# Inverse of rotations matrix
r = Rmatrix.T
# matrix[row][column]
# inverse_matrix = rotateCameraMatrixInverse * translateCameraMatrixInverse
# world_to_camera_matrix
return [
[r[0][0], r[0][1], r[0][2], -t.x],
[r[1][0], r[1][1], r[1][2], -t.y],
[r[2][0], r[2][1], r[2][2], -t.z],
[0, 0, 0, 1],
]
def get_projected_point(point, projection_constant):
return Vector(
point.x / point.z * projection_constant,
point.y / point.z * projection_constant,
projection_constant,
point.name,
point.alias,
)
def plot_2d_points(points):
p = points
x1 = [p[0].x, p[1].x, p[3].x, p[2].x, p[0].x]
y1 = [p[0].y, p[1].y, p[3].y, p[2].y, p[0].y]
x2 = [p[4].x, p[5].x, p[7].x, p[6].x, p[4].x]
y2 = [p[4].y, p[5].y, p[7].y, p[6].y, p[4].y]
x3 = [p[0].x, p[4].x]
y3 = [p[0].y, p[4].y]
x4 = [p[1].x, p[5].x]
y4 = [p[1].y, p[5].y]
x5 = [p[2].x, p[6].x]
y5 = [p[2].y, p[6].y]
x6 = [p[3].x, p[7].x]
y6 = [p[3].y, p[7].y]
fig = plt.figure()
ax = fig.add_subplot(111)
lines = plt.plot(x1, y1)
lines2 = plt.plot(x2, y2)
lines3 = plt.plot(x3, y3)
lines4 = plt.plot(x4, y4)
lines5 = plt.plot(x5, y5)
lines6 = plt.plot(x6, y6)
plt.setp(lines, color='r', linewidth=5.0)
plt.setp(lines2, color='b', linewidth=5.0)
plt.setp(lines3, color='g', linewidth=5.0)
plt.setp(lines4, color='g', linewidth=5.0)
plt.setp(lines5, color='g', linewidth=5.0)
plt.setp(lines6, color='g', linewidth=5.0)
plt.xlim(-300, 300)
plt.ylim(-300, 300)
ax.set_aspect('equal', adjustable='box')
plt.show()
def render_cube(cube, cube_wrt_camera_matrix, projection_constant):
projected_points = []
for point in cube.points:
transformed_point = point.get_transformed_point(cube_wrt_camera_matrix)
projected_point = get_projected_point(transformed_point, projection_constant)
projected_points.append(projected_point)
print(projected_points)
plot_2d_points(projected_points)
# -----------------------------------
# RENDER SCENE
# -----------------------------------
PROJECTION_CONSTANT = 1 * 600
CAMERA_POSITION = Vector(0, 0, 5)
CAMERA_ORIENTATION = Vector(0, 0, 45)
world_wrt_camera_matrix = get_world_wrt_camera_matrix(CAMERA_POSITION, CAMERA_ORIENTATION)
# euler angle vector (rot.x, rot.y, rot.z) in degrees
r = Vector(-30, 0, 0)
# translate vector
t = Vector(0, 0, 0)
# scale magnitude
s = 1.25
cube = Cube(r, s, t)
cube_wrt_camera_matrix = np.matmul(world_wrt_camera_matrix, cube.wrt_world_matrix)
render_cube(cube, cube_wrt_camera_matrix, PROJECTION_CONSTANT)