def _rotate(vertex, point=None, x=None, y=None, z=None):
"""rotates a vertex around a point around any or all axes"""
alpha, beta, gamma = x, y, z
if point == None:
point = (0, 0, 0)
#translate vertex to revolve around origo:
rotated_vertex = vector_subtract(vertex, point)
#convert vertex into a 1-row matrix: (x, y, z) --> ((x, y, z))
rotated_vertex = (rotated_vertex,)
if alpha != None:
rotation_matrix_x = ((1, 0, 0),
(0, cos(alpha), sin(alpha)),
(0, -sin(alpha), cos(alpha)))
rotated_vertex = matrix_multiply(rotated_vertex, rotation_matrix_x)
if beta != None:
rotation_matrix_y = ((cos(beta), 0, -sin(beta)),
(0, 1, 0),
(sin(beta), 0, cos(beta)))
rotated_vertex = matrix_multiply(rotated_vertex, rotation_matrix_y)
if gamma != None:
rotation_matrix_z = ((cos(gamma), sin(gamma), 0),
(-sin(gamma), cos(gamma), 0),
(0, 0, 1))
rotated_vertex = matrix_multiply(rotated_vertex, rotation_matrix_z)
#return vertex translated to revolve around point:
return vector_add(rotated_vertex[0], point)
def _calculate_ray_collision(self, solid, triangle, S, V):
"""calculates at what point, if any, a ray hits a triangle
P(t) = S + tV
P is a point on the line / ray
S is the starting point of the ray
V is the direction vector for the line / ray
The value t represents where on the line point P is located.
t = 0 <-> point is in starting point
t < 0 <-> point is behind starting point
t > 0 <-> point is in front of starting point
"""
T = triangle['vertices'] #vertices for triangle
N = triangle['normal'] #normal for triangle's plane
try:
# D = -N*T[0] | signed distance from origin
# L = <N, D> | 4d plane vector
# t = - ( L*S ) / ( L*V ) = - ( N*S - N*T[0] ) / ( N*V )
t = -(dot_product(N, S)-dot_product(N, T[0])) / dot_product(N, V)
except ZeroDivisionError:
print('Triangle\'s plane is parallel to ray, collision impossible')
return None
#point where ray hits triangle's plane:
P = vector_add(S, inner_product(t, V))
R = vector_subtract(P, T[0])
Q = triangle['Q']
M1 = triangle['M']
M2 = ((dot_product(R, Q[0]),),
(dot_product(R, Q[1]),))
w = matrix_multiply(M1, M2)
w = (1-w[0][0]-w[1][0], w[0][0], w[1][0])
if all([i > 0 for i in w]) and t > 0:
#point P is inside triangle / ray goes through triangle
#triangle is in front camera if t > 0
return P
else:
return None