def _create_triangles(self):
triangles = []
for face in self.faces:
T = self.get_vertices(face) #vertices t0, t1, t2
Q = (vector_subtract(T[1], T[0]), vector_subtract(T[2], T[0]))
normal = cross_product(Q[0], Q[1])
M = inverse(((dot_product(Q[0], Q[0]), dot_product(Q[0], Q[1])),
(dot_product(Q[0], Q[1]), dot_product(Q[1], Q[1]))))
triangles.append({'normal': normal, 'vertices': T, 'Q': Q, 'M': M})
return triangles
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
