def find_intersect_point_of_lines(line_0, line_1, use_double_rounding=False,
round_adjust=0, ignore_check=False):
# returns an arbitrary point where the provided lines intersect.
# if they do not intersect, None will be returned instead.
v0, d0 = matrices.Point(line_0[0]), matrices.Ray(line_0[1])
v1, d1 = matrices.Point(line_1[0]), matrices.Ray(line_1[1])
assert len(v0) == len(v1)
assert len(d0) == len(d1)
if d0.is_zero or d1.is_zero:
# one or both vectors are the zero-vector
return None
try:
reduced, result = matrices.Matrix(
[(a, -b) for a, b in zip(d0, d1)]).row_reduce(
matrices.Matrix([v0[i] - v1[i] for i in range(len(v0))]))
except matrices.CannotRowReduce:
return None
intersect_a = v0 - d0 * result[0][0]
intersect_b = v1 - d1 * result[1][0]
if ignore_check or matrices.are_vectors_equal(
intersect_a, intersect_b, use_double_rounding, round_adjust):
# point lies on both lines
return intersect_a + (intersect_b - intersect_a) / 2
return None
def find_intersect_point_of_planes(plane_0, plane_1, plane_2, use_double_rounding=False,
round_adjust=0, ignore_check=False):
try:
reduced, result = matrices.Matrix(
(plane_0[:-1], plane_1[:-1], plane_2[:-1])).row_reduce(
matrices.Matrix([plane_0[3], plane_1[3], plane_2[3]]))
except matrices.CannotRowReduce:
return None
return matrices.Point((result[0][0], result[1][0], result[2][0]))
def point_distance_to_line(point, line, use_double_rounding=False,
round_adjust=0):
mantissa_len = (53 if use_double_rounding else 23)
line_point = matrices.Point(line[0])
line_dir = matrices.Ray(line[1]).normalized
dist = matrices.Ray.cross(line_dir, line_point - point).mag
# return True if point is on forward side of plane, otherwise False
# take into account rounding errors for 32bit floats
delta_max = 2**(
int(ceil(log(abs(dist) + float_info.epsilon, 2))) -
mantissa_len) + abs(round_adjust)
if abs(dist) < delta_max:
# point lies on plane
return 0.0
return dist