def intersection_line_triangle(line, triangle, tol=1e-6):
"""Computes the intersection point of a line (ray) and a triangle
based on the Moeller Trumbore intersection algorithm
Parameters
----------
line : tuple
Two points defining the line.
triangle : list of list of float
XYZ coordinates of the triangle corners.
tol : float, optional
A tolerance for membership verification.
Default is ``1e-6``.
Returns
-------
point : tuple
The intersectin point.
None
If the intersection does not exist.
"""
a, b, c = triangle
ab = subtract_vectors(b, a)
ac = subtract_vectors(c, a)
n = cross_vectors(ab, ac)
plane = a, n
x = intersection_line_plane(line, plane, tol=tol)
if x:
if is_point_in_triangle(x, triangle):
return x
def in_triangle(self, triangle):
"""Determine if the point lies in the given triangle.
Parameters
----------
triangle : triangle
The triangle.
Returns
-------
bool
True, if the point lies in the triangle.
False, otherwise.
"""
return is_point_in_triangle(self, triangle)
def intersection_line_triangle(line, triangle, tol=1e-6):
"""Computes the intersection point of a line (ray) and a triangle
based on the Moeller Trumbore intersection algorithm
Parameters
----------
line : tuple
Two points defining the line.
triangle : list of list of float
XYZ coordinates of the triangle corners.
tol : float, optional
A tolerance for membership verification.
Default is ``1e-6``.
Returns
-------
point : tuple
The intersectin point.
None
If the intersection does not exist.
"""
# a, b, c = triangle
# v1 = subtract_vectors(line[1], line[0])
# p1 = line[0]
# # Find vectors for two edges sharing V1
# e1 = subtract_vectors(b, a)
# e2 = subtract_vectors(c, a)
# # Begin calculating determinant - also used to calculate u parameter
# p = cross_vectors(v1, e2)
# # if determinant is near zero, ray lies in plane of triangle
# det = dot_vectors(e1, p)
# if det > - epsilon and det < epsilon:
# return None
# inv_det = 1.0 / det
# # calculate distance from V1 to ray origin
# t = subtract_vectors(p1, a)
# # Calculate u parameter
# u = dot_vectors(t, p) * inv_det
# # The intersection lies outside of the triangle
# if u < 0.0 or u > 1.0:
# return None
# # Prepare to make_blocks v parameter
# q = cross_vectors(t, e1)
# # Calculate V parameter
# v = dot_vectors(v1, q) * inv_det
# # The intersection lies outside of the triangle
# if v < 0.0 or u + v > 1.0:
# return None
# t = dot_vectors(e2, q) * inv_det
# if t > epsilon:
# return add_vectors(p1, scale_vector(v1, t))
# # No hit
# return None
a, b, c = triangle
ab = subtract_vectors(b, a)
ac = subtract_vectors(c, a)
n = cross_vectors(ab, ac)
plane = a, n
x = intersection_line_plane(line, plane, tol=tol)
if x:
if is_point_in_triangle(x, triangle):
return x