def area_triangle(triangle):
"""Compute the area of a triangle defined by three points.
"""
return 0.5 * length_vector(normal_triangle(triangle, False))
def reflect_line_triangle(line, triangle, epsilon=1e-6):
"""Reflects a line at a triangle.
Parameters:
line (tuple): Two points defining the line.
triangle (sequence of sequence of float): XYZ coordinates of the triangle corners.
Returns:
line (tuple): The reflected line starting at the reflection point on the plane,
None otherwise.
Note:
The directions of the line and triangular face are important! The line will only be
reflected if it points (direction start -> end) in the direction of the triangular
face and if the line intersects with the front face of the triangular face (normal
direction of the face).
Examples:
.. code-block:: python
# tetrahedron points
pt1 = (0.0, 0.0, 0.0)
pt2 = (6.0, 0.0, 0.0)
pt3 = (3.0, 5.0, 0.0)
pt4 = (3.0, 2.0, 4.0)
# triangular tetrahedron faces
tris = []
tris.append([pt4,pt2,pt1])
tris.append([pt4,pt3,pt2])
tris.append([pt4,pt1,pt3])
tris.append([pt1,pt2,pt3])
# initial line (starting ray)
line = [(1.0,1.0,0.0),(1.0,1.0,1.0)]
# start reflection cycle inside the prism
polyline = []
polyline.append(line[0])
for i in range(10):
for tri in tris:
reflected_line = reflect_line_triangle(line, tri)
if reflected_line:
line = reflected_line
polyline.append(line[0])
break
print(polyline)
Note:
This example visualized in Rhino:
.. image:: /_images/reflect_line_triangle.*
"""
intx_pt = intersection_line_triangle(line, triangle, epsilon)
if not intx_pt:
return None
vec_line = subtract_vectors(line[1], line[0])
vec_normal = normal_triangle(triangle, normalised=True)
vec_reflect = mirror_vector_vector(vec_line, vec_normal)
if angle_smallest_vectors(vec_normal, vec_reflect) > 0.5 * pi:
return None
return [intx_pt, add_vectors(intx_pt, vec_reflect)]