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 or 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
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 : [point, point] | :class:`compas.geometry.Line`
Two points defining the line.
triangle : [point, point, point]
XYZ coordinates of the triangle corners.
tol : float, optional
A tolerance for membership verification.
Returns
-------
[float, float, float] | None
The intersection point between the line and the triangle,
or None if the line and the plane are parallel.
"""
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 inside the given triangle.
Parameters
----------
triangle : :class:`compas.geometry.Polygon` or list of three points.
The triangle.
Returns
-------
bool
True, if the point lies in the triangle.
False, otherwise.
Examples
--------
>>> from compas.geometry import Polygon
>>> tri = Polygon([Point(0.0, 0.0, 0.0), Point(1.0, 0.0, 0.0), Point(0.5, 1.0, 0.0)])
>>> point = Point(0.5, 0.5, 0.0)
>>> point.in_triangle(tri)
True
"""
return is_point_in_triangle(self, triangle)
def _find_closest_component(point, vertices, triangles, closest_tris,
closest_vi):
distance = None
projection = None
component = None
for tri in closest_tris:
# the triangle to process
triangle = triangles[tri]
# the local triangle frame
o, A = _triangle_xform(triangle)
# local coordinates
b = point - o
p = solve(A, b.T).T
b = triangle - o
t = solve(A, b.T).T
# find closest component of triangle
# compute distance to closest component
if is_point_in_triangle(p, t):
p[2] = 0
xyz = A.dot(p[:, None]).T + o
distance = 0
# why to list?
projection = xyz[0].tolist()
component = 'face', tri
break
if _is_point_in_edgezone(p, t[0], t[1]):
rst = _compute_point_on_segment(p, t[0], t[1])
xyz = A.dot(rst.T).T + o
d = sqrt(sum((rst - p[None, :])**2))
if distance is None or d < distance:
distance = d
# why to list?
projection = xyz[0].tolist()
component = 'edge', (None, None)
elif _is_point_in_edgezone(p, t[1], t[2]):
rst = _compute_point_on_segment(p, t[1], t[2])
xyz = A.dot(rst.T).T + o
d = sqrt(sum((rst - p[None, :])**2))
if distance is None or d < distance:
distance = d
# why to list?
projection = xyz[0].tolist()
component = 'edge', (None, None)
elif _is_point_in_edgezone(p, t[2], t[0]):
rst = _compute_point_on_segment(p, t[2], t[0])
xyz = A.dot(rst.T).T + o
d = sqrt(sum((rst - p[None, :])**2))
if distance is None or d < distance:
distance = d
# why to list?
projection = xyz[0].tolist()
component = 'edge', (None, None)
else:
xyz = vertices[closest_vi]
d = sqrt(sum((xyz - point)**2))
if distance is None or d < distance:
distance = d
# why to list?
projection = xyz.tolist()
component = 'vertex', closest_vi
return distance, projection, component
def in_triangle(self, triangle):
return is_point_in_triangle(self, triangle)