def is_point_on_segment(point, segment, tol=1e-6):
"""Determine if a point lies on a given line segment.
Parameters
----------
point : [float, float, float] | :class:`compas.geometry.Point`
A point.
segment : [point, point] | :class:`compas.geometry.Line`
A line segment.
tol : float, optional
A tolerance for membership verification.
Returns
-------
bool
True if the point is on the line segment.
False otherwise.
"""
a, b = segment
d_ab = distance_point_point(a, b)
if d_ab == 0:
return False
if not is_point_on_line(point, (a, b), tol=tol):
return False
d_pa = distance_point_point(a, point)
d_pb = distance_point_point(b, point)
if d_pa + d_pb <= d_ab + tol:
return True
return False
def is_point_on_polyline(point, polyline, tol=1e-6):
"""Determine if a point is on a polyline.
Parameters
----------
point : [float, float, float] | :class:`compas.geometry.Point`
A point.
polyline : sequence[point] | :class:`compas.geometry.Polyline`
A polyline.
tol : float, optional
The tolerance for membership verification.
Returns
-------
bool
True if the point is on the polyline.
False otherwise.
"""
for i in range(len(polyline) - 1):
a = polyline[i]
b = polyline[i + 1]
c = closest_point_on_segment(point, (a, b))
if distance_point_point(point, c) <= tol:
return True
return False
def is_point_on_polyline(point, polyline, tol=1e-6):
"""Determine if a point is on a polyline.
Parameters
----------
point : sequence of float
XYZ coordinates.
polyline : sequence of sequence of float
XYZ coordinates of the points of the polyline.
tol : float, optional
The tolerance for membership verification.
Default is ``1e-6``.
Returns
-------
bool
``True`` if the point is on the polyline.
``False`` otherwise.
"""
for i in range(len(polyline) - 1):
a = polyline[i]
b = polyline[i + 1]
c = closest_point_on_segment(point, (a, b))
if distance_point_point(point, c) <= tol:
return True
return False
def is_point_on_polyline(point, polyline, tol=1e-6):
"""Determine if a point is on a polyline.
Parameters
----------
point : [x, y, z] or :class:`compas.geometry.Point`
A point.
polyline : list of points or :class:`compas.geometry.Polyline`
A polyline.
tol : float, optional
The tolerance for membership verification.
Default is ``1e-6``.
Returns
-------
bool
``True`` if the point is on the polyline.
``False`` otherwise.
"""
for i in range(len(polyline) - 1):
a = polyline[i]
b = polyline[i + 1]
c = closest_point_on_segment(point, (a, b))
if distance_point_point(point, c) <= tol:
return True
return False
def is_point_on_segment(point, segment, tol=1e-6):
"""Determine if a point lies on a given line segment.
Parameters
----------
point : sequence of float
XYZ coordinates.
segment : tuple
Two points defining the line segment.
tol : float, optional
A tolerance for membership verification.
Default is ``1e-6``.
Returns
-------
bool
``True`` if the point is on the line segment.
``False`` otherwise.
"""
a, b = segment
if not is_point_on_line(point, segment, tol=tol):
return False
d_ab = distance_point_point(a, b)
if d_ab == 0:
return False
d_pa = distance_point_point(a, point)
d_pb = distance_point_point(b, point)
if d_pa + d_pb <= d_ab + tol:
return True
return False
def is_point_in_circle(point, circle):
"""Determine if a point lies in a circle.
Parameters
----------
point : [float, float, float] | :class:`compas.geometry.Point`
A point.
circle : [plane, float] | :class:`compas.geometry.Circle`
A circle.
Returns
-------
bool
True if the point lies in the circle.
False otherwise.
"""
plane, radius = circle
if is_point_on_plane(point, plane):
return distance_point_point(point, plane[0]) <= radius
return False
def is_point_in_circle(point, circle):
"""Determine if a point lies in a circle.
Parameters
----------
point : sequence of float
XYZ coordinates of a 3D point.
circle : tuple
center, radius, normal
Returns
-------
bool
``True`` if the point lies in the circle.
``False`` otherwise.
"""
plane, radius = circle
if is_point_on_plane(point, plane):
return distance_point_point(point, plane[0]) <= radius
return False
def is_point_in_circle(point, circle):
"""Determine if a point lies in a circle.
Parameters
----------
point : [x, y, z] or :class:`compas.geometry.Point`
A point.
circle : [point, float, vector]
A circle.
Returns
-------
bool
``True`` if the point lies in the circle.
``False`` otherwise.
"""
plane, radius = circle
if is_point_on_plane(point, plane):
return distance_point_point(point, plane[0]) <= radius
return False
def intersection_sphere_sphere(sphere1, sphere2):
"""Computes the intersection of 2 spheres.
There are 4 cases of sphere-sphere intersection : 1) the spheres intersect
in a circle, 2) they intersect in a point, 3) they overlap, 4) they do not
intersect.
Parameters
----------
sphere1 : tuple
center, radius of the sphere.
sphere2 : tuple
center, radius of the sphere.
Returns
-------
case : str
`point`, `circle`, or `sphere`
result : tuple
- point: xyz coordinates
- circle: center, radius, normal
- sphere: center, radius
Examples
--------
>>> sphere1 = (3.0, 7.0, 4.0), 10.0
>>> sphere2 = (7.0, 4.0, 0.0), 5.0
>>> result = intersection_sphere_sphere(sphere1, sphere2)
>>> if result:
... case, res = result
... if case == "circle":
... center, radius, normal = res
... elif case == "point":
... point = res
... elif case == "sphere":
... center, radius = res
References
--------
https://gamedev.stackexchange.com/questions/75756/sphere-sphere-intersection-and-circle-sphere-intersection
"""
center1, radius1 = sphere1
center2, radius2 = sphere2
distance = distance_point_point(center1, center2)
# Case 4: No intersection
if radius1 + radius2 < distance:
return None
# Case 4: No intersection, sphere is within the other sphere
elif distance + min(radius1, radius2) < max(radius1, radius2):
return None
# Case 3: sphere's overlap
elif radius1 == radius2 and distance == 0:
return "sphere", sphere1
# Case 2: point intersection
elif radius1 + radius2 == distance:
ipt = subtract_vectors(center2, center1)
ipt = scale_vector(ipt, radius1/distance)
ipt = add_vectors(center1, ipt)
return "point", ipt
# Case 2: point intersection, smaller sphere is within the bigger
elif distance + min(radius1, radius2) == max(radius1, radius2):
if radius1 > radius2:
ipt = subtract_vectors(center2, center1)
ipt = scale_vector(ipt, radius1/distance)
ipt = add_vectors(center1, ipt)
else:
ipt = subtract_vectors(center1, center2)
ipt = scale_vector(ipt, radius2/distance)
ipt = add_vectors(center2, ipt)
return "point", ipt
# Case 1: circle intersection
h = 0.5 + (radius1**2 - radius2**2)/(2 * distance**2)
ci = subtract_vectors(center2, center1)
ci = scale_vector(ci, h)
ci = add_vectors(center1, ci)
ri = sqrt(radius1**2 - h**2 * distance**2)
normal = scale_vector(subtract_vectors(center2, center1), 1/distance)
return "circle", (ci, ri, normal)
