def calculateCentroid(point_on_plane, plane_normal, cuboid_dimensions):
'''
Takes a description of a plane as a point on the plane
and a normal of the plane with a cuboids dimensions, with
one corner defined by [0, 0, 0] and the opposite by
cuboid_dimensions, and calculates the centroid formed by the
given plane intersecting with the cuboid.
'''
tol = 1e-08
dim = cuboid_dimensions
# print(point_on_plane, plane_normal)
axes = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
coordinate_set = [[0, 0, 0], [dim[0], 0, 0], [0, dim[1], 0], [dim[0], dim[1], 0], [0, 0, dim[2]], [dim[0], 0, dim[2]], [0, dim[1], dim[2]], [dim[0], dim[1], dim[2]]]
ipts = []
for axis in axes:
den = dot(axis, plane_normal)
if abs(den) < tol:
continue
for corner in coordinate_set:
num = dot(sub(point_on_plane, corner), plane_normal)
d = num / den
ipt = add(mult(axis, d), corner)
# check if all intersections are valid, taking care to be aware of minus signs.
ipt_0 = checkRange(ipt[0], 0.0, dim[0])
ipt_1 = checkRange(ipt[1], 0.0, dim[1])
ipt_2 = checkRange(ipt[2], 0.0, dim[2])
if ipt_0 and ipt_1 and ipt_2:
ipts.append(ipt)
unique_ipts = []
for p in ipts:
insert = True
for u in unique_ipts:
vdiff = sub(p, u)
if sqrt(dot(vdiff, vdiff)) < tol:
insert = False
if insert:
unique_ipts.append(p)
ca = CentroidAlgorithm(unique_ipts)
# wa = WeiszfeldsAlgorithm(unique_ipts)
plane_centre = ca.compute()
return plane_centre
def boundCoordinatesToCuboid(pt1, pt2, cuboid_dimensions):
'''
Takes two points and a cuboids dimensions, with
one corner defined by [0, 0, 0] and the opposite by
cuboid_dimensions, and returns a point that is inside the
cuboid. pt2 *must* be inside the cuboid.
'''
bounded_pt = pt1[:]
axes = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
coordinate_set = [[0, 0, 0], [cuboid_dimensions[0], cuboid_dimensions[1], cuboid_dimensions[2]]]
outside = [False, False, False]
for i, axis in enumerate(axes):
v1 = sub(pt1, coordinate_set[0])
v2 = sub(pt1, coordinate_set[1])
dir1 = dot(v1, axis)
dir2 = dot(v2, axis)
if copysign(1, dir1) == copysign(1, dir2):
if copysign(1, dir1) < 0:
outside[i] = 1
else:
outside[i] = 2
if any(outside):
indices = [i for i, x in enumerate(outside) if x]
ipt = None
for index in indices:
if outside[index] == 1:
ipt = calculateLinePlaneIntersection(pt1, pt2, coordinate_set[0], axes[index])
else:
ipt = calculateLinePlaneIntersection(pt1, pt2, coordinate_set[1], axes[index])
ipt_0 = checkRange(ipt[0], coordinate_set[0][0], coordinate_set[1][0])
ipt_1 = checkRange(ipt[1], coordinate_set[0][1], coordinate_set[1][1])
ipt_2 = checkRange(ipt[2], coordinate_set[0][2], coordinate_set[1][2])
if ipt_0 and ipt_1 and ipt_2:
bounded_pt = ipt
return bounded_pt
def boundCoordinatesToCuboid(pt1, pt2, cuboid_dimensions):
'''
Takes two points and a cuboids dimensions, with
one corner defined by [0, 0, 0] and the opposite by
cuboid_dimensions, and returns a point that is inside the
cuboid. pt2 *must* be inside the cuboid.
'''
bounded_pt = pt1[:]
axes = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
coordinate_set = [[0, 0, 0], [cuboid_dimensions[0], cuboid_dimensions[1], cuboid_dimensions[2]]]
outside = [False, False, False]
for i, axis in enumerate(axes):
v1 = sub(pt1, coordinate_set[0])
v2 = sub(pt1, coordinate_set[1])
dir1 = dot(v1, axis)
dir2 = dot(v2, axis)
if copysign(1, dir1) == copysign(1, dir2):
if copysign(1, dir1) < 0:
outside[i] = 1
else:
outside[i] = 2
if any(outside):
indices = [i for i, x in enumerate(outside) if x]
for index in indices:
if outside[index] == 1:
ipt = calculateLinePlaneIntersection(pt1, pt2, coordinate_set[0], axes[index])
else:
ipt = calculateLinePlaneIntersection(pt1, pt2, coordinate_set[1], axes[index])
ipt_0 = checkRange(ipt[0], coordinate_set[0][0], coordinate_set[1][0])
ipt_1 = checkRange(ipt[1], coordinate_set[0][1], coordinate_set[1][1])
ipt_2 = checkRange(ipt[2], coordinate_set[0][2], coordinate_set[1][2])
if ipt_0 and ipt_1 and ipt_2:
bounded_pt = ipt
return bounded_pt
