def boxCross(disk):
o = Options()
additiionalEmptiness = max(
o.getProperty('maxh_f'), # t oavoid errors
o.getProperty('maxh_sh'), # in netgen nesh
o.getProperty('maxh_m')) # generation
length = o.getProperty('cubeEdgeLength')
c = disk.c()
tc = disk.tc()
bc = disk.bc()
r = disk.r()
h = disk.h()
v = len(disk.facets())
vtb = Vector(bc, tc)
responce = ''
for facet in disk.facets():
vToFacet = facet - c
vInFacet = vtb.vectorMultiply(vToFacet)
realLength = vInFacet.l()
needLength = r * math.tan(math.pi / v)
vInFacet = vInFacet * (needLength / realLength)
x4 = facet + vInFacet + vtb / 2
x5 = facet - vInFacet + vtb / 2
x6 = facet + vInFacet - vtb / 2
x7 = facet - vInFacet - vtb / 2
if additiionalEmptiness > x4.x() or x5.x() < additiionalEmptiness:
return True
if additiionalEmptiness > x6.x() or x7.x() < additiionalEmptiness:
return True
if additiionalEmptiness > x4.y() or x5.y() < additiionalEmptiness:
return True
if additiionalEmptiness > x6.y() or x7.y() < additiionalEmptiness:
return True
if additiionalEmptiness > x4.z() or x5.z() < additiionalEmptiness:
return True
if additiionalEmptiness > x6.z() or x7.z() < additiionalEmptiness:
return True
if x4.x() > length - additiionalEmptiness or\
x5.x() > length - additiionalEmptiness:
return True
if x4.y() > length - additiionalEmptiness or\
x5.y() > length - additiionalEmptiness:
return True
if x4.z() > length - additiionalEmptiness or\
x5.z() > length - additiionalEmptiness:
return True
if x6.x() > length - additiionalEmptiness or\
x7.x() > length - additiionalEmptiness:
return True
if x6.y() > length - additiionalEmptiness or\
x7.y() > length - additiionalEmptiness:
return True
if x6.z() > length - additiionalEmptiness or\
x7.z() > length - additiionalEmptiness:
return True
return False
def disksCross(disk1, disk2):
o = Options()
epsilon = o.getProperty('roughEpsilon')
c1 = disk1.c()
tc1 = disk1.tc()
bc1 = disk1.bc()
c2 = disk2.c()
dc12 = c1 - c2
l = dc12.l()
r = disk1.r()
h = disk1.h()
v = len(disk1.facets())
if 2 * (r**2 + h**2 / 4)**0.5 < l**0.5:
return False
elif h > l:
return True
# http://mathworld.wolfram.com/Line-PlaneIntersection.html
# facet of disk2 and top or bottom of disk1
vtb1 = Vector(bc1, tc1)
tc2 = disk2.tc()
bc2 = disk2.bc()
vtb2 = Vector(bc2, tc2)
for (x1, x2, x3) in [
(
c1 + vtb1 / 2, # top
disk1.facets()[0] + vtb1 / 2,
disk1.facets()[1] + vtb1 / 2),
(
c1 - vtb1 / 2, # bottom
disk1.facets()[0] - vtb1 / 2,
disk1.facets()[1] - vtb1 / 2)
]:
v12 = Vector(x2, x1)
v32 = Vector(x2, x3)
for facet in disk2.facets():
vToFacet = Vector(c2, facet)
vInFacet = vtb2.vectorMultiply(vToFacet)
realLength = vInFacet.l()
needLength = r * math.tan(math.pi / v)
vInFacet = vInFacet * (needLength / realLength)
for (x4, x5) in [
(
facet + vInFacet + vtb2 / 2, # top edge
facet - vInFacet + vtb2 / 2),
(
facet + vInFacet - vtb2 / 2, # bottom edge
facet - vInFacet - vtb2 / 2)
]:
v42 = Vector(x2, x4)
v52 = Vector(x2, x5)
det1 = np.linalg.det(
np.array([[v12.x(), v12.y(), v12.z()],
[v32.x(), v32.y(), v32.z()],
[v42.x(), v42.y(), v42.z()]]))
det2 = np.linalg.det(
np.array([[v12.x(), v12.y(), v12.z()],
[v32.x(), v32.y(), v32.z()],
[v52.x(), v52.y(), v52.z()]]))
if -epsilon < det1 < epsilon or -epsilon < det2 < epsilon:
l = ((r / math.cos(math.pi / v))**2 + h**2 / 4)**0.5
if Vector(x1, x4).l() < r / math.cos(math.pi / v):
return True
if Vector(x1, x5).l() < r / math.cos(math.pi / v):
return True
#return True
elif det1 * det2 < -epsilon:
v45 = Vector(x4, x5)
pti = x4 + v45 * abs(det1) / (abs(det1) + abs(det2))
if Vector(x1, pti).l() < r:
return True
for facet1 in disk1.facets():
x1 = facet1
vToFacet1 = Vector(x1, c1)
vInFacet1 = vtb1.vectorMultiply(vToFacet1)
needLength = r * math.tan(math.pi / v)
realLength = vInFacet1.l()
vInFacet *= needLength / realLength
x2 = x1 + vInFacet + vtb1 / 2
x3 = x1 - vInFacet + vtb1 / 2
v12 = Vector(x2, x1)
v32 = Vector(x2, x3)
for facet2 in disk2.facets():
vToFacet = Vector(c2, facet)
vInFacet = vtb2.vectorMultiply(vToFacet)
realLength = vInFacet.l()
needLength = r * math.tan(math.pi / v)
vInFacet = vInFacet * (needLength / realLength)
for (x4, x5) in [
(
facet + vInFacet + vtb2 / 2, # top edge
facet - vInFacet + vtb2 / 2),
(
facet + vInFacet - vtb2 / 2, # bottom edge
facet - vInFacet - vtb2 / 2)
]:
v42 = Vector(x4, x2)
v52 = Vector(x5, x2)
det1 = np.linalg.det(
np.array([[v12.x(), v12.y(), v12.z()],
[v32.x(), v32.y(), v32.z()],
[v42.x(), v42.y(), v42.z()]]))
det2 = np.linalg.det(
np.array([[v12.x(), v12.y(), v12.z()],
[v32.x(), v32.y(), v32.z()],
[v52.x(), v52.y(), v52.z()]]))
if -epsilon < det1 < epsilon:
xi = x4
vectori = Vector(x1, xi)
cos = (abs(vectori.x() * vtb1.x() +
vectori.y() * vtb1.y() + vectori / z() * vtb1 /
z())) / vectori.l() / vtb1.l()
sin = (1 - cos**2)**0.5
axelen = cos * vectori.l()
norlen = sin * vectori.l()
if axelen < (vtb1 / 2).l() and norlen < needLength:
return True
elif -epsilon < det2 < epsilon:
xi = x5
vectori = Vector(x1, xi)
cos = (abs(vectori.x() * vtb1.x() +
vectori.y() * vtb1.y() + vectori / z() * vtb1 /
z())) / vectori.l() / vtb1.l()
sin = (1 - cos**2)**0.5
axelen = cos * vectori.l()
norlen = sin * vectori.l()
if axelen < (vtb1 / 2).l() and norlen < needLength:
return True
elif det1 * det2 < -epsilon:
xi = x4 + Vector(
x4, x5) * (abs(det1)) / (abs(det1) + abs(det2))
vectori = Vector(x1, xi)
cos = (abs(vectori.x() * vtb1.x() +
vectori.y() * vtb1.y() + vectori / z() * vtb1 /
z())) / vectori.l() / vtb1.l()
sin = (1 - cos**2)**0.5
axelen = cos * vectori.l()
norlen = sin * vectori.l()
if axelen < (vtb1 / 2).l() and norlen < needLength:
return True
return False
def boxCrossByDiskInTheShell(disk):
o = Options()
length = o.getProperty('cubeEdgeLength')
c = disk.c()
s = o.getProperty('shellThickness')
tc = disk.tc()
bc = disk.bc()
r = disk.r()
h = disk.h()
v = len(disk.facets())
vtb = Vector(bc, tc)
vtb = vtb * (2 * s + h) / h
responce = [0 for i in range(6)]
for facet in disk.facets():
ifcrossx = False
ifcrossy = False
ifcrossz = False
ptOnFacet = c + (facet - c) / r * (r + s)
vToFacet = facet - c
vInFacet = vtb.vectorMultiply(vToFacet)
realLength = vInFacet.l()
needLength = (r + s) * math.tan(math.pi / v)
vInFacet = vInFacet * (needLength / realLength)
x1 = ptOnFacet + vInFacet + vtb / 2
x2 = ptOnFacet + vInFacet - vtb / 2
x3 = ptOnFacet - vInFacet + vtb / 2
x4 = ptOnFacet - vInFacet - vtb / 2
if x1.x() * x2.x() < 0 or x1.x() * x3.x() < 0 or x1.x() * x4.x() < 0:
ifcrossx = True
if (x1.x() - length) * (x2.x() - length) < 0 or\
(x1.x() - length) * (x3.x() - length) < 0 or\
(x1.x() - length) * (x4.x() - length) < 0:
ifcrossx = True
if x1.y() * x2.y() < 0 or x1.y() * x3.y() < 0 or x1.y() * x4.y() < 0:
ifcrossy = True
if (x1.y() - length) * (x2.y() - length) < 0 or\
(x1.y() - length) * (x3.y() - length) < 0 or\
(x1.y() - length) * (x4.y() - length) < 0:
ifcrossy = True
if x1.z() * x2.z() < 0 or x1.z() * x3.z() < 0 or x1.z() * x4.z() < 0:
ifcrossz = True
if (x1.z() - length) * (x2.z() - length) < 0 or\
(x1.z() - length) * (x3.z() - length) < 0 or\
(x1.z() - length) * (x4.z() - length) < 0:
ifcrossz = True
if ifcrossx and not ifcrossy and not ifcrossz:
if 0 < c.y() < length and 0 < c.z() < length:
return True
if ifcrossy and not ifcrossx and not ifcrossz:
if 0 < c.x() < length and 0 < c.z() < length:
return True
if ifcrossz and not ifcrossy and not ifcrossx:
if 0 < c.y() < length and 0 < c.x() < length:
return True
if ifcrossx and ifcrossy and not ifcrossz:
if 0 < c.z() < length:
return True
if ifcrossx and ifcrossz and not ifcrossy:
if 0 < c.y() < length:
return True
if ifcrossz and ifcrossy and not ifcrossx:
if 0 < c.x() < length:
return True
if ifcrossx and ifcrossy and ifcrossz:
return True
return False
def diskDiskInTheShellCross(disk1, disk2):
o = Options()
epsilon = o.getProperty('roughEpsilon')
s = o.getProperty('shellThickness')
c1 = disk1.c()
tc1 = disk1.tc()
bc1 = disk1.bc()
c2 = disk2.c()
dc12 = c1 - c2
l = dc12.l()
r = disk1.r()
h = disk1.h()
v = len(disk1.facets())
if 2 * (r**2 + (h / 2 + 2 * s)**2)**0.5 < l:
return False
elif h + 2 * s > l:
return True
# facet of disk2 and top of disk1
vtb1 = Vector(bc1, tc1)
vtb1 = vtb1 * (2 * s + h) / h
tc2 = disk2.tc()
bc2 = disk2.bc()
vtb2 = Vector(bc2, tc2)
for (x1, x2, x3) in [
(
c1 + vtb1 / 2, # top
disk1.facets()[0] + vtb1 / 2,
disk1.facets()[1] + vtb1 / 2),
(
c1 - vtb1 / 2, # bottom
disk1.facets()[0] - vtb1 / 2,
disk1.facets()[1] - vtb1 / 2)
]:
v12 = Vector(x2, x1)
v32 = Vector(x2, x3)
for facet in disk2.facets():
vToFacet = Vector(c2, facet)
vInFacet = vtb2.vectorMultiply(vToFacet)
realLength = vInFacet.l()
needLength = r * math.tan(math.pi / v)
vInFacet = vInFacet * (needLength / realLength)
for (x4, x5) in [
(
facet + vInFacet + vtb2 / 2, # top edge
facet - vInFacet + vtb2 / 2),
(
facet + vInFacet - vtb2 / 2, # bottom edge
facet - vInFacet - vtb2 / 2)
]:
v42 = Vector(x2, x4)
v52 = Vector(x2, x5)
det1 = np.linalg.det(
np.array([[v12.x(), v12.y(), v12.z()],
[v32.x(), v32.y(), v32.z()],
[v42.x(), v42.y(), v42.z()]]))
det2 = np.linalg.det(
np.array([[v12.x(), v12.y(), v12.z()],
[v32.x(), v32.y(), v32.z()],
[v52.x(), v52.y(), v52.z()]]))
if -epsilon < det1 < epsilon or -epsilon < det2 < epsilon:
l = ((r / math.cos(math.pi / v))**2 + h**2 / 4)**0.5
if Vector(x1, x4).l() < r / math.cos(math.pi / v):
return True
if Vector(x1, x5).l() < r / math.cos(math.pi / v):
return True
elif det1 < -epsilon:
v45 = Vector(x4, x5)
pti = x4 + v45 * abs(det1) / (abs(det1) + abs(det2))
if Vector(x1, pti).l() < r:
return True
return False
def disksInTheShellCross(disk1, disk2):
o = Options()
epsilon = o.getProperty('roughEpsilon')
s = o.getProperty('shellThickness')
length = o.getProperty('cubeEdgeLength')
h = o.getProperty('polygonalDiskThickness')
v = o.getProperty('verticesNumber')
r = o.getProperty('polygonalDiskRadius')
c1 = disk1.c()
c2 = disk2.c()
vtb1 = Vector(disk1.bc(), disk1.tc())
vtb1 *= (2 * s + h) / h
vtb2 = Vector(disk2.bc(), disk2.tc())
vtb2 *= (2 * s + h) / h
# facet of disk2 and top/bottom of disk1:
for [x1, x2, x3] in [[
c1 + vtb1 / 2,
disk1.facets()[0] + vtb1 / 2,
disk1.facets()[1] + vtb1 / 2
],
[
c1 - vtb1 / 2,
disk1.facets()[0] - vtb1 / 2,
disk1.facets()[1] - vtb1 / 2
]]:
v12 = Vector(x2, x1)
v32 = Vector(x2, x3)
for facet2 in disk2.facets():
vToFacet = Vector(facet2, c2)
vToFacet *= (s + r) / r
vInFacet = vToFacet.vectorMultiply(vtb2)
realLength = vInFacet.l()
needLength = (r + s) * math.tan(math.pi / v)
vInFacet *= needLength / realLength
for [x4, x5] in [[
c2 + vToFacet + vtb2 / 2 + vInFacet,
c2 + vToFacet + vtb2 / 2 - vInFacet
],
[
c2 + vToFacet - vtb2 / 2 + vInFacet,
c2 + vToFacet - vtb2 / 2 - vInFacet
],
[
c2 + vToFacet + vtb2 / 2 + vInFacet,
c2 + vToFacet - vtb2 / 2 + vInFacet
],
[
c2 + vToFacet + vtb2 / 2 - vInFacet,
c2 + vToFacet - vtb2 / 2 - vInFacet
]]:
v42 = Vector(x2, x4)
v52 = Vector(x2, x5)
det1 = np.linalg.det(
np.array([[v12.x(), v12.y(), v12.z()],
[v32.x(), v32.y(), v32.z()],
[v42.x(), v42.y(), v42.z()]]))
det2 = np.linalg.det(
np.array([[v12.x(), v12.y(), v12.z()],
[v32.x(), v32.y(), v32.z()],
[v52.x(), v52.y(), v52.z()]]))
if abs(det1) < epsilon:
if Vector(x4, x1).l() < r + s:
return True
elif abs(det2) < epsilon:
if Vector(x5, x1).l() < r + s:
return True
elif det1 * det2 < 0:
tmpVector = Vector(
x4, x5) * abs(det1) / (abs(det1) + abs(det2))
if Vector(x1, x4 + tmpVector).l() < r + s:
return True
return False
