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 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 printToCSG(self, f):
o = Options()
l = o.getProperty('cubeEdgeLength')
h = 0.01
cellString = ' and plane(0, 0, {0}; 0, 0, {0})'.format(l - h)
cellString += ' and plane(0, {0}, 0; 0, {0}, 0)'.format(l - h)
cellString += ' and plane({0}, 0, 0; {0}, 0, 0)'.format(l - h)
cellString += ' and plane({1}, {1}, {1}; 0, 0, -{0})'.format(l - h, h)
cellString += ' and plane({1}, {1}, {1}; 0, -{0}, 0)'.format(l - h, h)
cellString += ' and plane({1}, {1}, {1}; -{0}, 0, 0)'.format(l - h, h)
h = o.getProperty('polygonalDiskThickness')
maxhFiller = o.getProperty('maxh_f')
st = 'solid polygonalDisk{3} = plane({0}, {1}, {2}; '
f.write(
st.format(self.values['topCenter'].x(),
self.values['topCenter'].y(),
self.values['topCenter'].z(), self.number()))
dx = self.values['topCenter'].x() - self.values['botCenter'].x()
dy = self.values['topCenter'].y() - self.values['botCenter'].y()
dz = self.values['topCenter'].z() - self.values['botCenter'].z()
f.write('{0}, {1}, {2}) '.format(dx, dy, dz))
st = 'and plane({0}, {1}, {2}; '
f.write(
st.format(self.values['botCenter'].x(),
self.values['botCenter'].y(),
self.values['botCenter'].z()))
dx = -self.values['topCenter'].x() + self.values['botCenter'].x()
dy = -self.values['topCenter'].y() + self.values['botCenter'].y()
dz = -self.values['topCenter'].z() + self.values['botCenter'].z()
f.write('{0}, {1}, {2})'.format(dx, dy, dz))
for facet in self.values['facets']:
f.write(' and plane({0}, {1}, {2}; '.format(
facet.x(), facet.y(), facet.z()))
c = self.c()
dfc = facet - c
f.write('{0}, {1}, {2})'.format(dfc.x(), dfc.y(), dfc.z()))
f.write(cellString)
f.write(';\n')
s = o.getProperty('shellThickness')
v = Vector(self.bc(), self.tc())
v = v * (2 * s + h) / 2 / h
pt = self.bc() / 2 + self.tc() / 2 + v
st = 'solid pdShell{0} = plane({1}, {2}, {3}; '
f.write(st.format(self.number(), pt.x(), pt.y(), pt.z()))
f.write('{0}, {1}, {2}) '.format(v.x(), v.y(), v.z()))
pt = self.bc() / 2 + self.tc() / 2 - v
f.write('and plane({1}, {2}, {3}; '.format(self.number(), pt.x(),
pt.y(), pt.z()))
f.write('{0}, {1}, {2}) '.format(-v.x(), -v.y(), -v.z()))
for facet in self.values['facets']:
vToFacet = Vector(self.c(), facet)
l = vToFacet.l()
vToFacet = vToFacet * ((l + s) / l)
f.write(' and plane({0}, {1}, {2}; '.format(
c.x() + vToFacet.x(),
c.y() + vToFacet.y(),
c.z() + vToFacet.z()))
f.write('{0}, {1}, {2})'.format(vToFacet.x(), vToFacet.y(),
vToFacet.z()))
f.write(cellString)
f.write(';\n')
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
