def octahedron(r=1, a=None, shell=False):
if a is None:
a = r / math.sqrt(2) * 2
he = a * 1 / 2 # half the edge length
c = a * math.sqrt(2) / 2 # circumsphere radius
return zencad.polyhedron(
pnts=points([
[0, 0, c], # 0: top
[-he, he, 0], # 1: front left
[he, he, 0], # 2: front right
[he, -he, 0], # 3: rear right
[-he, -he, 0], # 4: rear left
[0, 0, -c], # 5: bottom
]),
faces=[
[1, 0, 2], # top front
[2, 0, 3], # top right
[3, 0, 4], # top rear
[4, 0, 1], # top left
[5, 1, 2], # bottom front
[5, 2, 3], # bottom right
[5, 3, 4], # bottom rear
[4, 1, 5], # bottom left
],
shell=shell)
def interpolate2(lst, degmin=3, degmax=7):
if isinstance(lst[0][0], pyservoce.point3):
return pyservoce.interpolate2(lst, degmin=degmin, degmax=degmax)
else:
lst = [points(l) for l in lst]
return pyservoce.interpolate2(lst, degmin=degmin, degmax=degmax)
def tetrahedron(r=1, a=None, shell=False):
if a is None:
a = r / math.sqrt(3 / 2) * 2
he = a * 1 / 2
# half the edge length
fi = a * math.sqrt(3) / 6
# faces - incircle radius
fc = a * math.sqrt(3) / 3
# faces - circumcircle radius
i = a * math.sqrt(6) / 12
# insphere radius
c = a * math.sqrt(6) / 4
# circumsphere radius
return zencad.polyhedron(
pnts=points([
[0, 0, c], # 0: top
[0, fc, -i], # 1: bottom front
[-he, -fi, -i], # 2: bottom rear left
[he, -fi, -i], # 3: bottom rear right
]),
faces=[
[1, 0, 3], # right
[2, 0, 1], # left
[3, 0, 2], # rear
[2, 1, 3], # bottom
],
shell=shell)
def hexahedron(r=1, a=None, shell=False):
if a is None:
a = r / math.sqrt(3) * 2
he = a * 1 / 2 # half the edge length
return zencad.polyhedron(
pnts=points([
[-he, -he, -he], # 0
[-he, -he, he], # 1
[-he, he, -he], # 2
[-he, he, he], # 3
[he, -he, -he], # 4
[he, -he, he], # 5
[he, he, -he], # 6
[he, he, he], # 7
]),
faces=[
[0, 1, 3, 2],
[4, 5, 7, 6],
[2, 3, 7, 6],
[0, 1, 5, 4],
[0, 2, 6, 4],
[1, 3, 7, 5],
],
shell=shell)
def bezier(pnts, weights=None):
"""Построение дуги круга по трем точкам"""
pnts = points(pnts)
if weights:
return pyservoce.bezier(pnts, weights)
else:
return pyservoce.bezier(pnts)
def polyhedron(pnts, faces, shell=False):
pnts = points(pnts)
shl = pyservoce.polyhedron_shell(pnts, faces)
if shell:
return shl
else:
return shl.fill()
def _polygon(pnts, wire=False):
pnts = points(pnts)
if wire:
return wire_module._polysegment(pnts, closed=True)
mk = BRepBuilderAPI_MakePolygon()
for i in range(len(pnts)):
mk.Add(pnts[i].Pnt())
mk.Close()
return Shape(BRepBuilderAPI_MakeFace(mk.Shape()).Face())
def dodecahedron(r=1, a=None, shell=False):
if a is None:
a = r / (math.sqrt(3) * (1 + math.sqrt(5)) / 2) * 2
# coordinates of the "cube"
c = a * (1 + math.sqrt(5)) / 4
# phi / 2
# coordinates of the "rectangular cuboid"
r1 = a * 0
r2 = a * (3 + math.sqrt(5)) / 4
# (phi + 1) / 2
r3 = a * 1 / 2
return zencad.polyhedron(
pnts=points([
[r1, r2, r3], # 0: front top
[r1, r2, -r3], # 1: front bottom
[r1, -r2, r3], # 2: rear top
[r1, -r2, -r3], # 3: rear bottom
[r3, r1, r2], # 4: top right
[r3, r1, -r2], # 5: bottom right
[-r3, r1, r2], # 6: top left
[-r3, r1, -r2], # 7: bottom left
[c, c, c], # 8: top front right
[c, c, -c], # 9: bottom front right
[c, -c, c], # 10: top rear right
[c, -c, -c], # 11: bottom rear right
[-c, c, c], # 12: top front left
[-c, c, -c], # 13: bottom front left
[-c, -c, c], # 14: top rear left
[-c, -c, -c], # 15: bottom rear left
[r2, r3, r1], # 16: right front
[r2, -r3, r1], # 17: right rear
[-r2, r3, r1], # 18: left front
[-r2, -r3, r1], # 19: left rear
]),
faces=[
[8, 16, 9, 1, 0], # front right
[12, 6, 4, 8, 0], # top front
[1, 13, 18, 12, 0], # front left
[9, 5, 7, 13, 1], # bottom front
[14, 19, 15, 3, 2], # rear left
[3, 11, 17, 10, 2], # rear right
[10, 4, 6, 14, 2], # top rear
[15, 7, 5, 11, 3], # bottom rear
[10, 17, 16, 8, 4], # right top
[9, 16, 17, 11, 5], # right bottom
[12, 18, 19, 14, 6], # left top
[15, 19, 18, 13, 7], # left bottom
],
shell=shell)
def icosahedron(r=1, a=None, shell=False):
if a is None:
a = r / (math.sqrt(
(5 - math.sqrt(5)) / 2) * (1 + math.sqrt(5)) / 2) * 2
c1 = a * 0
# coordinate 1
c2 = a * 1 / 2
# coordinate 2
c3 = a * (1 + math.sqrt(5)) / 4
# coordinate 3; phi / 2
return zencad.polyhedron(
pnts=points([
[c3, c1, c2], # 0: right top
[c3, c1, -c2], # 1: right bottom
[-c3, c1, c2], # 2: left top
[-c3, c1, -c2], # 3: left bottom
[c2, c3, c1], # 4: front right
[c2, -c3, c1], # 5: rear right
[-c2, c3, c1], # 6: front left
[-c2, -c3, c1], # 7: rear left
[c1, c2, c3], # 8: top front
[c1, c2, -c3], # 9: bottom front
[c1, -c2, c3], # 10: top rear
[c1, -c2, -c3], # 11: bottom rear
]),
faces=[
[1, 0, 5], # right rear
[4, 0, 1], # right front
[5, 0, 10], # top rear right
[8, 0, 4], # top front right
[10, 0, 8], # top right
[4, 1, 9], # bottom front right
[9, 1, 11], # bottom right
[11, 1, 5], # bottom rear right
[3, 2, 6], # left front
[6, 2, 8], # top front left
[7, 2, 3], # left rear
[8, 2, 10], # top left
[10, 2, 7], # top rear left
[7, 3, 11], # bottom rear left
[9, 3, 6], # bottom front left
[11, 3, 9], # bottom left
[6, 4, 9], # front bottom
[8, 4, 6], # front top
[7, 5, 10], # rear top
[11, 5, 7], # rear bottom
],
shell=shell)
def bspline(pnts,
knots,
muls,
degree,
periodic=False,
check_rational=True,
weights=None):
"""Построение дуги круга по трем точкам"""
pnts = points(pnts)
if weights:
return pyservoce.bspline(pnts=pnts,
knots=knots,
weights=weights,
multiplicities=muls,
degree=degree,
periodic=periodic,
check_rational=check_rational)
else:
return pyservoce.bspline(pnts=pnts,
knots=knots,
multiplicities=muls,
degree=degree,
periodic=periodic)
def _rounded_polysegment(pnts, r, closed=False):
# Для того, чтобы закрыть контур, не теряя скругления, перекрёстно добавляем две точки,
# Две в начале, другую в конце.
pnts = points(pnts)
if closed:
pnts.insert(0, pnts[-1])
pnts.append(pnts[1])
cpnts = pnts[1:-1]
pairs = []
pairs_tang = []
pairs.append((None, pnts[0]))
for i in range(len(cpnts)):
a = segment(pnts[i], pnts[i + 1]).unlazy()
b = segment(pnts[i + 1], pnts[i + 2]).unlazy()
ad1 = a.d1(a.range()[1])
bd1 = b.d1(b.range()[0])
n = numpy.cross(bd1, ad1)
if numpy.linalg.norm(n) == 0:
pairs.append((cpnts[i], cpnts[i]))
pairs_tang.append(None)
continue
abn = numpy.cross(ad1, n)
bbn = numpy.cross(bd1, n)
temp = (abn + bbn)
bn = temp / numpy.linalg.norm(temp) * r
c = cpnts[i] + bn
ca = project(c, a)
cb = project(c, b)
pairs.append((ca, cb))
pairs_tang.append((ad1, bd1))
pairs.append((pnts[-1], None))
nodes = []
for i in range(len(cpnts)):
nodes.append(segment(pairs[i][1], pairs[i + 1][0]))
if pairs_tang[i] is not None:
nodes.append(
interpolate(pnts=[pairs[i + 1][0], pairs[i + 1][1]],
tangs=[pairs_tang[i][0], pairs_tang[i][1]]))
nodes.append(segment(pairs[-2][1], pairs[-1][0]))
# Для замыкания необходимо удалить крайние сегменты.
if closed:
del nodes[0]
del nodes[-1]
result = sew(nodes)
# И, наконец, зашиваем прореху.
if closed:
result = sew(
[result,
segment(result.endpoints()[0],
result.endpoints()[1])])
return result
def interpolate(pnts, tangs=[], closed=False):
return pyservoce.interpolate_curve3(points(pnts), vectors(tangs), closed)
def chamfer(shp, r, refs=None):
if refs is None:
return pyservoce.chamfer(shp, r)
else:
return pyservoce.chamfer(shp, r, points(refs))
def fillet(shp, r, refs=None):
if refs is None:
return pyservoce.fillet(shp, r)
else:
return pyservoce.fillet(shp, r, points(refs))
def thicksolid(shp, t, refs):
return pyservoce.thicksolid(shp, points(refs), t)
def thicksolid(proto, t, refs):
return pyservoce.thicksolid(proto, points(refs), t)
def polygon(pnts, wire=False):
if wire:
return pyservoce.polysegment(points(pnts), True)
else:
return pyservoce.polygon(points(pnts))
def _segment(a, b) -> Shape:
a, b = points((a, b))
return Shape(BRepBuilderAPI_MakeEdge(to_Pnt(a), to_Pnt(b)).Edge())
def polysegment(lst, closed=False):
return pyservoce.polysegment(points(lst), closed)
def rounded_polysegment(pnts, r, closed=False):
pnts = points(pnts)
# Для того, чтобы закрыть контур, не теряя скругления, перекрёстно добавляем две точки,
# Две в начале, другую в конце.
if closed:
pnts.insert(0, pnts[-1])
pnts.append(pnts[1])
cpnts = pnts[1:-1]
pairs = []
pairs_tangs = []
pairs.append((None, pnts[0]))
for i in range(len(cpnts)):
a = pyservoce.segment(pnts[i], pnts[i + 1])
b = pyservoce.segment(pnts[i + 1], pnts[i + 2])
ad1 = a.d1(a.range()[1])
bd1 = b.d1(b.range()[0])
n = bd1.cross(ad1)
if n.iszero():
pairs.append((cpnts[i], cpnts[i]))
pairs_tangs.append(None)
continue
abn = ad1.cross(n)
bbn = bd1.cross(n)
bn = (abn + bbn).normalize() * r
c = cpnts[i] + bn
ca = pyservoce.project(c, a)
cb = pyservoce.project(c, b)
pairs.append((ca, cb))
pairs_tangs.append((ad1, bd1))
pairs.append((pnts[-1], None))
nodes = []
for i in range(len(cpnts)):
nodes.append(pyservoce.segment(pairs[i][1], pairs[i + 1][0]))
if pairs_tangs[i] is not None:
nodes.append(
pyservoce.interpolate(
pnts=[pairs[i + 1][0], pairs[i + 1][1]],
tang=[pairs_tangs[i][0], pairs_tangs[i][1]]))
nodes.append(pyservoce.segment(pairs[-2][1], pairs[-1][0]))
# Для замыкания необходимо удалить крайние сегменты.
if closed:
del nodes[0]
del nodes[-1]
result = pyservoce.make_wire(nodes)
# И, наконец, зашиваем прореху.
if closed:
result = pyservoce.make_wire([
result,
pyservoce.segment(result.endpoints()[0],
result.endpoints()[1])
])
return result
