Mod: shaping is stable now
Mod: shaping improved documentation Remove: not necessary modules or moved
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@ -1,17 +1,16 @@
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# -*- coding: utf-8 -*-
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# This file is part of anisotropy.
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# License: GNU GPL version 3, see the file "LICENSE" for details.
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from . import utils
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from . import conversion
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from . import metrics
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from .mesh import Mesh
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from .mesh import Mesh, MeshingParameters
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__all__ = [
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"utils",
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"conversion",
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"metrics",
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"Mesh"
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"Mesh",
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"MeshingParameters"
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]
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@ -196,7 +196,7 @@ class Mesh:
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mesh.write(path)
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@property
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def volumes(self) -> list[ndarray]: # delete?
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def volumes(self) -> list[ndarray]:
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"""Volumes.
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:return:
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@ -220,7 +220,7 @@ class Mesh:
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return np.sum([ metrics.volume(cell) for cell in self.volumes ])
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@property
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def faces(self) -> list[ndarray]: # delete?
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def faces(self) -> list[ndarray]:
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"""Boundary faces.
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:return:
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@ -1,9 +1,21 @@
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# -*- coding: utf-8 -*-
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# This file is part of anisotropy.
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# License: GNU GPL version 3, see the file "LICENSE" for details.
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"""
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Shaping is a library for using OCC shapes, provides more convient
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functionality with power NumPy and Python OOP and contains interesing
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primitives.
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"""
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from .shape import ShapeError, Shape
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from . import utils
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from .shape import Shape
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from .periodic import Periodic
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from .simple import Simple
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from .faceCentered import FaceCentered
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from .bodyCentered import BodyCentered
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from . import primitives
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__all__ = [
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"utils",
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"primitives",
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"Shape",
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"Periodic"
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]
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@ -1,173 +0,0 @@
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# -*- coding: utf-8 -*-
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# This file is part of anisotropy.
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# License: GNU GPL version 3, see the file "LICENSE" for details.
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from netgen.occ import *
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import numpy
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from numpy import pi, sqrt, arccos
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from .occExtended import *
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from . import Periodic
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from . import ShapeError
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class BodyCentered(Periodic):
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def __init__(
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self,
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direction: list = None,
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**kwargs
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):
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Periodic.__init__(
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self,
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alpha = kwargs.get("alpha", 0.01),
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r0 = kwargs.get("r0", 1),
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filletsEnabled = kwargs.get("filletsEnabled", True),
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gamma = pi - 2 * arccos(sqrt(2 / 3))
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)
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# Parameters
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self.direction = direction
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self.alphaMin = 0.01
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self.alphaMax = 0.18
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# Objects
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self.lattice = None
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self.cell = None
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self.shape = None
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@property
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def L(self):
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return self.r0 * 4 / sqrt(3)
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def build(self):
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#
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zero = Pnt(0, 0, 0)
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# Lattice
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spheres = numpy.array([], dtype = object)
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for zn in range(3):
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z = zn * self.L
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z2 = z - 0.5 * self.L
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for yn in range(3):
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y = yn * self.L
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y2 = y - 0.5 * self.L
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for xn in range(3):
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x = xn * self.L
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x2 = x - 0.5 * self.L
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spheres = numpy.append(spheres, Sphere(Pnt(x, y, z), self.radius))
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# shifted
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spheres = numpy.append(spheres, Sphere(Pnt(x2, y2, z2), self.radius))
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lattice = spheres.sum()
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lattice = lattice.Scale(zero, self.maximize)
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if self.filletsEnabled:
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lattice = lattice.MakeFillet(lattice.edges, self.fillets * self.maximize)
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self.lattice = lattice.Scale(zero, self.minimize)
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# Inlet face
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if (self.direction == numpy.array([1., 0., 0.])).prod():
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length = 2 * self.r0
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width = self.L / 2
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diag = self.L * sqrt(2)
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height = self.L
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xl = sqrt(diag ** 2 + diag ** 2) * 0.5
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yw = xl
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zh = height
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vertices = numpy.array([
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(xl, 0, 0),
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(0, yw, 0),
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(0, yw, zh),
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(xl, 0, zh)
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])
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extr = diag
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elif (self.direction == numpy.array([0., 0., 1.])).prod():
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length = 2 * self.r0
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width = self.L / 2
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diag = self.L * sqrt(2)
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height = self.L
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xl = sqrt(diag ** 2 + diag ** 2) * 0.5
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yw = xl
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zh = height
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vertices = numpy.array([
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(0, yw, 0),
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(xl, 0, 0),
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(2 * xl, yw, 0),
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(xl, 2 * yw, 0)
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])
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extr = height
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elif (self.direction == numpy.array([1., 1., 1.])).prod():
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length = 2 * self.r0
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width = self.L / 2
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diag = self.L * sqrt(2)
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height = diag / 3
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xl = -self.L / 4
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yw = -self.L / 4
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zh = -self.L / 4
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vertices = numpy.array([
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(self.L / 3 + xl, self.L / 3 + yw, 4 * self.L / 3 + zh),
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(self.L + xl, 0 + yw, self.L + zh),
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(4 * self.L / 3 + xl, self.L / 3 + yw, self.L / 3 + zh),
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(self.L + xl, self.L + yw, 0 + zh),
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(self.L / 3 + xl, 4 * self.L / 3 + yw, self.L / 3 + zh),
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(0 + xl, self.L + yw, self.L + zh)
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])
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extr = self.L * sqrt(3)
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else:
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raise Exception(f"Direction { self.direction } is not implemented")
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# Cell
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circuit = Wire([ Segment(Pnt(*v1), Pnt(*v2)) for v1, v2 in zip(vertices, numpy.roll(vertices, -1, axis = 0)) ])
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inletface = Face(circuit)
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inletface.name = "inlet"
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vecFlow = self.normal(inletface)
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# ISSUE: don't use face.Extrude(length), only face.Extrude(length, vector)
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self.cell = inletface.Extrude(extr, Vec(*vecFlow))
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# Boundaries
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symetryId = 0
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for face in self.cell.faces:
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fNorm = self.normal(face)
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fAngle = self.angle(vecFlow, fNorm)
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if fAngle == 0 or fAngle == numpy.pi:
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if (face.center.pos() == inletface.center.pos()).prod():
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face.name = "inlet"
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else:
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face.name = "outlet"
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else:
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face.name = f"symetry{ symetryId }"
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symetryId += 1
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# Main shape
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self.shape = self.cell - self.lattice
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if not len(self.shape.solids) == 1:
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raise ShapeError("Expected single solid shape")
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else:
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self.shape = self.shape.solids[0]
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# Boundaries (walls)
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for face in self.shape.faces:
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if face.name not in ["inlet", "outlet", *[ f"symetry{ n }" for n in range(6) ]]:
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face.name = "wall"
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@ -1,182 +0,0 @@
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# -*- coding: utf-8 -*-
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# This file is part of anisotropy.
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# License: GNU GPL version 3, see the file "LICENSE" for details.
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from netgen.occ import *
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import numpy
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from numpy import pi, sqrt
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from .occExtended import *
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from . import Periodic
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from . import ShapeError
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class FaceCentered(Periodic):
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def __init__(
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self,
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direction: list = None,
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**kwargs
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):
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Periodic.__init__(
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self,
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alpha = kwargs.get("alpha", 0.01),
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r0 = kwargs.get("r0", 1),
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filletsEnabled = kwargs.get("filletsEnabled", True),
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gamma = 2 / 3 * pi
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)
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# Parameters
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self.direction = direction
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self.alphaMin = 0.01
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self.alphaMax = 0.13
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# Objects
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self.lattice = None
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self.cell = None
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self.shape = None
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@property
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def L(self):
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return self.r0 * 4 / sqrt(2)
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def build(self):
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#
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zero = Pnt(0, 0, 0)
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# Lattice
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spheres = numpy.array([], dtype = object)
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x0 = 0#-0.5 * self.L * (3 - 1)
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x20 = 0#-0.5 * self.L * 3
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z0 = -0.5 * self.L * (3 - 2)
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z20 = -0.5 * self.L * (3 - 1)
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for zn in range(3):
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z = z0 + zn * self.L
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z2 = z20 + zn * self.L
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for yn in range(3):
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y = yn * 2 * self.r0
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y2 = yn * 2 * self.r0 + self.r0
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for xn in range(3):
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x = x0 + xn * 2 * self.r0
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x2 = x20 + xn * 2 * self.r0 + self.r0
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# TODO: fix rotations (arcs intersection -> incorrect boolean operations
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spheres = numpy.append(spheres, Sphere(Pnt(x, y, z), self.radius).Rotate(Axis(Pnt(x, y, z), X), 45).Rotate(Axis(Pnt(x, y, z), Z), 45))
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# shifted
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spheres = numpy.append(spheres, Sphere(Pnt(x2, y2, z2), self.radius).Rotate(Axis(Pnt(x2, y2, z2), X), 45).Rotate(Axis(Pnt(x2, y2, z2), Z), 45))
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lattice = spheres.sum()
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lattice = lattice.Move(Vec(-self.r0 * 2, -self.r0 * 2, 0)).Rotate(Axis(zero, Z), 45)
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lattice = lattice.Scale(zero, self.maximize)
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if self.filletsEnabled:
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lattice = lattice.MakeFillet(lattice.edges, self.fillets * self.maximize)
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self.lattice = lattice.Scale(zero, self.minimize)
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# Inlet face
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if (self.direction == numpy.array([1., 0., 0.])).prod():
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length = 2 * self.r0
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width = self.L / 2
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diag = self.L * sqrt(3)
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height = diag / 3
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xl = sqrt(length ** 2 + length ** 2) * 0.5
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yw = xl
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zh = width
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vertices = numpy.array([
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(0, 0, -zh),
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(-xl, yw, -zh),
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(-xl, yw, zh),
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(0, 0, zh)
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])
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extr = length
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elif (self.direction == numpy.array([0., 0., 1.])).prod():
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length = 2 * self.r0
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width = self.L / 2
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diag = self.L * sqrt(3)
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height = diag / 3
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xl = sqrt(length ** 2 + length ** 2) * 0.5
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yw = xl
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zh = width
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vertices = numpy.array([
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(0, 0, -zh),
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(xl, yw, -zh),
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(0, 2 * yw, -zh),
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(-xl, yw, -zh)
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])
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extr = 2 * width
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elif (self.direction == numpy.array([1., 1., 1.])).prod():
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length = 2 * self.r0
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width = self.L / 2
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diag = self.L * sqrt(3)
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height = diag / 3
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xl = -(3 - 2) * self.L / 3
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yw = -(3 - 2) * self.L / 3
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zh = -(3 - 2) * self.L / 3
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vertices = numpy.array([
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(-2 * width / 3 + xl, -2 * width / 3 + yw, width / 3 + zh),
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(0 + xl, -width + yw, 0 + zh),
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(width / 3 + xl, -2 * width / 3 + yw, -2 * width / 3 + zh),
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(0 + xl, 0 + yw, -width + zh),
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(-2 * width / 3 + xl, width / 3 + yw, -2 * width / 3 + zh),
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(-width + xl, 0 + yw, 0 + zh)
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])
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extr = sqrt(3) * self.L
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else:
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raise Exception(f"Direction { self.direction } is not implemented")
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# Cell
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circuit = Wire([ Segment(Pnt(*v1), Pnt(*v2)) for v1, v2 in zip(vertices, numpy.roll(vertices, -1, axis = 0)) ])
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inletface = Face(circuit)
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inletface.name = "inlet"
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vecFlow = self.normal(inletface)
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# ISSUE: don't use face.Extrude(length), only face.Extrude(length, vector)
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self.cell = inletface.Extrude(extr, Vec(*vecFlow))
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# Boundaries
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symetryId = 0
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for face in self.cell.faces:
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fNorm = self.normal(face)
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fAngle = self.angle(vecFlow, fNorm)
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if fAngle == 0 or fAngle == numpy.pi:
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if (face.center.pos() == inletface.center.pos()).prod():
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face.name = "inlet"
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else:
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face.name = "outlet"
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else:
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face.name = f"symetry{ symetryId }"
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symetryId += 1
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# Main shape
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self.shape = self.cell - self.lattice
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if not len(self.shape.solids) == 1:
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raise ShapeError("Expected single solid shape")
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else:
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self.shape = self.shape.solids[0]
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# Boundaries (walls)
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for face in self.shape.faces:
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if face.name not in ["inlet", "outlet", *[ f"symetry{ n }" for n in range(6) ]]:
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face.name = "wall"
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@ -1,41 +0,0 @@
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# -*- coding: utf-8 -*-
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# This file is part of anisotropy.
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# License: GNU GPL version 3, see the file "LICENSE" for details.
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from functools import wraps
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from netgen import occ
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import numpy
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def add_method(cls):
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"""Add method to existing class. Use it as decorator.
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"""
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def decorator(func):
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@wraps(func)
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def wrapper(self, *args, **kwargs):
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return func(self, *args, **kwargs)
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setattr(cls, func.__name__, wrapper)
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return func
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return decorator
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@add_method(occ.gp_Pnt)
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def pos(self) -> numpy.array:
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return numpy.array([self.x, self.y, self.z])
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# ISSUE: netgen.occ.Face.Extrude: the opposite face has the same name and normal vector as an initial face.
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#def reconstruct(shape):
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# """Reconstruct shape with new objects.
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# """
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# faces = []
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#
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# for face in shape.faces:
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# faceNew = occ.Face(face.wires[0])
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# faceNew.name = face.name
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# faces.append(faceNew)
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#
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# return occ.Solid(faces)
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@ -1,9 +1,6 @@
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# -*- coding: utf-8 -*-
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# This file is part of anisotropy.
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# License: GNU GPL version 3, see the file "LICENSE" for details.
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from netgen.occ import *
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from numpy import pi, sqrt, cos, arccos, fix
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import numpy as np
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from . import Shape
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@ -13,33 +10,35 @@ class Periodic(Shape):
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self,
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alpha: float = None,
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r0: float = 1,
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#L: float = None,
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#radius: float = None,
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L: float = None,
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filletsEnabled: bool = True,
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#fillets: float = None,
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gamma = None,
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**kwargs
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):
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"""Constructor method.
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"""A Periodic object contains periodic structure.
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:param alpha:
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Spheres overlap parameter.
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:param r0:
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Initial spheres radius.
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:param L:
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Side length of periodic cell. Depends on r0.
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:param gamma:
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Angle between lines that connect centers of spheres.
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:param filletsEnabled:
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Enable fillets beetween spheres.
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If True, calculate fillets beetween spheres.
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"""
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Shape.__init__(self)
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# Parameters
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self.alpha = alpha
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self.r0 = r0
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self.L = L
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||||
|
||||
self.theta = 0.5 * pi
|
||||
# for lattice
|
||||
# self.theta = 0.5 * pi
|
||||
|
||||
self.gamma = gamma or pi - 2 * (0.5 * self.theta)
|
||||
self.gamma = gamma or np.pi - 2 * (0.5 * 0.5 * np.pi)
|
||||
self.filletsEnabled = filletsEnabled
|
||||
self.filletsScale = 0.8
|
||||
|
||||
@ -47,51 +46,24 @@ class Periodic(Shape):
|
||||
self.maximize = 1e+2
|
||||
self.minimize = 1e-2
|
||||
|
||||
|
||||
@property
|
||||
def L(self):
|
||||
"""(Override) Parameter depending on the ``r0``.
|
||||
"""
|
||||
pass
|
||||
|
||||
@property
|
||||
def radius(self):
|
||||
def radius(self) -> float:
|
||||
"""Spheres radius
|
||||
|
||||
:return:
|
||||
Radius.
|
||||
"""
|
||||
return self.r0 / (1 - self.alpha)
|
||||
|
||||
@property
|
||||
def fillets(self):
|
||||
analytical = self.r0 * sqrt(2) / sqrt(1 - cos(self.gamma)) - self.radius
|
||||
# ISSUE: MakeFilletAll : Fillet can't be computed on the given shape with the given radius.
|
||||
# Temporary solution: degrade the precision (minRound <= analytical).
|
||||
"""Fillets radius beetween spheres.
|
||||
|
||||
:return:
|
||||
Radius.
|
||||
"""
|
||||
analytical = self.r0 * np.sqrt(2) / np.sqrt(1 - np.cos(self.gamma)) - self.radius
|
||||
rTol = 3
|
||||
minRound = fix(10 ** rTol * analytical) * 10 ** -rTol
|
||||
minRound = np.fix(10 ** rTol * analytical) * 10 ** -rTol
|
||||
|
||||
return minRound * self.filletsScale
|
||||
|
||||
def lattice(self,
|
||||
theta = 0.5 * pi
|
||||
):
|
||||
zero = Pnt(0, 0, 0)
|
||||
maximize = 1e+2
|
||||
minimize = 1e-2
|
||||
|
||||
# Lattice
|
||||
spheres = numpy.array([], dtype = object)
|
||||
|
||||
for zn in range(3):
|
||||
z = zn * self.L
|
||||
for yn in range(3):
|
||||
y = yn * self.L
|
||||
for xn in range(3):
|
||||
x = xn * self.L
|
||||
spheres = numpy.append(spheres, Sphere(Pnt(x, y, z), self.radius))
|
||||
|
||||
lattice = spheres.sum()
|
||||
lattice = lattice.Scale(zero, maximize)
|
||||
|
||||
if self.filletsEnabled:
|
||||
lattice = lattice.MakeFillet(lattice.edges, self.fillets * maximize)
|
||||
|
||||
self.lattice = lattice.Scale(zero, minimize)
|
||||
|
||||
499
anisotropy/shaping/primitives.py
Normal file
499
anisotropy/shaping/primitives.py
Normal file
@ -0,0 +1,499 @@
|
||||
# -*- coding: utf-8 -*-
|
||||
|
||||
from __future__ import annotations
|
||||
from numpy import ndarray
|
||||
|
||||
import numpy as np
|
||||
import netgen.occ as ng_occ
|
||||
|
||||
from . import Periodic
|
||||
from . import utils
|
||||
|
||||
|
||||
def simple(alpha: float, direction: list | ndarray, **kwargs) -> Periodic:
|
||||
"""Simple periodic structure.
|
||||
|
||||
:param alpha:
|
||||
Spheres overlap parameter.
|
||||
:param direction:
|
||||
Flow direction vector. This parameter affects the geometry type
|
||||
and boundary (faces) names.
|
||||
:return:
|
||||
Periodic object.
|
||||
"""
|
||||
# base object
|
||||
pc = Periodic(
|
||||
alpha = alpha,
|
||||
gamma = np.pi - 2 * (0.5 * 0.5 * np.pi)
|
||||
)
|
||||
|
||||
# additional parameters
|
||||
pc.__dict__.update(kwargs)
|
||||
pc.L = 2 * pc.r0
|
||||
pc.direction = np.asarray(direction)
|
||||
|
||||
# additional attributes
|
||||
pc.cell: ng_occ.Solid = None
|
||||
pc.lattice: ng_occ.Solid = None
|
||||
|
||||
# constants
|
||||
zero = ng_occ.Pnt(0, 0, 0)
|
||||
|
||||
# Lattice
|
||||
spheres = []
|
||||
|
||||
for zn in range(3):
|
||||
z = zn * pc.L
|
||||
|
||||
for yn in range(3):
|
||||
y = yn * pc.L
|
||||
|
||||
for xn in range(3):
|
||||
x = xn * pc.L
|
||||
|
||||
spheres.append(ng_occ.Sphere(ng_occ.Pnt(x, y, z), pc.radius))
|
||||
|
||||
lattice = np.sum(spheres)
|
||||
lattice = lattice.Scale(zero, pc.maximize)
|
||||
|
||||
if pc.filletsEnabled:
|
||||
lattice = lattice.MakeFillet(lattice.edges, pc.fillets * pc.maximize)
|
||||
|
||||
pc.lattice = lattice.Scale(zero, pc.minimize)
|
||||
|
||||
# Inlet face
|
||||
if np.all(pc.direction == [1., 0., 0.]):
|
||||
length = pc.L * np.sqrt(2)
|
||||
width = pc.L * np.sqrt(2)
|
||||
height = pc.L
|
||||
|
||||
xl = np.sqrt(length ** 2 * 0.5)
|
||||
yw = xl
|
||||
zh = height
|
||||
|
||||
vertices = np.array([
|
||||
(xl, 0, 0),
|
||||
(0, yw, 0),
|
||||
(0, yw, zh),
|
||||
(xl, 0, zh)
|
||||
])
|
||||
extr = width
|
||||
|
||||
elif np.all(pc.direction == [0., 0., 1.]):
|
||||
length = pc.L * np.sqrt(2)
|
||||
width = pc.L * np.sqrt(2)
|
||||
height = pc.L
|
||||
|
||||
xl = np.sqrt(length ** 2 * 0.5)
|
||||
yw = xl
|
||||
zh = height
|
||||
|
||||
vertices = np.array([
|
||||
(0, yw, 0),
|
||||
(xl, 0, 0),
|
||||
(2 * xl, yw, 0),
|
||||
(xl, 2 * yw, 0)
|
||||
])
|
||||
extr = height
|
||||
|
||||
elif np.all(pc.direction == [1., 1., 1.]):
|
||||
length = pc.L * np.sqrt(2)
|
||||
width = pc.L * np.sqrt(2)
|
||||
height = pc.L
|
||||
|
||||
xl = -pc.L - pc.L / 6
|
||||
yw = -pc.L - pc.L / 6
|
||||
zh = -pc.L / 6
|
||||
|
||||
vertices = np.array([
|
||||
(pc.L + xl, pc.L + yw, pc.L + zh),
|
||||
(5 * pc.L / 3 + xl, 2 * pc.L / 3 + yw, 2 * pc.L / 3 + zh),
|
||||
(2 * pc.L + xl, pc.L + yw, 0 + zh),
|
||||
(5 * pc.L / 3 + xl, 5 * pc.L / 3 + yw, -pc.L / 3 + zh),
|
||||
(pc.L + xl, 2 * pc.L + yw, 0 + zh),
|
||||
(2 * pc.L / 3 + xl, 5 * pc.L / 3 + yw, 2 * pc.L / 3 + zh)
|
||||
])
|
||||
extr = pc.L * np.sqrt(3)
|
||||
|
||||
else:
|
||||
raise Exception(f"Direction { pc.direction } is not implemented")
|
||||
|
||||
# Cell
|
||||
circuit = ng_occ.Wire([
|
||||
ng_occ.Segment(ng_occ.Pnt(*v1), ng_occ.Pnt(*v2))
|
||||
for v1, v2 in zip(vertices, np.roll(vertices, -1, axis = 0))
|
||||
])
|
||||
inletface = ng_occ.Face(circuit)
|
||||
inletface.name = "inlet"
|
||||
|
||||
vecFlow = utils.normal(inletface)
|
||||
pc.cell = inletface.Extrude(extr, ng_occ.Vec(*vecFlow))
|
||||
|
||||
# Boundary faces
|
||||
symetryId = 0
|
||||
|
||||
for face in pc.cell.faces:
|
||||
fNorm = utils.normal(face)
|
||||
fAngle = utils.angle(vecFlow, fNorm)
|
||||
|
||||
if fAngle == 0 or fAngle == np.pi:
|
||||
if np.all(utils.pos(face.center) == utils.pos(inletface.center)):
|
||||
face.name = "inlet"
|
||||
|
||||
else:
|
||||
face.name = "outlet"
|
||||
|
||||
else:
|
||||
face.name = f"symetry{ symetryId }"
|
||||
symetryId += 1
|
||||
|
||||
# Main shape
|
||||
pc.shape = pc.cell - pc.lattice
|
||||
|
||||
assert len(pc.shape.solids) == 1, "Expected single solid shape"
|
||||
|
||||
pc.shape = pc.shape.solids[0]
|
||||
|
||||
# Boundary faces (walls)
|
||||
for face in pc.shape.faces:
|
||||
if face.name not in ["inlet", "outlet", *[ f"symetry{ n }" for n in range(6) ]]:
|
||||
face.name = "wall"
|
||||
|
||||
return pc
|
||||
|
||||
|
||||
def body_centered(alpha: float, direction: list | ndarray, **kwargs) -> Periodic:
|
||||
"""Body centered periodic structure.
|
||||
|
||||
:param alpha:
|
||||
Spheres overlap parameter.
|
||||
:param direction:
|
||||
Flow direction vector. This parameter affects the geometry type
|
||||
and boundary (faces) names.
|
||||
:return:
|
||||
Periodic object.
|
||||
"""
|
||||
# base object
|
||||
pc = Periodic(
|
||||
alpha = alpha,
|
||||
gamma = np.pi - 2 * np.arccos(np.sqrt(2 / 3))
|
||||
)
|
||||
|
||||
# additional parameters
|
||||
pc.__dict__.update(kwargs)
|
||||
pc.L = 4 / np.sqrt(3) * pc.r0
|
||||
pc.direction = np.asarray(direction)
|
||||
|
||||
# additional attributes
|
||||
pc.cell: ng_occ.Solid = None
|
||||
pc.lattice: ng_occ.Solid = None
|
||||
|
||||
# constants
|
||||
zero = ng_occ.Pnt(0, 0, 0)
|
||||
|
||||
# Lattice
|
||||
spheres = []
|
||||
|
||||
for zn in range(3):
|
||||
z = zn * pc.L
|
||||
z2 = z - 0.5 * pc.L
|
||||
|
||||
for yn in range(3):
|
||||
y = yn * pc.L
|
||||
y2 = y - 0.5 * pc.L
|
||||
|
||||
for xn in range(3):
|
||||
x = xn * pc.L
|
||||
x2 = x - 0.5 * pc.L
|
||||
|
||||
spheres.append(ng_occ.Sphere(ng_occ.Pnt(x, y, z), pc.radius))
|
||||
# shifted
|
||||
spheres.append(ng_occ.Sphere(ng_occ.Pnt(x2, y2, z2), pc.radius))
|
||||
|
||||
lattice = np.sum(spheres)
|
||||
lattice = lattice.Scale(zero, pc.maximize)
|
||||
|
||||
if pc.filletsEnabled:
|
||||
lattice = lattice.MakeFillet(lattice.edges, pc.fillets * pc.maximize)
|
||||
|
||||
pc.lattice = lattice.Scale(zero, pc.minimize)
|
||||
|
||||
# Inlet face
|
||||
if np.all(pc.direction == [1., 0., 0.]):
|
||||
# length = 2 * pc.r0
|
||||
# width = pc.L / 2
|
||||
diag = pc.L * np.sqrt(2)
|
||||
height = pc.L
|
||||
|
||||
xl = np.sqrt(diag ** 2 + diag ** 2) * 0.5
|
||||
yw = xl
|
||||
zh = height
|
||||
|
||||
vertices = np.array([
|
||||
(xl, 0, 0),
|
||||
(0, yw, 0),
|
||||
(0, yw, zh),
|
||||
(xl, 0, zh)
|
||||
])
|
||||
extr = diag
|
||||
|
||||
elif np.all(pc.direction == [0., 0., 1.]):
|
||||
# length = 2 * pc.r0
|
||||
# width = pc.L / 2
|
||||
diag = pc.L * np.sqrt(2)
|
||||
height = pc.L
|
||||
|
||||
xl = np.sqrt(diag ** 2 + diag ** 2) * 0.5
|
||||
yw = xl
|
||||
zh = height
|
||||
|
||||
vertices = np.array([
|
||||
(0, yw, 0),
|
||||
(xl, 0, 0),
|
||||
(2 * xl, yw, 0),
|
||||
(xl, 2 * yw, 0)
|
||||
])
|
||||
extr = height
|
||||
|
||||
elif np.all(pc.direction == [1., 1., 1.]):
|
||||
# length = 2 * pc.r0
|
||||
# width = pc.L / 2
|
||||
diag = pc.L * np.sqrt(2)
|
||||
height = diag / 3
|
||||
|
||||
xl = -pc.L / 4
|
||||
yw = -pc.L / 4
|
||||
zh = -pc.L / 4
|
||||
|
||||
vertices = np.array([
|
||||
(pc.L / 3 + xl, pc.L / 3 + yw, 4 * pc.L / 3 + zh),
|
||||
(pc.L + xl, 0 + yw, pc.L + zh),
|
||||
(4 * pc.L / 3 + xl, pc.L / 3 + yw, pc.L / 3 + zh),
|
||||
(pc.L + xl, pc.L + yw, 0 + zh),
|
||||
(pc.L / 3 + xl, 4 * pc.L / 3 + yw, pc.L / 3 + zh),
|
||||
(0 + xl, pc.L + yw, pc.L + zh)
|
||||
])
|
||||
extr = pc.L * np.sqrt(3)
|
||||
|
||||
else:
|
||||
raise Exception(f"Direction { pc.direction } is not implemented")
|
||||
|
||||
# Cell
|
||||
circuit = ng_occ.Wire([
|
||||
ng_occ.Segment(ng_occ.Pnt(*v1), ng_occ.Pnt(*v2))
|
||||
for v1, v2 in zip(vertices, np.roll(vertices, -1, axis = 0))
|
||||
])
|
||||
inletface = ng_occ.Face(circuit)
|
||||
inletface.name = "inlet"
|
||||
|
||||
vecFlow = utils.normal(inletface)
|
||||
pc.cell = inletface.Extrude(extr, ng_occ.Vec(*vecFlow))
|
||||
|
||||
# Boundary faces
|
||||
symetryId = 0
|
||||
|
||||
for face in pc.cell.faces:
|
||||
fNorm = utils.normal(face)
|
||||
fAngle = utils.angle(vecFlow, fNorm)
|
||||
|
||||
if fAngle == 0 or fAngle == np.pi:
|
||||
if np.all(utils.pos(face.center) == utils.pos(inletface.center)):
|
||||
face.name = "inlet"
|
||||
|
||||
else:
|
||||
face.name = "outlet"
|
||||
|
||||
else:
|
||||
face.name = f"symetry{ symetryId }"
|
||||
symetryId += 1
|
||||
|
||||
# Main shape
|
||||
pc.shape = pc.cell - pc.lattice
|
||||
|
||||
assert len(pc.shape.solids) == 1, "Expected single solid shape"
|
||||
|
||||
pc.shape = pc.shape.solids[0]
|
||||
|
||||
# Boundary faces (walls)
|
||||
for face in pc.shape.faces:
|
||||
if face.name not in ["inlet", "outlet", *[ f"symetry{ n }" for n in range(6) ]]:
|
||||
face.name = "wall"
|
||||
|
||||
return pc
|
||||
|
||||
|
||||
def face_centered(alpha: float, direction: list | ndarray, **kwargs) -> Periodic:
|
||||
"""Face centered periodic structure.
|
||||
|
||||
:param alpha:
|
||||
Spheres overlap parameter.
|
||||
:param direction:
|
||||
Flow direction vector. This parameter affects the geometry type
|
||||
and boundary (faces) names.
|
||||
:return:
|
||||
Periodic object.
|
||||
"""
|
||||
# base class
|
||||
pc = Periodic(
|
||||
alpha = alpha,
|
||||
gamma = 2 / 3 * np.pi
|
||||
)
|
||||
|
||||
# additional parameters
|
||||
pc.__dict__.update(kwargs)
|
||||
pc.L = 4 / np.sqrt(2) * pc.r0
|
||||
pc.direction = np.asarray(direction)
|
||||
|
||||
# additional attributes
|
||||
pc.cell: ng_occ.Solid = None
|
||||
pc.lattice: ng_occ.Solid = None
|
||||
|
||||
# constants
|
||||
zero = ng_occ.Pnt(0, 0, 0)
|
||||
|
||||
# Lattice
|
||||
spheres = []
|
||||
x0 = 0
|
||||
x20 = 0
|
||||
z0 = -0.5 * pc.L * (3 - 2)
|
||||
z20 = -0.5 * pc.L * (3 - 1)
|
||||
|
||||
for zn in range(3):
|
||||
z = z0 + zn * pc.L
|
||||
z2 = z20 + zn * pc.L
|
||||
|
||||
for yn in range(3):
|
||||
y = yn * 2 * pc.r0
|
||||
y2 = yn * 2 * pc.r0 + pc.r0
|
||||
|
||||
for xn in range(3):
|
||||
x = x0 + xn * 2 * pc.r0
|
||||
x2 = x20 + xn * 2 * pc.r0 + pc.r0
|
||||
|
||||
# TODO: fix rotations (arcs intersection -> incorrect boolean operations
|
||||
spheres.append(
|
||||
ng_occ.Sphere(ng_occ.Pnt(x, y, z), pc.radius)
|
||||
.Rotate(ng_occ.Axis(ng_occ.Pnt(x, y, z), ng_occ.X), 45)
|
||||
.Rotate(ng_occ.Axis(ng_occ.Pnt(x, y, z), ng_occ.Z), 45)
|
||||
)
|
||||
# shifted
|
||||
spheres.append(
|
||||
ng_occ.Sphere(ng_occ.Pnt(x2, y2, z2), pc.radius)
|
||||
.Rotate(ng_occ.Axis(ng_occ.Pnt(x2, y2, z2), ng_occ.X), 45)
|
||||
.Rotate(ng_occ.Axis(ng_occ.Pnt(x2, y2, z2), ng_occ.Z), 45)
|
||||
)
|
||||
|
||||
lattice = np.sum(spheres)
|
||||
lattice = (
|
||||
lattice.Move(ng_occ.Vec(-pc.r0 * 2, -pc.r0 * 2, 0))
|
||||
.Rotate(ng_occ.Axis(zero, ng_occ.Z), 45)
|
||||
)
|
||||
lattice = lattice.Scale(zero, pc.maximize)
|
||||
|
||||
if pc.filletsEnabled:
|
||||
lattice = lattice.MakeFillet(lattice.edges, pc.fillets * pc.maximize)
|
||||
|
||||
pc.lattice = lattice.Scale(zero, pc.minimize)
|
||||
|
||||
# Inlet face
|
||||
if np.all(pc.direction == [1., 0., 0.]):
|
||||
length = 2 * pc.r0
|
||||
width = pc.L / 2
|
||||
# diag = pc.L * np.sqrt(3)
|
||||
# height = diag / 3
|
||||
|
||||
xl = np.sqrt(length ** 2 + length ** 2) * 0.5
|
||||
yw = xl
|
||||
zh = width
|
||||
|
||||
vertices = np.array([
|
||||
(0, 0, -zh),
|
||||
(-xl, yw, -zh),
|
||||
(-xl, yw, zh),
|
||||
(0, 0, zh)
|
||||
])
|
||||
extr = length
|
||||
|
||||
elif np.all(pc.direction == [0., 0., 1.]):
|
||||
length = 2 * pc.r0
|
||||
width = pc.L / 2
|
||||
# diag = pc.L * np.sqrt(3)
|
||||
# height = diag / 3
|
||||
|
||||
xl = np.sqrt(length ** 2 + length ** 2) * 0.5
|
||||
yw = xl
|
||||
zh = width
|
||||
|
||||
vertices = np.array([
|
||||
(0, 0, -zh),
|
||||
(xl, yw, -zh),
|
||||
(0, 2 * yw, -zh),
|
||||
(-xl, yw, -zh)
|
||||
])
|
||||
extr = 2 * width
|
||||
|
||||
elif np.all(pc.direction == [1., 1., 1.]):
|
||||
length = 2 * pc.r0
|
||||
width = pc.L / 2
|
||||
# diag = pc.L * np.sqrt(3)
|
||||
# height = diag / 3
|
||||
|
||||
xl = -(3 - 2) * pc.L / 3
|
||||
yw = -(3 - 2) * pc.L / 3
|
||||
zh = -(3 - 2) * pc.L / 3
|
||||
|
||||
vertices = np.array([
|
||||
(-2 * width / 3 + xl, -2 * width / 3 + yw, width / 3 + zh),
|
||||
(0 + xl, -width + yw, 0 + zh),
|
||||
(width / 3 + xl, -2 * width / 3 + yw, -2 * width / 3 + zh),
|
||||
(0 + xl, 0 + yw, -width + zh),
|
||||
(-2 * width / 3 + xl, width / 3 + yw, -2 * width / 3 + zh),
|
||||
(-width + xl, 0 + yw, 0 + zh)
|
||||
])
|
||||
extr = np.sqrt(3) * pc.L
|
||||
|
||||
else:
|
||||
raise Exception(f"Direction { pc.direction } is not implemented")
|
||||
|
||||
# Cell
|
||||
circuit = ng_occ.Wire([
|
||||
ng_occ.Segment(ng_occ.Pnt(*v1), ng_occ.Pnt(*v2))
|
||||
for v1, v2 in zip(vertices, np.roll(vertices, -1, axis = 0))
|
||||
])
|
||||
inletface = ng_occ.Face(circuit)
|
||||
inletface.name = "inlet"
|
||||
|
||||
vecFlow = utils.normal(inletface)
|
||||
pc.cell = inletface.Extrude(extr, ng_occ.Vec(*vecFlow))
|
||||
|
||||
# Boundary faces
|
||||
symetryId = 0
|
||||
|
||||
for face in pc.cell.faces:
|
||||
fNorm = utils.normal(face)
|
||||
fAngle = utils.angle(vecFlow, fNorm)
|
||||
|
||||
if fAngle == 0 or fAngle == np.pi:
|
||||
if np.all(utils.pos(face.center) == utils.pos(inletface.center)):
|
||||
face.name = "inlet"
|
||||
|
||||
else:
|
||||
face.name = "outlet"
|
||||
|
||||
else:
|
||||
face.name = f"symetry{ symetryId }"
|
||||
symetryId += 1
|
||||
|
||||
# Main shape
|
||||
pc.shape = pc.cell - pc.lattice
|
||||
|
||||
assert len(pc.shape.solids) == 1, "Expected single solid shape"
|
||||
|
||||
pc.shape = pc.shape.solids[0]
|
||||
|
||||
# Boundary faces (walls)
|
||||
for face in pc.shape.faces:
|
||||
if face.name not in ["inlet", "outlet", *[ f"symetry{ n }" for n in range(6) ]]:
|
||||
face.name = "wall"
|
||||
|
||||
return pc
|
||||
@ -1,80 +1,95 @@
|
||||
# -*- coding: utf-8 -*-
|
||||
# This file is part of anisotropy.
|
||||
# License: GNU GPL version 3, see the file "LICENSE" for details.
|
||||
|
||||
from netgen.occ import *
|
||||
import numpy
|
||||
from numpy import linalg
|
||||
import os
|
||||
from __future__ import annotations
|
||||
from numpy import ndarray
|
||||
from os import PathLike
|
||||
from pathlib import Path
|
||||
|
||||
import numpy as np
|
||||
import netgen.occ as ng_occ
|
||||
import pathlib
|
||||
|
||||
class ShapeError(Exception):
|
||||
pass
|
||||
from . import utils
|
||||
|
||||
|
||||
class Shape(object):
|
||||
def __init__(self):
|
||||
"""A Shape object contains OCC shape.
|
||||
"""
|
||||
self.groups = {}
|
||||
self.shape = None
|
||||
|
||||
def write(self, filename: PathLike):
|
||||
"""Export a shape.
|
||||
@property
|
||||
def geometry(self) -> ng_occ.OCCGeometry:
|
||||
"""Shape as OCCGeometry object.
|
||||
"""
|
||||
return ng_occ.OCCGeometry(self.shape)
|
||||
|
||||
@property
|
||||
def type(self) -> ng_occ.TopAbs_ShapeEnum:
|
||||
"""Type of the shape. (shortcut)
|
||||
"""
|
||||
return self.shape.type
|
||||
|
||||
@property
|
||||
def volume(self) -> float:
|
||||
"""Volume of the shape. (shortcut)
|
||||
"""
|
||||
return self.shape.volume
|
||||
|
||||
@property
|
||||
def center(self) -> ndarray:
|
||||
"""Center of the shape.
|
||||
"""
|
||||
return np.array(utils.pos(self.shape.center))
|
||||
|
||||
def write(self, filename: PathLike):
|
||||
"""Export a shape to the file.
|
||||
Supported formats: step.
|
||||
|
||||
:param filename:
|
||||
Name of the file to store the given shape in.
|
||||
|
||||
:return:
|
||||
Output, error messages and returncode
|
||||
Path of the file.
|
||||
"""
|
||||
out, err, returncode = "", "", 0
|
||||
path = Path(filename).resolve()
|
||||
path = pathlib.Path(filename).resolve()
|
||||
ext = path.suffix[1: ]
|
||||
|
||||
try:
|
||||
if ext == "step":
|
||||
self.shape.WriteStep(path)
|
||||
self.shape.WriteStep(str(path))
|
||||
|
||||
else:
|
||||
raise NotImplementedError(f"{ ext } is not supported")
|
||||
|
||||
except NotImplementedError as e:
|
||||
err = e
|
||||
returncode = 1
|
||||
|
||||
except Exception as e:
|
||||
err = e
|
||||
returncode = 1
|
||||
|
||||
return out, err, returncode
|
||||
raise NotImplementedError(f"Shape format '{ ext }' is not supported")
|
||||
|
||||
def read(self, filename: PathLike):
|
||||
path = Path(filename).resolve()
|
||||
"""Import a shape from the file.
|
||||
Supported formats: step, iges, brep.
|
||||
|
||||
:param filename:
|
||||
Path of the file.
|
||||
"""
|
||||
path = pathlib.Path(filename).resolve()
|
||||
ext = path.suffix[1: ]
|
||||
|
||||
if ext in ["step", "iges", "brep"]:
|
||||
self.shape = OCCGeometry(path).shape
|
||||
self.shape = ng_occ.OCCGeometry(str(path)).shape
|
||||
|
||||
else:
|
||||
raise NotImplementedError(f"Shape format '{ext}' is not supported")
|
||||
|
||||
return self
|
||||
|
||||
def patches(self, group: bool = False, shiftIndex: bool = False, prefix: str = None):
|
||||
def patches(
|
||||
self,
|
||||
group: bool = False,
|
||||
shiftIndex: bool = False,
|
||||
prefix: str = None
|
||||
) -> list | dict:
|
||||
"""Get patches indices with their names.
|
||||
|
||||
:param group:
|
||||
Group indices together with the same patches names.
|
||||
|
||||
:param shiftIndex:
|
||||
Start numerating with one instead of zero.
|
||||
|
||||
:param prefix:
|
||||
Add string prefix to the index.
|
||||
|
||||
:return:
|
||||
List if group = False else dictionary.
|
||||
"""
|
||||
@ -105,24 +120,3 @@ class Shape(object):
|
||||
patches_.append((item, face.name))
|
||||
|
||||
return patches_
|
||||
|
||||
def normal(self, face: FACE) -> numpy.array:
|
||||
"""
|
||||
:return:
|
||||
Normal vector to face.
|
||||
"""
|
||||
_, u, v = face.surf.D1(0, 0)
|
||||
|
||||
return numpy.cross([u.x, u.y, u.z], [v.x, v.y, v.z])
|
||||
|
||||
|
||||
def angle(self, vec1: numpy.array, vec2: numpy.array) -> float:
|
||||
"""
|
||||
:return:
|
||||
Angle between two vectors in radians.
|
||||
"""
|
||||
inner = numpy.inner(vec1, vec2)
|
||||
norms = linalg.norm(vec1) * linalg.norm(vec2)
|
||||
cos = inner / norms
|
||||
|
||||
return numpy.arccos(numpy.clip(cos, -1.0, 1.0))
|
||||
|
||||
@ -1,170 +0,0 @@
|
||||
# -*- coding: utf-8 -*-
|
||||
# This file is part of anisotropy.
|
||||
# License: GNU GPL version 3, see the file "LICENSE" for details.
|
||||
|
||||
from netgen.occ import *
|
||||
import numpy
|
||||
from numpy import pi, sqrt
|
||||
|
||||
from .occExtended import *
|
||||
from . import Periodic
|
||||
from . import ShapeError
|
||||
|
||||
class Simple(Periodic):
|
||||
def __init__(
|
||||
self,
|
||||
direction: list = None,
|
||||
**kwargs
|
||||
):
|
||||
Periodic.__init__(
|
||||
self,
|
||||
alpha = kwargs.get("alpha", 0.01),
|
||||
r0 = kwargs.get("r0", 1),
|
||||
filletsEnabled = kwargs.get("filletsEnabled", True)
|
||||
)
|
||||
|
||||
# Parameters
|
||||
self.direction = direction
|
||||
self.alphaMin = 0.01
|
||||
self.alphaMax = 0.28
|
||||
|
||||
# Objects
|
||||
self.lattice = None
|
||||
self.cell = None
|
||||
self.shape = None
|
||||
|
||||
|
||||
@property
|
||||
def L(self):
|
||||
return 2 * self.r0
|
||||
|
||||
|
||||
def build(self):
|
||||
#
|
||||
zero = Pnt(0, 0, 0)
|
||||
|
||||
# Lattice
|
||||
spheres = numpy.array([], dtype = object)
|
||||
|
||||
for zn in range(3):
|
||||
z = zn * self.L
|
||||
|
||||
for yn in range(3):
|
||||
y = yn * self.L
|
||||
|
||||
for xn in range(3):
|
||||
x = xn * self.L
|
||||
|
||||
spheres = numpy.append(spheres, Sphere(Pnt(x, y, z), self.radius))
|
||||
|
||||
lattice = spheres.sum()
|
||||
lattice = lattice.Scale(zero, self.maximize)
|
||||
|
||||
if self.filletsEnabled:
|
||||
lattice = lattice.MakeFillet(lattice.edges, self.fillets * self.maximize)
|
||||
|
||||
self.lattice = lattice.Scale(zero, self.minimize)
|
||||
|
||||
# Inlet face
|
||||
if (self.direction == numpy.array([1., 0., 0.])).prod():
|
||||
length = self.L * numpy.sqrt(2)
|
||||
width = self.L * numpy.sqrt(2)
|
||||
height = self.L
|
||||
|
||||
xl = numpy.sqrt(length ** 2 * 0.5)
|
||||
yw = xl
|
||||
zh = height
|
||||
|
||||
vertices = numpy.array([
|
||||
(xl, 0, 0),
|
||||
(0, yw, 0),
|
||||
(0, yw, zh),
|
||||
(xl, 0, zh)
|
||||
])
|
||||
extr = width
|
||||
|
||||
elif (self.direction == numpy.array([0., 0., 1.])).prod():
|
||||
length = self.L * numpy.sqrt(2)
|
||||
width = self.L * numpy.sqrt(2)
|
||||
height = self.L
|
||||
|
||||
xl = numpy.sqrt(length ** 2 * 0.5)
|
||||
yw = xl
|
||||
zh = height
|
||||
|
||||
vertices = numpy.array([
|
||||
(0, yw, 0),
|
||||
(xl, 0, 0),
|
||||
(2 * xl, yw, 0),
|
||||
(xl, 2 * yw, 0)
|
||||
])
|
||||
extr = height
|
||||
|
||||
elif (self.direction == numpy.array([1., 1., 1.])).prod():
|
||||
length = self.L * numpy.sqrt(2)
|
||||
width = self.L * numpy.sqrt(2)
|
||||
height = self.L
|
||||
|
||||
xl = -self.L - self.L / 6
|
||||
yw = -self.L - self.L / 6
|
||||
zh = -self.L / 6
|
||||
|
||||
vertices = numpy.array([
|
||||
(self.L + xl, self.L + yw, self.L + zh),
|
||||
(5 * self.L / 3 + xl, 2 * self.L / 3 + yw, 2 * self.L / 3 + zh),
|
||||
(2 * self.L + xl, self.L + yw, 0 + zh),
|
||||
(5 * self.L / 3 + xl, 5 * self.L / 3 + yw, -self.L / 3 + zh),
|
||||
(self.L + xl, 2 * self.L + yw, 0 + zh),
|
||||
(2 * self.L / 3 + xl, 5 * self.L / 3 + yw, 2 * self.L / 3 + zh)
|
||||
])
|
||||
extr = self.L * sqrt(3)
|
||||
|
||||
else:
|
||||
raise Exception(f"Direction { self.direction } is not implemented")
|
||||
|
||||
#
|
||||
|
||||
|
||||
# Cell
|
||||
circuit = Wire([ Segment(Pnt(*v1), Pnt(*v2)) for v1, v2 in zip(vertices, numpy.roll(vertices, -1, axis = 0)) ])
|
||||
inletface = Face(circuit)
|
||||
inletface.name = "inlet"
|
||||
|
||||
vecFlow = self.normal(inletface)
|
||||
# ISSUE: don't use face.Extrude(length), only face.Extrude(length, vector)
|
||||
self.cell = inletface.Extrude(extr, Vec(*vecFlow))
|
||||
|
||||
# Boundaries
|
||||
symetryId = 0
|
||||
|
||||
for face in self.cell.faces:
|
||||
fNorm = self.normal(face)
|
||||
fAngle = self.angle(vecFlow, fNorm)
|
||||
|
||||
if fAngle == 0 or fAngle == numpy.pi:
|
||||
if (face.center.pos() == inletface.center.pos()).prod():
|
||||
face.name = "inlet"
|
||||
|
||||
else:
|
||||
face.name = "outlet"
|
||||
|
||||
else:
|
||||
face.name = f"symetry{ symetryId }"
|
||||
symetryId += 1
|
||||
|
||||
|
||||
# Main shape
|
||||
self.shape = self.cell - self.lattice
|
||||
|
||||
if not len(self.shape.solids) == 1:
|
||||
raise ShapeError("Expected single solid shape")
|
||||
|
||||
else:
|
||||
self.shape = self.shape.solids[0]
|
||||
|
||||
# Boundaries (walls)
|
||||
for face in self.shape.faces:
|
||||
if face.name not in ["inlet", "outlet", *[ f"symetry{ n }" for n in range(6) ]]:
|
||||
face.name = "wall"
|
||||
|
||||
|
||||
47
anisotropy/shaping/utils.py
Normal file
47
anisotropy/shaping/utils.py
Normal file
@ -0,0 +1,47 @@
|
||||
# -*- coding: utf-8 -*-
|
||||
|
||||
from numpy import ndarray
|
||||
|
||||
import numpy as np
|
||||
import netgen.occ as ng_occ
|
||||
|
||||
|
||||
def pos(point: ng_occ.gp_Pnt) -> ndarray:
|
||||
"""Extract coordinates from point.
|
||||
|
||||
:param point:
|
||||
OCC point object
|
||||
:return:
|
||||
Array of coordinates.
|
||||
"""
|
||||
return np.array([ point.x, point.y, point.z ])
|
||||
|
||||
|
||||
def normal(face: ng_occ.Face) -> ndarray:
|
||||
"""Calculate normal vector from face.
|
||||
|
||||
:param face:
|
||||
OCC face object.
|
||||
:return:
|
||||
Normal vector from face.
|
||||
"""
|
||||
_, u, v = face.surf.D1(0, 0)
|
||||
|
||||
return np.cross([u.x, u.y, u.z], [v.x, v.y, v.z])
|
||||
|
||||
|
||||
def angle(vec1: ndarray, vec2: ndarray) -> float:
|
||||
"""Angle between two vectors.
|
||||
|
||||
:param vec1:
|
||||
Array of points that represents first vector.
|
||||
:param vec2:
|
||||
Array of points that represents second vector.
|
||||
:return:
|
||||
Angle between two vectors in radians.
|
||||
"""
|
||||
inner = np.inner(vec1, vec2)
|
||||
norms = np.linalg.norm(vec1) * np.linalg.norm(vec2)
|
||||
cos = inner / norms
|
||||
|
||||
return np.arccos(np.clip(cos, -1.0, 1.0))
|
||||
Loading…
Reference in New Issue
Block a user