# encoding: utf-8
# 2022 © Vasileios Angelidakis <vasileios.angelidakis@ncl.ac.uk>
"""
Auxiliary functions for the Potential Blocks
"""
import math, random, doctest, geom, numpy
from yade import Vector3, Quaternion, utils
from yade.wrapper import *
from math import sin, cos, tan, sqrt, pi, radians # atan, atan2
import logging
logging.basicConfig(level=logging.INFO)
from numpy import array
#from yade import utils # FIXME: I only use utils._commonBodySetup
from yade.utils import _commonBodySetup, randomColor
try: # use psyco if available
import psyco
psyco.full()
except ImportError:
pass
#**********************************************************************************
#creates Potential Blocks, defining the coefficients of their faces
[docs]
def potentialblock(material, a=[], b=[], c=[], d=[], r=0.0, R=0.0, mask=1, isBoundary=False, fixed=False, color=[-1, -1, -1]):
"""creates potential block.
:param Material material: material of new body
:param [float] a,b,c,d: lists of plane coefficients of the particle faces (see PotentialBlock docs)
:param float r: radius of inner Potential Particle (see PotentialBlock docs)
:param float R: distance R of the Potential Blocks (see PotentialBlock docs)
:param bool isBoundary: whether this is a boundary body (see PotentialBlock docs)
"""
# TODO: In this function, I can introduce all the other attributes of the PBs, like: fixedNormal, boundaryNormal -> Naah, the invocation gets too long. I can use *kw!!!
pb = Body()
pb.mask = mask
pb.aspherical = True
pb.shape = PotentialBlock(
a=a, b=b, c=c, d=d, r=r, R=R, isBoundary=isBoundary, AabbMinMax=True
) #id=len(O.bodies) #FIXME: Check if I need id for vtk output
if color[0] == -1:
pb.shape.color = randomColor(seed=random.randint(0, 1E6))
else:
pb.shape.color = color
utils._commonBodySetup(pb, pb.shape.volume, pb.shape.inertia, material, pos=pb.shape.position, fixed=fixed)
pb.state.ori = pb.shape.orientation
return pb
#**********************************************************************************
#creates cuboidal particle using the Potential Blocks
[docs]
def cuboid(material, edges=Vector3(1, 1, 1), r=0.0, R=0.0, center=[0, 0, 0], mask=1, isBoundary=False, fixed=False, color=[-1, -1, -1]):
"""creates cuboid using the Potential Blocks
:param Vector3 edges: edges of the cuboid
:param Material material: material of new body (FrictMat)
:param Vector3 center: center of the new body
"""
aa = [1, -1, 0, 0, 0, 0]
bb = [0, 0, 1, -1, 0, 0]
cc = [0, 0, 0, 0, 1, -1]
dd = [edges[0] / 2., edges[0] / 2., edges[1] / 2., edges[1] / 2., edges[2] / 2., edges[2] / 2.]
if not r:
r = min(dd) / 2.
cuboid = potentialblock(material=material, a=aa, b=bb, c=cc, d=array(dd) - r, r=r, R=R, mask=mask, isBoundary=isBoundary, fixed=fixed, color=color)
cuboid.state.pos = center
return cuboid
#**********************************************************************************
#creates Aabb boundary plates using the Potential Blocks, around a given cuboidal space
[docs]
def aabbPlates(material, extrema=None, thickness=0.0, r=0.0, R=0.0, mask=1, isBoundary=False, fixed=True, color=None):
"""Return 6 cuboids that will wrap existing packing as walls from all sides. #FIXME: Correct this comment
:param Material material: material of new bodies (FrictMat)
:param [Vector3, Vector3] extrema: extremal points of the Aabb of the packing, as a list of two Vector3, or any equivalent type (will not be calculated if not specified)
:param float thickness: wall thickness (equal to 1/10 of the smallest dimension if not specified)
:param float r: radius of inner Potential Particle (see PotentialBlock docs)
:param float R: distance R of the Potential Blocks (see PotentialBlock docs)
:param int mask: groupMask for the new bodies
:returns: a list of 6 PotentialBlock Bodies enclosing the packing, in the order minX,maxX,minY,maxY,minZ,maxZ.
"""
walls = []
# if not extrema: extrema=aabbExtrema() #TODO: aabbExtrema() is not compatible with non-spherical particles yet
if not thickness:
thickness = min(extrema[1][0] - extrema[0][0], extrema[1][1] - extrema[0][1], extrema[1][2] - extrema[0][2]) / 10.
randColor = False
if not color:
randColor = True
for axis in [0, 1, 2]:
mi, ma = extrema
center = [(mi[i] + ma[i]) / 2. for i in range(3)]
extents = [(ma[i] - mi[i]) for i in range(3)]
extents[axis] = thickness / 2.
if randColor:
color = randomColor(seed=random.randint(0, 1E6))
for j in [0, 1]:
center[axis] = extrema[j][axis] + (j - .5) * thickness / 2.
walls.append(
cuboid(material=material, edges=extents, r=r, R=R, center=center, mask=mask, isBoundary=isBoundary, fixed=fixed, color=color)
)
walls[-1].shape.wire = True
return walls
#**********************************************************************************
#creates cylindrical boundary plates using the Potential Blocks, using a given radius and around a given axis
[docs]
def cylindricalPlates(
material, radius=0.0, height=0.0, thickness=0.0, numFaces=3, r=0.0, R=0.0, mask=1, isBoundary=False, fixed=True, lid=[True, True], color=None
):
"""Return numFaces cuboids that will wrap existing packing as walls from all sides. #FIXME: Correct this comment
:param Material material: material of new bodies (FrictMat)
:param float radius: radius of the cylinder
:param float height: height of cylinder
:param float thickness: thickness of cylinder faces (equal to 1/10 of the cylinder inradius if not specified)
:param int numFaces: number of cylinder faces (>3)
:param float r: radius of inner Potential Particle (see PotentialBlock docs)
:param float R: distance R of the Potential Blocks (see PotentialBlock docs)
:param int mask: groupMask for the new bodies
:param lid [bool]: list of booleans, whether to create the bottom and top lids of the cylindrical plates
:returns: a list of cuboidal Potential Blocks forming a hollow cylinder
"""
# TODO: Check facetCylinder for orientation of the cylinder
# TODO: Add center of the cylinder
walls = []
if not thickness:
thickness = min(radius, height / 2.) / 10.
angle = radians(360) / numFaces
axis = Vector3(0, 0, 1) #TODO: To make it work for any axis - have to change: center, edges
randColor = False
if not color:
randColor = True
for i in range(0, numFaces):
center = Vector3((radius + thickness / 2.) * cos(i * angle), (radius + thickness / 2.) * sin(i * angle), height / 2.) #*(axis.asDiagonal())
if randColor:
color = [abs(cos(i * angle)), abs(sin(i * angle)), 1]
walls.append(
cuboid(
material=material,
edges=Vector3(thickness, 2 * (radius) * tan(pi / numFaces), height),
r=r,
R=R,
center=center,
mask=mask,
isBoundary=isBoundary,
fixed=fixed,
color=color
)
)
walls[-1].state.ori = Quaternion(axis, i * angle)
walls[-1].shape.wire = True
color = [0.36, 0.54, 0.66]
if lid[0] == True:
# Create top plate
walls.append(
prism(
material=material,
radius1=radius,
thickness=thickness,
numFaces=numFaces,
r=r,
R=R,
color=color,
mask=mask,
isBoundary=isBoundary,
fixed=fixed
)
)
walls[-1].state.pos = axis * (height + thickness / 2)
walls[-1].state.ori = Quaternion(axis, i * angle) #FIXME: Here I use i outside the loop?
if lid[1] == True:
# Create bottom plate
walls.append(
prism(
material=material,
radius1=radius,
thickness=thickness,
numFaces=numFaces,
r=r,
R=R,
color=color,
mask=mask,
isBoundary=isBoundary,
fixed=fixed
)
)
walls[-1].state.pos = -axis * thickness / 2
walls[-1].state.ori = Quaternion(axis, i * angle) #FIXME: Here I use i outside the loop?
return walls
##**********************************************************************************
#creates regular prism with N faces
[docs]
def prism(material, radius1=0.0, radius2=-1, thickness=0.0, numFaces=3, r=0.0, R=0.0, center=None, color=[1, 0, 0], mask=1, isBoundary=False, fixed=False):
"""Return regular prism with numFaces
:param Material material: material of new bodies (FrictMat)
:param float radius1: inradius of the start cross-section of the prism
:param float radius2: inradius of the end cross-section of the prism (equal to radius1 if not specified)
:param float thickness: thickness of the prism (equal to radius1 if not specified)
:param int numFaces: number of prisms' faces (>3)
:param float r: radius of inner Potential Particle (see PotentialBlock docs)
:param float R: distance R of the Potential Blocks (see PotentialBlock docs)
:param Vector3 center: center of the Potential Blocks (not currently used)
:param int mask: groupMask for the new bodies
:returns: an axial-symmetric Potential Block with variable cross-section, which can become either a regular prism (radius1=radius2), a pyramid (radius2=0) or a cylinder or cone respectively, for a large enough numFaces value.
"""
aa = []
bb = []
cc = []
dd = []
if radius2 == -1:
radius2 = radius1
if not thickness:
thickness = radius1
angle = radians(360) / numFaces
for i in range(0, numFaces):
aTemp = cos(i * angle)
bTemp = sin(i * angle)
cTemp = (radius1 - radius2) / thickness
dTemp = (radius1 + radius2) / 2
magnitude = Vector3(aTemp, bTemp, cTemp).norm()
aa.append(aTemp / magnitude)
bb.append(bTemp / magnitude)
cc.append(cTemp / magnitude)
dd.append(dTemp / magnitude)
aa.extend([0.0, 0.0])
bb.extend([0.0, 0.0])
cc.extend([1.0, -1.0])
dd.extend([thickness / 2., thickness / 2.])
if not r:
r = min(dd) / 2.
prism = potentialblock(material=material, a=aa, b=bb, c=cc, d=array(dd) - r, r=r, R=R, mask=mask, isBoundary=isBoundary, fixed=fixed, color=color)
# if center: prism.state.pos=prism.state.pos+center; print(center) #FIXME: Maybe assign center if not (0,0,0), but add it to the local position, rather than overwriting it
return prism
##**********************************************************************************
#TODO: export PotentialBlock to stl file: This would better fit in the export module
##**********************************************************************************
#TODO: creates masonry arch: I can do it in two ways:
# 1. Geometrically, using the angles or
# 2. Using BlockGen, demonstrating that we can do non-permanent joints
# Explore multi-ring arches: For the inner ring, I must replicate the interlocking geometry
##**********************************************************************************
#TODO: creates a model for periodic and aperiodic masonry
##**********************************************************************************
#TODO: creates SAG mill with chosen: radius, width, optionally rigid boundaries or no boundaries, dent size
##**********************************************************************************
#creates PotentialBlock or PotentialParticle from polyhedra # FIXME: Unfinished
#def polyhedra2PotentialBlock(b,r=None,R=0.0): #maybe polyhedra2Potential or polyhedra2PotentialShape #FIXME: Haven't checked it yet
# """Calculate coefficients of the planes comprising the faces of a polyhedron, in the format used by the PotentialBlock and PotentialParticle shape classes
# :param Body b: Body with b.shape=Polyhedra
# :param vector(Real) aa: Coefficients 'a' of planes: ax+by+cz-d-r=0
# :param vector(Real) bb: Coefficients 'b' of planes: ax+by+cz-d-r=0
# :param vector(Real) cc: Coefficients 'c' of planes: ax+by+cz-d-r=0
# :param vector(Real) dd: Coefficients 'd' of planes: ax+by+cz-d-r=0
# :param Real r: Suggested radius of PotentialBlock or PotentialParticle to be generated
# """
# Faces=b.shape.GetSurfaces()
# Vertices = [b.state.ori*v for v in b.shape.v] # vertices in global coords
# aa=[]
# bb=[]
# cc=[]
# dd=[]
# for fv in range(len(Faces)):
# v1=Vertices[Faces[fv][0]] #1st vertex on plane fv
# v2=Vertices[Faces[fv][1]] #2nd vertex on plane fv
# v3=Vertices[Faces[fv][2]] #3rd vertex on plane fv
# n1=v2-v1 #1st vector on face fv
# n2=v3-v1 #2nd vector on face fv
# nNormal=n1.cross(n2) #normal vector of face fv
# nNormal.normalize()
# aTemp=nNormal[0]
# bTemp=nNormal[1]
# cTemp=nNormal[2]
# dTemp = (aTemp*v1[0] + bTemp*v1[1] + cTemp*v1[2])
# aa.append(aTemp)
# bb.append(bTemp)
# cc.append(cTemp)
# dd.append(dTemp)
## if not r: r=0.5*abs(min(dd)) # Recommended value. This assignment here is only meaningful if the particle is centered to its centroid
# pb=potentialblock(material=material,a=aa,b=bb,c=cc,d=array(dd)-r,r=r,R=R,mask=mask,isBoundary=isBoundary,fixed=fixed,color=color)
# return pb
## b2=Body()
## b2.aspherical=True
## color=Vector3(random.random(),random.random(),random.random())
## b2.shape=PotentialBlock(k=0.0, r=r, R=0.0, a=aa, b=bb, c=cc, d=array(dd)-r, AabbMinMax=True, color=color)
## utils._commonBodySetup(b2, b2.shape.volume, b2.shape.inertia, material='frictmat', pos=b1.state.pos, fixed=False)
## b2.state.ori=b2.shape.orientation
## O.bodies.append(b2)
# return aa,bb,cc,dd,r
##**********************************************************************************
#TODO: creates polyhedra from PotentialBlock or PotentialParticle
#from numpy import arange
##**********************************************************************************
##TODO: creates ellipsoidal particle using the Potential Blocks # FIXME: Unfinished
#def ellipsoid(material, axes=Vector3(1,1,1), numFaces=20, r=0.0, R=None, center=[0,0,0], mask=1, isBoundary=False, fixed=False, color=[-1,-1,-1]):
# """creates polyhedral ellipsoid using the Potential Blocks
# :param Vector3 axes: axes of the ellipsoid
# :param int numFaces: number of particle faces (the total number of faces will be near this value, not exactly it)
# :param Material material: material of new body (FrictMat)
# :param Vector3 center: center of the new body
# """
# thetaStep=pi/8.
# phiStep=pi/8.
# aa=[]; bb=[]; cc=[]; dd=[];
## for theta in arange(0, 2*pi, thetaStep):
## for phi in arange(-pi/2+pi/4., pi/2., phiStep):
## aa.extend([cos(phi)*s(theta)])
## bb.extend([cos(phi)*sin(theta)])
## cc.extend([sin(phi)])
## dd.extend([1.-r])
# for theta in arange(0, pi+thetaStep, thetaStep):
# for phi in arange(0, 2*pi, phiStep):
# aa.extend([sin(theta)*cos(phi)])
# bb.extend([sin(theta)*sin(phi)])
# cc.extend([cos(theta)])
# dd.extend([1.-r])
# # FIXME: Here, I have to correct the edge size, using a scaleFactor
# # FIXME: I also have to fix the shape itself
# ellipsoid = potentialblock(material=material,a=aa,b=bb,c=cc,d=dd,r=r,R=R,mask=mask,isBoundary=isBoundary,fixed=fixed,color=color)
# ellipsoid.state.pos = center
# return ellipsoid
#**********************************************************************************
#creates platonic solids using the Potential Blocks
[docs]
def platonic_solid(
material,
numFaces,
edge=0.0,
ri=0.0,
rm=0.0,
rc=0.0,
volume=0.0,
r=0.0,
R=None,
center=[0, 0, 0],
mask=1,
isBoundary=False,
fixed=False,
color=[-1, -1, -1]
):
errors = 0
"""creates platonic solids using the Potential Blocks
User must specify either the edge, the inradius, the circumradius or the volume of the particle (only one of them)
:param int numFaces: number of particle faces (regular 4: tetrahedron, 6: hexahedron (cube), 8: octahedron, 12: dodecahedron, 20: icosahedron)
:param float edge: edge of the platonic solid
:param float ri: inradius of the platonic solid
:param float rm: midradius of the platonic solid
:param float rc: circumradius of the platonic solid
:param float volume: volume of the platonic solid
:param Material material: material of new body (FrictMat)
:param Vector3 center: center of the new body
"""
inputParams = [edge, ri, rm, rc, volume]
count = sum(1 for i in inputParams if i > 0.0)
if (count > 1):
logging.error(' Assign only one of: edge - ri - rm - rc - volume')
return (None)
gamma = 1 / sqrt(3)
delta = sqrt((5 - sqrt(5)) / 10.)
epsilon = sqrt((5 + sqrt(5)) / 10.)
zeta = sqrt((3 - sqrt(5)) / 6.)
eta = sqrt((3 + sqrt(5)) / 6.)
# Schläfli symbols {p,q}: https://en.wikipedia.org/wiki/Platonic_solid
p = {4: 3, 6: 4, 8: 3, 12: 5, 20: 3}
q = {4: 3, 6: 3, 8: 4, 12: 3, 20: 5}
h = {4: 4, 6: 6, 8: 6, 12: 10, 20: 10} # Coxeter number
t = cos(pi / q[numFaces]) / sin(pi / h[numFaces]) # tan(theta/2)
if (numFaces == 4): #tetrahedron
aa = array([+gamma, +gamma, -gamma, -gamma])
bb = array([-gamma, +gamma, +gamma, -gamma])
cc = array([+gamma, -gamma, +gamma, -gamma])
elif (numFaces == 6): #hexahedron (cube)
aa = [1, -1, 0, 0, 0, 0]
bb = [0, 0, 1, -1, 0, 0]
cc = [0, 0, 0, 0, 1, -1]
elif (numFaces == 8): #octahedron
aa = array([+gamma, -gamma, -gamma, +gamma, +gamma, -gamma, +gamma, -gamma])
bb = array([+gamma, -gamma, +gamma, -gamma, -gamma, +gamma, +gamma, -gamma])
cc = array([+gamma, -gamma, +gamma, -gamma, +gamma, -gamma, -gamma, +gamma])
elif (numFaces == 12): #dodecahedron
aa = array([delta, -delta, delta, -delta, 0, 0, 0, 0, epsilon, -epsilon, -epsilon, epsilon])
bb = array([epsilon, -epsilon, -epsilon, epsilon, delta, -delta, delta, -delta, 0, 0, 0, 0])
cc = array([0, 0, 0, 0, epsilon, -epsilon, -epsilon, epsilon, delta, -delta, delta, -delta])
elif (numFaces == 20): #icosahedron: first 8 faces
aa = [
+gamma,
-gamma,
-gamma,
+gamma,
+gamma,
-gamma,
+gamma,
-gamma,
]
bb = [
+gamma,
-gamma,
+gamma,
-gamma,
-gamma,
+gamma,
+gamma,
-gamma,
]
cc = [
+gamma,
-gamma,
+gamma,
-gamma,
+gamma,
-gamma,
-gamma,
+gamma,
]
# icosahedron: rest 12 faces
aa.extend([+zeta, -zeta, +zeta, -zeta, 0, 0, 0, 0, +eta, -eta, +eta, -eta])
bb.extend([+eta, -eta, -eta, +eta, +zeta, -zeta, +zeta, -zeta, 0, 0, 0, 0])
cc.extend([0, 0, 0, 0, +eta, -eta, -eta, +eta, +zeta, -zeta, -zeta, +zeta])
else:
errors += 1
logging.error('Invalid numFaces. Should be either: {4: tetrahedron, 6: cube, 8: octahedron, 12: dodecahedron, 20: icosahedron}')
return (None)
# if errors==0:
if edge > 0.:
ri = (edge / 2.) / tan(pi / p[numFaces]) * t
rm = (edge / 2.) * cos(pi / p[numFaces]) / sin(pi / h[numFaces])
rc = (edge / 2.) * tan(pi / q[numFaces]) * t
elif ri > 0.:
edge = 2 * ri * tan(pi / p[numFaces]) / t
rm = (edge / 2.) * cos(pi / p[numFaces]) / sin(pi / h[numFaces])
rc = (edge / 2.) * tan(pi / q[numFaces]) * t
elif rm > 0.:
edge = 2 * rm * sin(pi / h[numFaces]) / cos(pi / p[numFaces])
ri = (edge / 2.) / tan(pi / p[numFaces]) * t
rc = (edge / 2.) * tan(pi / q[numFaces]) * t
elif rc > 0.:
edge = 2 * rc / (tan(pi / q[numFaces]) * t)
ri = (edge / 2.) / tan(pi / p[numFaces]) * t
rm = (edge / 2.) * cos(pi / p[numFaces]) / sin(pi / h[numFaces])
elif volume > 0.:
edge = (24 * volume * (tan(pi / p[numFaces])**2) / (t * numFaces * p[numFaces]))**(1 / 3)
ri = (edge / 2.) / tan(pi / p[numFaces]) * t
rm = (edge / 2.) * cos(pi / p[numFaces]) / sin(pi / h[numFaces])
rc = (edge / 2.) * tan(pi / q[numFaces]) * t
dd = [ri] * numFaces
if not r:
r = min(dd) / 2.
platonic = potentialblock(material=material, a=aa, b=bb, c=cc, d=array(dd) - r, r=r, R=R, mask=mask, isBoundary=isBoundary, fixed=fixed, color=color)
platonic.shape.edge = edge
platonic.shape.ri = ri # Add inradius attribute from Python (visible only to Python objects/functions)
platonic.shape.rm = rm # Add midradius attribute from Python (visible only to Python objects/functions)
platonic.shape.rc = rc # Add circumradius attribute from Python (visible only to Python objects/functions)
platonic.state.pos = center
platonic.state.ori = platonic.shape.orientation
return platonic
