def getBField(BCm, source_ref):
# Used in all getB()
# BCm is the obtained magnetic field in Cm
# the field is well known in the magnet coordinates
from magpylib._lib.mathLibPrivate import angleAxisRotation
# rotate field vector back
B = angleAxisRotation(source_ref.angle, source_ref.axis, BCm)
return B
def rotateToCS(pos, source_ref):
# Used in all getB()
from magpylib._lib.mathLibPrivate import angleAxisRotation
# secure input type and check input format
p1 = array(pos, dtype=float64, copy=False)
# relative position between mag and obs
posRel = p1 - source_ref.position
# rotate this vector into the CS of the magnet (inverse rotation)
# Leave this alone for now pylint: disable=invalid-unary-operand-type
p21newCm = angleAxisRotation(source_ref.angle, -source_ref.axis, posRel)
return p21newCm
def rotatePosition(position, angle, axis, anchor=[0, 0, 0]):
"""
This function uses angle-axis rotation to rotate the `position` vector by
the `angle` argument about an axis defined by the `axis` vector which passes
through the center of rotation `anchor` vector. Scalar input is either integer
or float.Vector input format can be either list, tuple or array of any data
type (float, int).
Parameters
----------
position : vec3
Input position to be rotated.
angle : scalar [deg]
Angle of rotation in untis of [deg]
axis : vec3
Axis of rotation
anchor : vec3
The Center of rotation which defines the position of the axis of rotation
Returns
-------
newPosition : arr3
Rotated position
Example
-------
>>> magpylib as magPy
>>> from numpy import pi
>>> position0 = [1,1,0]
>>> angle = -90
>>> axis = [0,0,1]
>>> centerOfRotation = [1,0,0]
>>> positionNew = magPy.math.rotatePosition(position0,angle,axis,anchor=centerOfRotation)
>>> print(positionNew)
[2. 0. 0.]
"""
pos = array(position, dtype=float64, copy=False)
ang = float(angle)
ax = array(axis, dtype=float64, copy=False)
anchor = array(anchor, dtype=float64, copy=False)
pos12 = pos-anchor
pos12Rot = angleAxisRotation(ang, ax, pos12)
posRot = pos12Rot+anchor
return posRot
def displaySystem(self, markers=listOfPos, suppress=False, direc=False,
subplotAx=None):
"""
Shows the collection system in an interactive pyplot and returns a matplotlib figure identifier.
WARNING
-------
As a result of an inherent problem in matplotlib the
Poly3DCollections z-ordering fails when bounding boxes intersect.
Parameters
----------
markers : list[scalar,scalar,scalar,[label]]
List of position vectors to add visual markers to the display, optional label.
Default: [[0,0,0]]
Example
-------
>>> from magpylib import Collection, source
>>> c=source.current.Circular(3,7)
>>> x = Collection(c)
>>> marker0 = [0,0,0,"Neutral Position"]
>>> marker1 = [10,10,10]
>>> x.displaySystem(markers=[ marker0,
... marker1])
Parameters
----------
suppress : bool
If True, only return Figure information, do not show. Interactive mode must be off.
Default: False.
Example
-------
>>> ## Suppress matplotlib.pyplot.show()
>>> ## and returning figure from showing up
>>> from matplotlib import pyplot
>>> pyplot.ioff()
>>> figureData = Collection.displayFigure(suppress=True)
Parameters
----------
direc : bool
Set to True to show current directions and magnetization vectors.
Default: False
Return
------
matplotlib Figure object
graphics object is displayed through plt.show()
Example
-------
>>> from magpylib import source, Collection
>>> pm1 = source.magnet.Box(mag=[0,0,1000],dim=[1,1,1],pos=[-1,-1,-1],angle=45,axis=[0,0,1])
>>> pm2 = source.magnet.Cylinder(mag=[0,0,1000],dim=[2,2],pos=[0,-1,1],angle=45,axis=[1,0,0])
>>> pm3 = source.magnet.Sphere(mag=[0,0,1000],dim=3,pos=[-2,1,2],angle=45,axis=[1,0,0])
>>> C1 = source.current.Circular(curr=100,dim=6)
>>> col = Collection(pm1,pm2,pm3,C1)
>>> col.displaySystem()
Parameters
----------
subplotAx : matplotlib subplot axe instance
Use an existing matplotlib subplot instance to draw the 3D system plot into.
Default: None
Example
-------
>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from magpylib.source.magnet import Box
>>> from magpylib import Collection
>>> #create collection of one magnet
>>> s1 = Box(mag=[ 500,0, 500], dim=[3,3,3], pos=[ 0,0, 3], angle=45, axis=[0,1,0])
>>> c = Collection(s1)
>>> #create positions
>>> xs = np.linspace(-8,8,100)
>>> zs = np.linspace(-6,6,100)
>>> posis = [[x,0,z] for z in zs for x in xs]
>>> #calculate fields
>>> Bs = c.getBsweep(posis)
>>> #reshape array and calculate amplitude
>>> Bs = np.array(Bs).reshape([100,100,3])
>>> Bamp = np.linalg.norm(Bs,axis=2)
>>> X,Z = np.meshgrid(xs,zs)
>>> # Define figure
>>> fig = plt.figure()
>>> ## Define ax for 2D
>>> ax1 = fig.add_subplot(1, 2, 1, axisbelow=True)
>>> ## Define ax for 3D displaySystem
>>> ax2 = fig.add_subplot(1, 2, 2, axisbelow=True,projection='3d')
>>> ## field plot 2D
>>> ax1.contourf(X,Z,Bamp,100,cmap='rainbow')
>>> U,V = Bs[:,:,0], Bs[:,:,2]
>>> ax1.streamplot(X, Z, U, V, color='k', density=2)
>>> ## plot Collection system in 3D ax subplot
>>> c.displaySystem(subplotAx=ax2)
Raises
------
AssertionError
If Marker position list is poorly defined. i.e. listOfPos=(x,y,z) instead of lisOfPos=[(x,y,z)]
"""
if subplotAx is None:
fig = plt.figure(dpi=80, figsize=(8, 8))
ax = fig.gca(projection='3d')
else:
ax = subplotAx
# count magnets
Nm = 0
for s in self.sources:
if type(s) is Box or type(s) is Cylinder or type(s) is Sphere:
Nm += 1
cm = plt.cm.hsv # Linter complains about this but it is working pylint: disable=no-member
# select colors
colors = [cm(x) for x in linspace(0, 1, Nm+1)]
ii = -1
SYSSIZE = finfo(float).eps # Machine Epsilon for moment
dipolesList = []
magnetsList = []
currentsList = []
markersList = []
# Check input and Add markers to the Markers list before plotting
for m in markers:
assert isDisplayMarker(m), "Invalid marker definition in displaySystem:" + str(
m) + ". Needs to be [vec3] or [vec3,string]"
markersList += [m]
for s in self.sources:
if type(s) is Box:
ii += 1 # increase color counter
P = s.position
D = s.dimension/2
# create vertices in canonical basis
v0 = array([D, D*array([1, 1, -1]), D*array([1, -1, -1]), D*array([1, -1, 1]),
D*array([-1, 1, 1]), D*array([-1, 1, -1]), -D, D*array([-1, -1, 1])])
# rotate vertices + displace
v = array([angleAxisRotation(s.angle, s.axis, d)+P for d in v0])
# create faces
faces = [[v[0], v[1], v[2], v[3]],
[v[0], v[1], v[5], v[4]],
[v[4], v[5], v[6], v[7]],
[v[2], v[3], v[7], v[6]],
[v[0], v[3], v[7], v[4]],
[v[1], v[2], v[6], v[5]]]
# plot
boxf = Poly3DCollection(
faces, facecolors=colors[ii], linewidths=0.5, edgecolors='k', alpha=1)
ax.add_collection3d(boxf)
# check system size
maxSize = amax(abs(v))
if maxSize > SYSSIZE:
SYSSIZE = maxSize
if direc is True:
s.color = colors[ii]
magnetsList.append(s)
elif type(s) is Cylinder:
ii += 1 # increase color counter
P = s.position
R, H = s.dimension/2
resolution = 20
# vertices
phis = linspace(0, 2*pi, resolution)
vertB0 = array([[R*cos(p), R*sin(p), -H] for p in phis])
vertT0 = array([[R*cos(p), R*sin(p), H] for p in phis])
# rotate vertices+displacement
vB = array(
[angleAxisRotation(s.angle, s.axis, d)+P for d in vertB0])
vT = array(
[angleAxisRotation(s.angle, s.axis, d)+P for d in vertT0])
# faces
faces = [[vT[i], vB[i], vB[i+1], vT[i+1]]
for i in range(resolution-1)]
faces += [vT, vB]
# plot
coll = Poly3DCollection(
faces, facecolors=colors[ii], linewidths=0.5, edgecolors='k', alpha=1)
ax.add_collection3d(coll)
# check system size
maxSize = max([amax(abs(vB)), amax(abs(vT))])
if maxSize > SYSSIZE:
SYSSIZE = maxSize
if direc is True:
s.color = colors[ii]
magnetsList.append(s)
elif type(s) is Sphere:
ii += 1 # increase color counter
P = s.position
R = s.dimension/2
resolution = 12
# vertices
phis = linspace(0, 2*pi, resolution)
thetas = linspace(0, pi, resolution)
vs0 = [[[R*cos(phi)*sin(th), R*sin(phi)*sin(th), R*cos(th)]
for phi in phis] for th in thetas]
# rotate vertices + displacement
vs = array(
[[angleAxisRotation(s.angle, s.axis, v)+P for v in vss] for vss in vs0])
# faces
faces = []
for j in range(resolution-1):
faces += [[vs[i, j], vs[i+1, j], vs[i+1, j+1], vs[i, j+1]]
for i in range(resolution-1)]
# plot
boxf = Poly3DCollection(
faces, facecolors=colors[ii], linewidths=0.5, edgecolors='k', alpha=1)
ax.add_collection3d(boxf)
# check system size
maxSize = amax(abs(vs))
if maxSize > SYSSIZE:
SYSSIZE = maxSize
if direc is True:
s.color = colors[ii]
magnetsList.append(s)
elif type(s) is Line:
P = s.position
vs0 = s.vertices
# rotate vertices + displacement
vs = array(
[angleAxisRotation(s.angle, s.axis, v)+P for v in vs0])
# plot
ax.plot(vs[:, 0], vs[:, 1], vs[:, 2], lw=1, color='k')
# check system size
maxSize = amax(abs(vs))
if maxSize > SYSSIZE:
SYSSIZE = maxSize
if direc is True:
# These don't move in the original object,
sCopyWithVertices = deepcopy(s)
sCopyWithVertices.vertices = vs # We just draw the frame rotation, discard changes
currentsList.append(sCopyWithVertices)
elif type(s) is Circular:
P = s.position
R = s.dimension/2
resolution = 20
# vertices
phis = linspace(0, 2*pi, resolution)
vs0 = array([[R*cos(p), R*sin(p), 0] for p in phis])
# rotate vertices + displacement
vs = array(
[angleAxisRotation(s.angle, s.axis, v)+P for v in vs0])
# plot
ax.plot(vs[:, 0], vs[:, 1], vs[:, 2], lw=1, color='k')
# check system size
maxSize = amax(abs(vs))
if maxSize > SYSSIZE:
SYSSIZE = maxSize
if direc is True:
# Send the Circular vertice information
sCopyWithVertices = deepcopy(s)
sCopyWithVertices.vertices = vs # to the object drawing list
currentsList.append(sCopyWithVertices)
elif type(s) is Dipole:
P = rotatePosition(s.position, s.angle, s.axis)
maxSize = amax(abs(P))
if maxSize > SYSSIZE:
SYSSIZE = maxSize
dipolesList.append(s)
for m in markersList: # Draw Markers
ax.scatter(m[0], m[1], m[2], s=20, marker='x')
if(len(m) > 3):
zdir = None
ax.text(m[0], m[1], m[2], m[3], zdir)
# Goes up to 3rd Position
maxSize = max([abs(pos) for pos in m[:3]])
if maxSize > SYSSIZE:
SYSSIZE = maxSize
for d in dipolesList:
drawDipole(d.position, d.moment,
d.angle, d.axis,
SYSSIZE, ax)
if direc is True: # Draw the Magnetization axes and current directions
drawCurrentArrows(currentsList, SYSSIZE, ax)
drawMagAxis(magnetsList, SYSSIZE, ax)
#for tick in ax.xaxis.get_ticklabels()+ax.yaxis.get_ticklabels()+ax.zaxis.get_ticklabels():
# tick.set_fontsize(12)
ax.set_xlabel('x[mm]')#, fontsize=12)
ax.set_ylabel('y[mm]')#, fontsize=12) #change font size through rc parameters
ax.set_zlabel('z[mm]')#, fontsize=12)
ax.set(
xlim=(-SYSSIZE, SYSSIZE),
ylim=(-SYSSIZE, SYSSIZE),
zlim=(-SYSSIZE, SYSSIZE),
)
plt.tight_layout()
if suppress is False:
plt.show(block=False)
return plt.gcf()