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axes3d.py
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axes3d.py
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#!/usr/bin/env python
from misc import rotation3D
from mpl_toolkits.mplot3d import Axes3D as _Axes3D
from mpl_toolkits.mplot3d import proj3d
from matplotlib import cm
import numpy as np
import cm as tcm
import matplotlib.pyplot as plt
from matplotlib.patches import FancyArrowPatch
from modest.tikhonov import Perturb
class Arrow3D(FancyArrowPatch):
'''
creates an artist object for a 3D arrow
'''
def __init__(self,xs,ys,zs,*args,**kwargs):
'''
arguments:
xs: the x coordinates of both sides of the arrow
ys: the y coordinates of both sides of the arrow
zs: the z coordinates of both sides of the arrow
'''
FancyArrowPatch.__init__(self,(0,0),(0,0),*args,**kwargs)
self.verts = xs,ys,zs
def draw(self,renderer):
xp,yp,zp = proj3d.proj_transform(*self.verts,M=renderer.M)
self.set_positions((xp[0],yp[0]),(xp[1],yp[1]))
FancyArrowPatch.draw(self,renderer)
class Axes3D(_Axes3D):
def __init__(self,*args,**kwargs):
if (len(args) > 1) | kwargs.has_key('rect'):
_Axes3D.__init__(self,*args,**kwargs)
else:
rect = (0.1,0.1,0.8,0.8)
_Axes3D.__init__(self,*args,rect=rect,**kwargs)
self.cross_section_clim_set = False
self.pbaspect = np.array([1.0,1.0,1.0])
def cross_section(self,func,anchor,
zrot,yrot,xrot,
length,width,
Nl=20,Nw=20,
cmap=tcm.slip,
lw=1.0,
clim=None,
func_args=None,
func_kwargs=None,
**kwargs):
if func_args is None:
func_args = ()
if func_kwargs is None:
func_kwargs = {}
x = np.linspace(0,length,Nl)
y = np.linspace(0,-width,Nw)
x,y = np.meshgrid(x,y)
z = 0.0*x
R = rotation3D(zrot,yrot,xrot)
p = np.concatenate((x[None,:,:],
y[None,:,:],
z[None,:,:]),
axis=0)
p = np.einsum('ij,jkl->kli',R,p)
p += anchor
p = np.reshape(p,(Nl*Nw,3))
c = func(p,*func_args,**func_kwargs)
c = np.reshape(c,(Nl,Nw))
p = np.reshape(p,(Nl,Nw,3))
if not self.cross_section_clim_set:
self.sm = cm.ScalarMappable(cmap=cmap)
self.sm.set_array(c)
if (clim is not None):
self.sm.set_clim(clim[0],clim[1])
self.cross_section_clim_set = True
cnorm = self.sm.norm(c)#(c - clim[0])/(clim[1] - clim[0])
s = self.plot_surface(p[:,:,0],
p[:,:,1],
p[:,:,2],
shade=False,
facecolors=cmap(cnorm),
rstride=1,cstride=1,
**kwargs)
idx1 = np.array([[0,-1],[0,-1]])
idx2 = np.array([[0,0],[-1,-1]])
w = self.plot_wireframe(p[idx1,idx2,0],
p[idx1,idx2,1],
p[idx1,idx2,2],
color='k',lw=lw)
return self.sm
def vector_cross_section(self,func,anchor,
zrot,yrot,xrot,
length,width,
Nl=20,Nw=20,
lw=1.0,
minmag=0.05,
arrow_length=1000.0,
func_args=None,
func_kwargs=None,
**kwargs):
if func_args is None:
func_args = ()
if func_kwargs is None:
func_kwargs = {}
x = np.linspace(0,length,Nl)
y = np.linspace(0,-width,Nw)
x,y = np.meshgrid(x,y)
z = 0.0*x
R = rotation3D(zrot,yrot,xrot)
p = np.concatenate((x[None,:,:],
y[None,:,:],
z[None,:,:]),
axis=0)
p = np.einsum('ij,jkl->kli',R,p)
p += anchor
p = np.reshape(p,(Nl*Nw,3))
c = func(p,*func_args,**func_kwargs)
cmag = np.sqrt(c[:,0]**2 + c[:,1]**2 + c[:,2]**2)
#c = np.ma.masked_array(c,mask=cmag<minmag)
c *= arrow_length
ends = p + c
mscale = kwargs.pop('mutation_scale',1.0)
for i in range(len(p)):
if cmag[i] > minmag:
artist = Arrow3D(*zip(p[i],ends[i]),mutation_scale=cmag[i]*mscale,**kwargs)
self.add_artist(artist)
def set_pbaspect(self,x):
self.pbaspect = np.asarray(x)
def draw_basis(self,
center=None,
length=1.0,
labels=None,
fontsize=16,
**kwargs):
if center is None:
center = np.array([0.0,0.0,0.0])
center = np.asarray(center)
if labels is None:
labels = ['x','y','z']
self.plot([center[0]],[center[1]],[center[2]],'ko')
for v,i in enumerate(Perturb(np.zeros(3),length)):
ends = i + center
artist = Arrow3D(*zip(center,ends),**kwargs)
self.text(ends[0],ends[1],ends[2],labels[v],color=[0.3,0.3,0.3])
self.add_artist(artist)
def equal(self):
self.set_pbaspect([1.0,1.0,1.0])
d = np.max([np.diff(self.get_xlim3d()),
np.diff(self.get_ylim3d()),
np.diff(self.get_zlim3d())])/2.0
mx = np.mean(self.get_xlim3d())
my = np.mean(self.get_ylim3d())
mz = np.mean(self.get_zlim3d())
self.auto_scale_xyz((mx-d,mx+d),(my-d,my+d),(mz-d,mz+d))
def get_proj(self):
"""
Create the projection matrix from the current viewing position.
elev stores the elevation angle in the z plane
azim stores the azimuth angle in the x,y plane
dist is the distance of the eye viewing point from the object
point.
"""
relev, razim = np.pi * self.elev/180, np.pi * self.azim/180
xmin, xmax = self.get_xlim3d()/self.pbaspect[0]
ymin, ymax = self.get_ylim3d()/self.pbaspect[1]
zmin, zmax = self.get_zlim3d()/self.pbaspect[2]
# transform to uniform world coordinates 0-1.0,0-1.0,0-1.0
worldM = proj3d.world_transformation(xmin, xmax,
ymin, ymax,
zmin, zmax)
# look into the middle of the new coordinates
R = np.array([0.5, 0.5, 0.5])
xp = R[0] + np.cos(razim) * np.cos(relev) * self.dist
yp = R[1] + np.sin(razim) * np.cos(relev) * self.dist
zp = R[2] + np.sin(relev) * self.dist
E = np.array((xp, yp, zp))
self.eye = E
self.vvec = R - E
self.vvec = self.vvec / proj3d.mod(self.vvec)
if abs(relev) > np.pi/2:
# upside down
V = np.array((0, 0, -1))
else:
V = np.array((0, 0, 1))
zfront, zback = -self.dist, self.dist
viewM = proj3d.view_transformation(E, R, V)
perspM = proj3d.persp_transformation(zfront, zback)
M0 = np.dot(viewM, worldM)
M = np.dot(perspM, M0)
return M
if __name__ == '__main__':
def f(points):
return np.sqrt(np.sum(points**2,1))
fig = plt.figure()
ax = Axes3D(fig)
xrot = np.pi/2.0001
yrot = 0.0
zrot = 0.0
length = 2.0
width = 2.0
anchor = np.array([-1.0,0.0,1.0])
ax.cross_section(f,anchor,
zrot,yrot,xrot,
length,width,cmap=tcm.slip_r,Nl=50,Nw=50,clim=(0.0,2.0),zorder=10)
xrot = 0.01*np.pi
yrot = 0.0
zrot = 0.0
length = 2.0
width = 2.0
anchor = np.array([-1.0,0.0,0.0])
s = ax.cross_section(f,anchor,
zrot,yrot,xrot,
length,width,cmap=tcm.slip_r,Nl=50,Nw=50,zorder=0)
plt.colorbar(s)
ax.set_xlim(-3,3)
ax.set_ylim(-3,3)
ax.set_zlim(-3,3)
plt.show()