python-woo 1.0+dfsg1-2 / usr / lib / python2.7 / dist-packages / woo / post2d.py

# encoding: utf-8
# 2009 © Václav Šmilauer <eudoxos@arcig.cz>
"""
Module for 2d postprocessing, containing classes to project points from 3d to 2d in various ways,
providing basic but flexible framework for extracting arbitrary scalar values from particles/contacts
and plotting the results. There are 2 basic components: flatteners and extractors.

The algorithms operate on particles (default) or contacts, depending on the ``con`` parameter
of post2d.data.

Flatteners
----------
Instance of classes that convert 3d (model) coordinates to 2d (plot) coordinates. Their interface is
defined by the :obj:`woo.post2d.Flatten` class (``__call__``, ``planar``, ``normal``).

Extractors
----------
Callable objects returning scalar or vector value, given a body/interaction object.
If a 3d vector is returned, Flattener.planar is called, which should return only in-plane
components of the vector.

Example
-------
This example can be found in examples/concrete/uniax-post.py ::

 from woo import post2d
 import pylab # the matlab-like interface of matplotlib

 O.load('/tmp/uniax-tension.xml.bz2')

 # flattener that project to the xz plane
 flattener=post2d.AxisFlatten(useRef=False,axis=1)
 # return scalar given a Body instance
 extractDmg=lambda b: b.state.normDmg
 # will call flattener.planar implicitly
 # the same as: extractVelocity=lambda b: flattener.planar(b,b.state.vel)
 extractVelocity=lambda b: b.state.vel

 # create new figure
 pylab.figure()
 # plot raw damage
 post2d.plot(post2d.data(extractDmg,flattener))

 # plot smooth damage into new figure
 pylab.figure(); ax,map=post2d.plot(post2d.data(extractDmg,flattener,stDev=2e-3))
 # show color scale
 pylab.colorbar(map,orientation='horizontal')

 # raw velocity (vector field) plot
 pylab.figure(); post2d.plot(post2d.data(extractVelocity,flattener))

 # smooth velocity plot; data are sampled at regular grid
 pylab.figure(); ax,map=post2d.plot(post2d.data(extractVelocity,flattener,stDev=1e-3))
 # save last (current) figure to file
 pylab.gcf().savefig('/tmp/foo.png') 

 # show the figures
 pylab.show()

"""
from minieigen import *

from woo.dem import Particle,Sphere
import math
nan=float('nan')

class Flatten:
	"""Abstract class for converting 3d point into 2d. Used by post2d.data2d."""
	def __init__(self,dispScale=1.):
		self.dispScale=dispScale
	def __call__(self,b):
		"Given a :obj:`woo.dem.Particle` / :obj:`woo.dem.Contact` instance, should return either 2d coordinates as a 2-tuple, or None if the Body should be discarded." 
		pass
	def planar(self,pos,vec):
		"Given position and vector value, project the vector value to the flat plane and return its 2 in-plane components."
	def normal(self,pos,vec):
		"Given position and vector value, return lenght of the vector normal to the flat plane."
	def scaledPos(self,p):
		if self.dispScale==1: return p.pos
		else: return p.refPos+self.dispScale*(p.pos-p.refPos)

class HelixFlatten(Flatten):
	"""Class converting 3d point to 2d based on projection from helix.
	The y-axis in the projection corresponds to the rotation axis"""
	def __init__(self,useRef,thetaRange,dH_dTheta,axis=2,periodStart=0,dispScale=1.):
		"""
		:param bool useRef:       use reference positions rather than actual positions
		:param (θmin,θmax) thetaRange: particles outside this range will be discarded
		:param float dH_dTheta:   inclination of the spiral (per radian)
		:param {0,1,2} axis:      axis of rotation of the spiral
		:param float periodStart: height of the spiral for zero angle
		"""
		Flatten.__init__(self,dispScale)
		self.useRef,self.thetaRange,self.dH_dTheta,self.axis,self.periodStart=useRef,thetaRange,dH_dTheta,axis,periodStart
		self.ax1,self.ax2=(axis+1)%3,(axis+2)%3
	def _getPos(self,b):
		return b.refPos if self.useRef else self.scaledPos(b)
	def __call__(self,b):
		import woo.utils
		xy,theta=woo.utils.spiralProject(_getPos(b),self.dH_dTheta,self.axis,self.periodStart)
		if theta<thetaRange[0] or theta>thetaRange[1]: return None
		return xy
	def planar(self,b,vec):
		from math import sqrt
		pos=_getPos(b)
		pos[self.axis]=0; pos.Normalize()
		return pos.Dot(vec),vec[axis]
	def normal(self,pos,vec):
		ax=Vector3(0,0,0); ax[axis]=1; pos=_getPos(b)
		circum=ax.Cross(pos); circum.Normalize()
		return circum.Dot(vec)
		

class CylinderFlatten(Flatten):
	"""Class for converting 3d point to 2d based on projection onto plane from circle.
	The y-axis in the projection corresponds to the rotation axis; the x-axis is distance form the axis.
	"""
	def __init__(self,axis=2,useRef=False,origin=Vector3(0,0,0),dispScale=1.):
		"""
		:param useRef: (bool) use reference positions rather than actual positions
		:param axis: axis of the cylinder, ∈{0,1,2}
		"""
		if axis not in (0,1,2): raise IndexError("axis must be one of 0,1,2 (not %d)"%axis)
		self.useRef,self.axis,self.origin=useRef,axis,Vector3(origin)
		Flatten.__init__(self,dispScale)
	def _getPos(self,b):
		return (b.refPos if self.useRef else self.scaledPos(b))-self.origin
	def __call__(self,b):
		p=self._getPos(b)
		pp=Vector2(p[(self.axis+1)%3],p[(self.axis+2)%3])
		return pp.norm(),p[self.axis]
	def planar(self,b,vec):
		pos=self._getPos(b)
		pos[self.axis]=0;
		pos.normalize()
		return pos.dot(vec),vec[self.axis]
	def normal(self,b,vec):
		pos=self._getPos(b)
		ax=Vector3(0,0,0); ax[axis]=1
		circum=ax.cross(pos).normalized();
		return circum.Dot(vec)


class AxisFlatten(Flatten):
	def __init__(self,axis=2,useRef=False,swapAxes=False,dispScale=1.):
		"""
		:param bool useRef: use reference positions rather than actual positions (only meaningful when operating on Particles)
		:param {0,1,2}	axis: axis normal to the plane; the return value will be simply position with this component dropped.
		"""
		if axis not in (0,1,2): raise IndexError("axis must be one of 0,1,2 (not %d)"%axis)
		self.useRef,self.axis=useRef,axis
		self.ax1,self.ax2=(self.axis+1)%3,(self.axis+2)%3
		if swapAxes: self.ax1,self.ax2=self.ax2,self.ax1
		Flatten.__init__(self,dispScale)
	def _getPos(self,b):
		return ((b.refPos if self.useRef else self.scaledPos(b)) if isinstance(b,Particle) else b.geom.node.pos)
	def __call__(self,b):
		p=self._getPos(b)
		return (p[self.ax1],p[self.ax2])
	def planar(self,pos,vec):
		return vec[self.ax1],vec[self.ax2]
	def normal(self,pos,vec):
		return vec[self.axis]

class LocalAxisFlatten(AxisFlatten):
	def __init__(self,pos,ori,axis=2,useRef=False,swapAxes=False,dispScale=1.):
		'''Like :obj:`AxisFlatten`, but transform the point to local coordinates first, using given position (Vector3) and orientation (Quaternion).'''
		AxisFlatten.__init__(self,axis=axis,useRef=useRef,swapAxes=swapAxes,dispScale=dispScale)
		self.pos,self.ori=pos,ori
	def _getPos(self,b):
		return self.ori.conjugate()*(AxisFlatten._getPos(self,b)-self.pos)
	def planar(self,pos,vec):
		return AxisFlatten.planar(self,self.ori.conjugate()*(pos-self.pos),self.ori.conjugate()*(pos-self.pos))
	def normal(self,pos,vec):
		return AxisFlatten.normal(self,self.ori.conjugate()*(pos-self.pos),self.ori.conjugate()*(pos-self.pos))


def data(scene,extractor,flattener,con=False,onlyDynamic=True,stDev=None,relThreshold=3.,perArea=0,div=(50,50),margin=(0,0),radius=1):
	"""Filter all particles/contacts, project them to 2d and extract required scalar value;
	return either discrete array of positions and values, or smoothed data, depending on whether the stDev
	value is specified.

	The ``con`` parameter determines whether we operate on particles or contacts;
	the extractor provided should expect to receive body/interaction.

	:param callable extractor: receives :obj:`woo.dem.Particle` (or :obj:`woo.dem.Contact`, if ``con`` is ``True``) instance, should return scalar, a 2-tuple (vector fields) or None (to skip that body/interaction)
	:param callable flattener: :obj:`woo.post2d.Flatten` instance, receiving body/interaction, returns its 2d coordinates or ``None`` (to skip that body/interaction)
	:param bool con: operate on contacts rather than particles
	:param bool onlyDynamic: skip all non-dynamic particles
	:param float/None stDev: standard deviation for averaging, enables smoothing; ``None`` (default) means raw mode, where discrete points are returned
	:param float relThreshold: threshold for the gaussian weight function relative to stDev (smooth mode only)
	:param int perArea: if 1, compute weightedSum/weightedArea rather than weighted average (weightedSum/sumWeights); the first is useful to compute average stress; if 2, compute averages on subdivision elements, not using weight function
	:param (int,int) div: number of cells for the gaussian grid (smooth mode only)
	:param (float,float) margin: x,y margins around bounding box for data (smooth mode only)
	:param float/callable radius: Fallback value for radius (for raw plotting) for non-spherical particles or contacts; if a callable, receives body/interaction and returns radius
	:return: dictionary
	
	Returned dictionary always containing keys 'type' (one of 'rawScalar','rawVector','smoothScalar','smoothVector', depending on value of smooth and on return value from extractor), 'x', 'y', 'bbox'.
	
	Raw data further contains 'radii'.
	
	Scalar fields contain 'val' (value from *extractor*), vector fields have 'valX' and 'valY' (2 components returned by the *extractor*).
	"""
	from minieigen import Vector3
	from woo.dem import Sphere
	xx,yy,dd1,dd2,rr=[],[],[],[],[]
	nDim=0
	objects=scene.dem.con if con else scene.dem.par
	for b in objects:
		if not con and (len(b.shape.nodes)!=1 or (onlyDynamic and b.blocked=='xyzXYZ')): continue
		xy,d=flattener(b),extractor(b)
		if xy==None or d==None or math.isnan(d): continue
		if nDim==0: nDim=1 if isinstance(d,float) else 2
		if nDim==1: dd1.append(d);
		elif len(d)==2:
			dd1.append(d[0]); dd2.append(d[1])
		elif len(d)==3:
			d1,d2=flattener.planar(b,Vector3(d))
			dd1.append(d1); dd2.append(d2)
		else:
			raise RuntimeError("Extractor must return float or 2 or 3 (not %d) floats"%nDim)
		if stDev==None: # radii are needed in the raw mode exclusively
			if nDim==1 and math.isnan(d): rr.append(nan) # add NaN if value was also invalid
			else:
				if not con and isinstance(b.shape,Sphere): r=b.shape.radius
				else: r=(radius(b) if callable(radius) else radius)
				rr.append(r)
		xx.append(xy[0]); yy.append(xy[1]);
	if stDev==None:
		bbox=(min(xx),min(yy)),(max(xx),max(yy))
		if nDim==1: return {'type':'rawScalar','x':xx,'y':yy,'val':dd1,'radii':rr,'bbox':bbox}
		else: return {'type':'rawVector','x':xx,'y':yy,'valX':dd1,'valY':dd2,'radii':rr,'bbox':bbox}
	
	from woo.WeightedAverage2d import GaussAverage
	import numpy
	if min(len(xx),len(yy)==0): raise RuntimeError('Nothing to plot (extractor did not return any values)')
	lo,hi=(min(xx),min(yy)),(max(xx),max(yy))
	llo=lo[0]-margin[0],lo[1]-margin[1]; hhi=hi[0]+margin[0],hi[1]+margin[1]
	ga=GaussAverage(llo,hhi,div,stDev,relThreshold)
	ga2=GaussAverage(llo,hhi,div,stDev,relThreshold)
	for i in range(0,len(xx)):
		ga.add(dd1[i],(xx[i],yy[i]))
		if nDim>1: ga2.add(dd2[i],(xx[i],yy[i]))
	step=[(hhi[i]-llo[i])/float(div[i]) for i in [0,1]]
	xxx,yyy=[numpy.arange(llo[i]+.5*step[i],hhi[i],step[i]) for i in [0,1]]
	ddd=numpy.zeros((len(yyy),len(xxx)),float)
	ddd2=numpy.zeros((len(yyy),len(xxx)),float)
	# set the type of average we are going to use
	if perArea==0:
		def compAvg(gauss,coord,cellCoord): return float(gauss.avg(coord))
	elif perArea==1:
		def compAvg(gauss,coord,cellCoord): return gauss.avgPerUnitArea(coord)
	elif perArea==2:
		def compAvg(gauss,coord,cellCoord):
			s=gauss.cellSum(cellCoord);
			return (s/gauss.cellArea) if s>0 else nan
	elif perArea==3:
		def compAvg(gauss,coord,cellCoord):
			s=gauss.cellSum(cellCoord);
			return s if s>0 else nan
	else: raise RuntimeError('Invalid value of *perArea*, must be one of 0,1,2,3.')
	#
	for cx in range(0,div[0]):
		for cy in range(0,div[1]):
			ddd[cy,cx]=compAvg(ga,(xxx[cx],yyy[cy]),(cx,cy))
			if nDim>1: ddd2[cy,cx]=compAvg(ga2,(xxx[cx],yyy[cy]),(cx,cy))
	if nDim==1: return {'type':'smoothScalar','x':xxx,'y':yyy,'val':ddd,'bbox':(llo,hhi),'perArea':perArea,'grid':ga} 
	else: return {'type':'smoothVector','x':xxx,'y':yyy,'valX':ddd,'valY':ddd2,'bbox':(llo,hhi),'grid':ga,'grid2':ga2}
	
def plot(data,axes=None,clabel=True,cbar=False,rawVecColorRadius=True,bbox=None,aspect='equal',**kw):
	"""Given output from post2d.data, plot the scalar as discrete or smooth plot.

	For raw discrete data, plot filled circles with radii of particles, colored by the scalar value.

	For smooth discrete data, plot image with optional contours and contour labels.

	For vector data (raw or smooth), plot quiver (vector field), with arrows colored by the magnitude.

	:param axes: matplotlib.axes\ instance where the figure will be plotted; if None, will be created from scratch.
	:param data: value returned by :obj:`woo.post2d.data`
	:param bool clabel: show contour labels (smooth mode only), or annotate cells with numbers inside (with perArea==2)
	:param bool cbar: show colorbar (equivalent to calling pylab.colorbar(mappable) on the returned mappable)
	:param rawVecColorRadius: if True, use radius associated with each point to color arrows in raw quiver plot.
	:param bbox: if given, use this as axes limits instead of bbox computed from data points
	:param clip_path: clip plotted image maps, contour lines or patches with this clip path (should be an instance of ``matplotlib.patches.Patch``). 

	:return: tuple of ``(axes,mappable)``; mappable can be used in further calls to pylab.colorbar.
	"""
	import matplotlib.figure, math
	if not axes:
		# see http://stackoverflow.com/a/18261110/761090 
		fig=matplotlib.figure.Figure()
		axes=fig.add_subplot(1,1,1)
		# this is to make sure the 
		#canvas=matplotlib.backends.backend_agg.FigureCanvasAgg(fig)
		#import matplotlib.figure, matplotlib.backends.backend_agg
	if data['type']=='rawScalar':
		from matplotlib.patches import Circle
		import matplotlib.collections,numpy
		patches=[]
		for x,y,d,r in zip(data['x'],data['y'],data['val'],data['radii']):
			patches.append(Circle(xy=(x,y),radius=r))
		coll=matplotlib.collections.PatchCollection(patches,linewidths=0.,**kw)
		coll.set_array(numpy.array(data['val']))
		# if clip_path: coll.set_clip_path(clip_path)
		axes.add_collection(coll)
		if bbox:
			axes.set_xlim(bbox[0][0],bbox[1][0]); axes.set_ylim(bbox[0][1],bbox[1][1])
		else:
			bb=coll.get_datalim(coll.get_transform())
			axes.set_xlim(bb.xmin,bb.xmax); axes.set_ylim(bb.ymin,bb.ymax)
		if cbar: axes.get_figure().colorbar(coll)
		axes.grid(True); axes.set_aspect(aspect)
		return axes,coll
	elif data['type']=='smoothScalar':
		# for imshow - do not depend on axes limits (if passed as the bbox param)
		imgExtent=data['bbox'][0][0],data['bbox'][1][0],data['bbox'][0][1],data['bbox'][1][1] 
		if not bbox: bbox=data['bbox']
		if data['perArea'] in (0,1):
			img=axes.imshow(data['val'],extent=imgExtent,origin='lower',aspect=aspect,**kw)
			ct=axes.contour(data['x'],data['y'],data['val'],colors='k',origin='lower',extend='both')
			#if clip_path and 0:
			#	img.set_clip_path(clip_path)
			#	# XXX: does not work
			#	# http://matplotlib.1069221.n5.nabble.com/Clipping-Contours-td39474.html
			#	# for coll in ct.collections: coll.set_clip_path(clip_path)
			if clabel: axes.clabel(ct,inline=1,fontsize=10)
		else:
			img=axes.imshow(data['val'],extent=imgExtent,origin='lower',aspect=aspect,interpolation='nearest',**kw)
			# if clip_path: img.set_clip_path(clip_path)
			xStep=(data['x'][1]-data['x'][0]) if len(data['x'])>1 else 0
			for y,valLine in zip(data['y'],data['val']):
				for x,val in zip(data['x'],valLine): axes.text(x-.4*xStep,y,('-' if math.isnan(val) else '%5g'%val),size=4)
		axes.update_datalim(bbox)
		axes.set_xlim(bbox[0][0],bbox[1][0]); axes.set_ylim(bbox[0][1],bbox[1][1])
		if cbar: axes.get_figure().colorbar(img)
		axes.grid(True if data['perArea'] in (0,1) else False); axes.set_aspect(aspect)
		return axes,img
	elif data['type'] in ('rawVector','smoothVector'):
		import numpy
		if not bbox: bbox=data['bbox']
		valX,valY=numpy.array(data['valX']),numpy.array(data['valY']) # rawVector data are plain python lists
		if data['type']=='rawVector' and rawVecColorRadius: scalars=numpy.array(data['radii'])
		else: scalars=numpy.sqrt(valX**2+valY**2) # use vector magnitudes
		# numpy.sqrt computes element-wise sqrt
		quiv=axes.quiver(data['x'],data['y'],data['valX'],data['valY'],scalars,**kw)
		# if clip_path: quiv.set_clip_path(clip_path)
		#axes.update_datalim(bbox)
		axes.set_xlim(bbox[0][0],bbox[1][0]); axes.set_ylim(bbox[0][1],bbox[1][1])
		if cbar: axes.get_figure().colorbar(coll)
		axes.grid(True); axes.set_aspect(aspect)
		return axes,quiv