escript/py_src/faultsystems.py

########################################################
#
# Copyright (c) 2003-2009 by University of Queensland
# Earth Systems Science Computational Center (ESSCC)
# http://www.uq.edu.au/esscc
#
# Primary Business: Queensland, Australia
# Licensed under the Open Software License version 3.0
# http://www.opensource.org/licenses/osl-3.0.php
#
########################################################

__copyright__="""Copyright (c) 2003-2009 by University of Queensland
Earth Systems Science Computational Center (ESSCC)
http://www.uq.edu.au/esscc
Primary Business: Queensland, Australia"""
__license__="""Licensed under the Open Software License version 3.0
http://www.opensource.org/licenses/osl-3.0.php"""
__url__="https://launchpad.net/escript-finley"

from esys.escript import *
from esys.escript.pdetools import Locator
import numpy
import math

class FaultSystem:
  """
  The FaultSystem class defines a system of faults in the Earth crust. 
 
  A fault system is defined by set of faults index by a tag. Each fault is defined by a starting point V0 and a list of 
  strikes ``strike`` and length ``l``. The strikes and the length is used to define a polyline with points ``V[i]`` such that

  - ``V[0]=V0``
  - ``V[i]=V[i]+ls[i]*array(cos(strike[i]),sin(strike[i]),0)''

  So ``strike`` defines the angle between the direction of the fault segment and the x0 axis. ''ls[i]``==0 is allowed.

  In case of a 3D model a fault plane is defined through a dip and depth. 

  The class provides a mechanism to parametrise each fault with the domain [0,w0_max] x [0, w1_max]  (to [0,w0_max] in the 2D case).
  """
  NOTAG="__NOTAG__"
  MIN_DEPTH_ANGLE=0.1
  def __init__(self,dim=3):
    """
    Sets up the fault system

    :param dim: spatial dimension
    :type dim: ``int`` of value 2 or 3
    """
    if not (dim == 2 or dim == 3):
       raise ValueError,"only dimension2 2 and 3 are supported."
    self.__dim=dim
    self.__top={}
    self.__ls={}
    self.__strikes={}
    self.__strike_vectors={}
    self.__medDepth={}
    self.__total_length={}
    if dim ==2:
       self.__depths=None
       self.__depth_vectors=None
       self.__dips=None
       self.__bottom=None
       self.__normals=None
    else:
       self.__depths={}
       self.__depth_vectors={}
       self.__dips={}
       self.__bottom={}
       self.__normals={}
    self.__offsets={}
    self.__w1_max={}
    self.__w0_max={}
    self.__center=None
    self.__orientation = None
  def getStart(self,tag=None):
     """
     returns the starting point of fault ``tag``
     :rtype: `numpy.ndarray'.
     """
     return self.getTopPolyline(tag)[0]

  def getTags(self):
     """
     returns a list of the tags used by the fault system
     :rtype: ``list``
     """
     return self.__top.keys()
  def getDim(self):
     """
     returns the spatial dimension
     :rtype: ``int``
     """
     return self.__dim

  def getTopPolyline(self, tag=None):
     """
     returns the polyline used to describe fault tagged by ``tag`` 
      
     :param tag: the tag of the fault
     :type tag: ``float`` or ``str``
     :return: the list of vertices defining the top of the fault.  The coordinates are `numpy.ndarray'.
     """
     if tag==None: tag=self.NOTAG
     return self.__top[tag]
  def getStrikes(self, tag=None):
     """
     returns the strike of the segements in fault ``tag``
     :rtype: ``list`` of ``float``
     """
     if tag==None: tag=self.NOTAG
     return self.__strikes[tag]
  def getStrikeVectors(self, tag=None):
     """
     returns the strike vectors of fault ``tag``
     :rtype: ``list`` of `numpy.ndarray'.
     """
     if tag==None: tag=self.NOTAG
     return self.__strike_vectors[tag]
  def getLengths(self, tag=None):
     """
     returns the lengths of segments in fault ``tag``
     :rtype: ``list`` of `float``
     """
     if tag==None: tag=self.NOTAG
     return self.__ls[tag]

  def getTotalLength(self, tag=None):
     """
     returns the total unrolled length of fault ``tag``
     :rtype: `float``
     """
     if tag==None: tag=self.NOTAG
     return self.__total_length[tag]

  def getMediumDepth(self,tag=None):
     """
     returns the medium depth of fault ``tag``
     :rtype: ``float``
     """
     if tag==None: tag=self.NOTAG
     return self.__medDepth[tag]

  def getDips(self, tag=None):
     """
     returns the list of the dips of the segements in fault ``tag``
     :param tag: the tag of the fault
     :type tag: ``float`` or ``str``
     :return: the list of segment dips. In the 2D case None is returned.
     """
     if tag==None: tag=self.NOTAG
     if self.getDim()==3:
         return self.__dips[tag]
     else:
         return None

  def getBottomPolyline(self, tag=None):
     """
     returns the list of the vertices defining the bottom of the fault ``tag``
     :param tag: the tag of the fault
     :type tag: ``float`` or ``str``
     :return: the list of vertices. In the 2D case None is returned.
     """
     if tag==None: tag=self.NOTAG
     if self.getDim()==3:
         return self.__bottom[tag]
     else:
         return None

  def getSegmentNormals(self, tag=None):
     """
     returns the list of the normals of the segments in fault ``tag``
     :param tag: the tag of the fault
     :type tag: ``float`` or ``str``
     :return: the list of vectors normal to the segments. In the 2D case None is returned.
     """
     if tag==None: tag=self.NOTAG
     if self.getDim()==3:
         return self.__normals[tag]
     else:
         return None

  def getDepthVectors(self, tag=None):
     """
     returns the list of the depth vector at top vertices in fault ``tag``.
     :param tag: the tag of the fault
     :type tag: ``float`` or ``str``
     :return: the list of segment depths. In the 2D case None is returned.
     """
     if tag==None: tag=self.NOTAG
     if self.getDim()==3:
         return self.__depth_vectors[tag]
     else:
         return None
  def getDepths(self, tag=None):
     """
     returns the list of the depths of the segements in fault ``tag``.
     :param tag: the tag of the fault
     :type tag: ``float`` or ``str``
     :return: the list of segment depths. In the 2D case None is returned.
     """
     if tag==None: tag=self.NOTAG
     if self.getDim()==3:
         return self.__depths[tag]
     else:
         return None

  def getW0Range(self,tag=None):
     """
     returns the range of the parameterization in ``w0``
     :rtype: two ``float``
     """
     return self.getW0Offsets(tag)[0], self.getW0Offsets(tag)[-1]

  def getW1Range(self,tag=None):
     """
     returns the range of the parameterization in ``w1``
     :rtype: two ``float``
     """
     if tag==None: tag=self.NOTAG
     return -self.__w1_max[tag],0

  def getW0Offsets(self, tag=None):
     """
     returns the offsets for the parametrization of fault ``tag``. 

     :return: the offsets in the parametrization
     :rtype: ``list`` of ``float``
     """
     if tag==None: tag=self.NOTAG
     return self.__offsets[tag]


  def getCenterOnSurface(self):
      """
      returns the center point of the fault system at the surface 
      :rtype: `numpy.ndarray`
      """
      if self.__center == None:
        self.__center=numpy.zeros((3,),numpy.float)
        counter=0
        for t in self.getTags():
            for s in self.getTopPolyline(t):
                self.__center[:2]+=s[:2]
                counter+=1
        self.__center/=counter
      return self.__center[:self.getDim()]

  def getOrientationOnSurface(self):
      """
      returns the orientation of the fault system in RAD on the surface around the fault system center
      :rtype: ``float``
      """
      if self.__orientation == None:
          center=self.getCenterOnSurface()
          covariant=numpy.zeros((2,2))
          for t in self.getTags():
              for s in self.getTopPolyline(t):
                covariant[0,0]+=(center[0]-s[0])**2
                covariant[0,1]+=(center[1]-s[1])*(center[0]-s[0])
                covariant[1,1]+=(center[1]-s[1])**2
                covariant[1,0]+=(center[1]-s[1])*(center[0]-s[0])
          e, V=numpy.linalg.eigh(covariant)
          if e[0]>e[1]:
             d=V[:,0]
          else:
             d=V[:,1]
          if abs(d[0])>0.:
             self.__orientation=atan(d[1]/d[0])
          else:
             self.__orientation=math.pi/2
      return self.__orientation 
  def transform(self, rot=0, shift=numpy.zeros((3,))):
     """
     applies a shift and a consecutive rotation in the x0x1 plane.
    
     :param rot: rotation angle in RAD
     :type rot: ``float``
     :param shift: shift vector to be applied before rotation
     :type shift: `numpy.ndarray` of size 2 or 3
     """
     if self.getDim() == 2:
        mat=numpy.array([[cos(rot), -sin(rot)], [sin(rot), cos(rot)] ])
     else:
        mat=numpy.array([[cos(rot), -sin(rot),0.], [sin(rot), cos(rot),0.], [0.,0.,1.] ])

     for t in self.getTags():
         strikes=[ s+ rot for s in self.getStrikes(t) ]
         V0=self.getStart(t)

         self.addFault(strikes = [ s+ rot for s in self.getStrikes(t) ], \
                       ls = self.getLengths(t), \
                       V0=numpy.dot(mat,self.getStart(t)+shift), \
                       tag =t, \
                       dips=self.getDips(t),\
                       depths=self.getDepths(t), \
                       w0_offsets=self.getW0Offsets(t), \
                       w1_max=-self.getW1Range(t)[0]) 

  def addFault(self, strikes, ls, V0=[0.,0.,0.],tag=None, dips=None, depths= None, w0_offsets=None, w1_max=None):
     """
     adds a new fault to the fault system. The fault is named by ``tag``. 

     The fault is defined by a starting point V0 and a list of ``strikes`` and length ``ls``. The strikes and the length 
     is used to define a polyline with points ``V[i]`` such that

     - ``V[0]=V0``
     - ``V[i]=V[i]+ls[i]*array(cos(strikes[i]),sin(strikes[i]),0)''

     So ``strikes`` defines the angle between the direction of the fault segment and the x0 axis. In 3D ''ls[i]``==0 is allowed.

     In case of a 3D model a fault plane is defined through a dip ``dips`` and depth ``depths``. 
     From the dip and the depth the polyline ``bottom`` of the bottom of the fault is computed.


     Each segment in the fault is decribed by the for vertices ``v0=top[i]``, ``v1``==``top[i+1]``, ``v2=bottom[i]`` and ``v3=bottom[i+1]`` 
     The segment is parametrized by ``w0`` and ``w1`` with ``w0_offsets[i]<=w0<=w0_offsets[i+1]`` and ``-w1_max<=w1<=0``. Moreover 
   
     - ``(w0,w1)=(w0_offsets[i]  ,       0)->v0``
     - ``(w0,w1)=(w0_offsets[i+1],       0)->v1``
     - ``(w0,w1)=(w0_offsets[i]  , -w1_max)->v2``
     - ``(w0,w1)=(w0_offsets[i+1], -w1_max)->v3``

     If no ``w0_offsets`` is given, 
  
     - ``w0_offsets[0]=0``
     - ``w0_offsets[i]=w0_offsets[i-1]+L[i]``

     where ``L[i]`` is the length of the segments on the top in 2D and in the middle of the segment in 3D. 

     If no ``w1_max`` is given, the average fault depth is used.


     :param strikes: list of strikes. This is the angle of the fault segment direction with x0 axis. Right hand rule applies.
     :type strikes: ``list`` of ``float``
     :param ls: list of fault lengths. In the case of a 3D fault a segment may have length 0. 
     :type ls: ``list`` of ``float``
     :param V0: start point of the fault
     :type V0: ``list`` or `numpy.ndarray' with 2 or 3 components. ``V0[2]`` must be zero.
     :param tag: the tag of the fault. If fault ``tag`` already exists it is overwritten.
     :type tag: ``float`` or ``str``
     :param dips: list of dip angles. Right hand rule around strike direction applies.
     :type dips: ``list`` of ``float``
     :param depths: list of segment depth. Value mut be positive in the 3D case.
     :type depths: ``list`` of ``float``
     :param w0_offsets: ``w0_offsets[i]`` defines the offset of the segment ``i`` in the fault to be used in the parametrization of the fault. If not present the cumulative length of the fault segments is used. 
     :type w0_offsets: ``list`` of ``float`` or ``None``
     :param w1_max: the maximum value used for parametrization of the fault in the depth direction. If not present the mean depth of the fault segments is used.
     :type w1_max: ``float``
     :note: In the three dimensional case the lists ``dip`` and ``top`` must have the same length.
     """
     if tag==None: 
         tag=self.NOTAG
     else:
         if self.NOTAG in self.getTags():
              raise ValueError,'Attempt to add a fault with no tag to a set of existing faults'
     if not isinstance(strikes, list): strikes=[strikes, ]
     n_segs=len(strikes)
     if not isinstance(ls, list): ls=[ ls for i in xrange(n_segs) ]
     if not n_segs==len(ls):
         raise ValueError,"number of strike direction and length must match."
     if len(V0)>2:
          if abs(V0[2])>0: raise Value,"start point needs to be surface (3rd component ==0)"
     if self.getDim()==2 and not  (dips==None and depths == None) :
           raise ValueError,'Spatial dimension two does not support dip and depth for faults.'
     if not dips == None:
        if not isinstance(dips, list): dips=[dips for i in xrange(n_segs) ]
        if n_segs != len(dips):
           raise ValueError,'length of dips must be one less then the length of top.'
     if not depths == None:
        if not isinstance(depths, list): depths=[depths for i in xrange(n_segs+1) ]
        if n_segs+1 != len(depths):
           raise ValueError,'length of depths must be one less then the length of top.'
     if w0_offsets != None:
       if len(w0_offsets) != n_segs+1:
          raise ValueError,'expected length of w0_offsets is %s'%(n_segs)
     self.__center=None
     self.__orientation = None
     #
     #  in the 2D case we don't allow zero length:
     #
     if self.getDim() == 2:
        for l in ls:
            if l<=0: raise ValueError,"length must be positive"
     else:
        for l in ls:
            if l<0: raise ValueError,"length must be non-negative"
        for i in xrange(n_segs+1):
           if depths[i]<0: raise ValueError,"negative depth."
     # 
     #   translate start point to numarray
     #
     V0= numpy.array(V0[:self.getDim()],numpy.double)
     #
     #  set strike vectors:
     #
     strike_vectors=[]
     top_polyline=[V0]   
     total_length=0
     for i in xrange(n_segs):
         v=numpy.zeros((self.getDim(),))
         v[0]=cos(strikes[i])
         v[1]=sin(strikes[i])
         strike_vectors.append(v)
         top_polyline.append(top_polyline[-1]+ls[i]*v)
         total_length+=ls[i]
     #
     #    normal and depth direction
     #
     if self.getDim()==3:
        normals=[]
        for i in xrange(n_segs):
           normals.append(numpy.array([sin(dips[i])*strike_vectors[i][1],-sin(dips[i])*strike_vectors[i][0], cos(dips[i])]) )
  
        d=numpy.cross(strike_vectors[0],normals[0])
        if d[2]>0:
             f=-1
        else:
             f=1
        depth_vectors=[f*depths[0]*d/numpy.linalg.norm(d) ]
        for i in xrange(1,n_segs):
            d=-numpy.cross(normals[i-1],normals[i])
            d_l=numpy.linalg.norm(d)
            if d_l<=0:
                 d=numpy.cross(strike_vectors[i],normals[i])
                 d_l=numpy.linalg.norm(d)
            else:
                 for L in [ strike_vectors[i], strike_vectors[i-1]]:
                    if numpy.linalg.norm(numpy.cross(L,d)) <= self.MIN_DEPTH_ANGLE * numpy.linalg.norm(L) * d_l:
                         raise ValueError,"%s-th depth vector %s too flat."%(i, d)
            if d[2]>0:
                f=-1
            else:
                f=1
            depth_vectors.append(f*d*depths[i]/d_l)
        d=numpy.cross(strike_vectors[n_segs-1],normals[n_segs-1])
        if d[2]>0:
             f=-1
        else:
             f=1
        depth_vectors.append(f*depths[n_segs]*d/numpy.linalg.norm(d))
        bottom_polyline=[ top_polyline[i]+depth_vectors[i] for i in xrange(n_segs+1) ]
     #
     #   calculate offsets if required:
     #
     if w0_offsets==None:
        w0_offsets=[0.] 
        for  i in xrange(n_segs):
            if self.getDim()==3:
               w0_offsets.append(w0_offsets[-1]+(float(numpy.linalg.norm(bottom_polyline[i+1]-bottom_polyline[i]))+ls[i])/2.)
            else:
               w0_offsets.append(w0_offsets[-1]+ls[i])
     w0_max=max(w0_offsets)
     if self.getDim()==3:
        self.__normals[tag]=normals
        self.__depth_vectors[tag]=depth_vectors
        self.__depths[tag]=depths
        self.__dips[tag]=dips
        self.__bottom[tag]=bottom_polyline
     self.__ls[tag]=ls
     self.__strikes[tag]=strikes
     self.__strike_vectors[tag]=strike_vectors
     self.__top[tag]=top_polyline
     self.__total_length[tag]=total_length
     self.__offsets[tag]=w0_offsets

     if self.getDim()==2:
        self.__medDepth[tag]=0.
     else:
        self.__medDepth[tag]=sum([ numpy.linalg.norm(v) for v in depth_vectors])/len(depth_vectors)
     if w1_max==None or self.getDim()==2: w1_max=self.__medDepth[tag]
     self.__w0_max[tag]=w0_max
     self.__w1_max[tag]=w1_max

  def getMaxValue(self,f, tol=sqrt(EPSILON)):
     """
     returns the tag of the fault of where ``f`` takes the maximum value and a `Locator` object which can be used to collect values from `Data` class objects at the location where the minimum is taken.

     :param f: a distribution of values 
     :type f: `escript.Data`
     :param tol: relative tolerance used to decide if point is on fault 
     :type f: ``tol``
     :return: the fault tag the maximum is taken, and a `Locator` object to collect the value at location of maximum value.
     """
     ref=-Lsup(f)*2
     f_max=ref
     t_max=None
     loc_max=None
     x=f.getFunctionSpace().getX()
     for t in self.getTags():
        p,m=self.getParametrization(x,tag=t, tol=tol)
        loc=((m*f)+(1.-m)*ref).maxGlobalDataPoint()
        f_t=f.getTupleForGlobalDataPoint(*loc)[0]
        if f_t>f_max:
           f_max=f_t
           t_max=t
           loc_max=loc

     if loc_max == None:
         return None, None
     else:
         return t_max, Locator(x.getFunctionSpace(),x.getTupleForGlobalDataPoint(*loc_max))

  def getMinValue(self,f, tol=sqrt(EPSILON)):
     """
     returns the tag of the fault of where ``f`` takes the minimum value and a `Locator` object which can be used to collect values from `Data` class objects at the location where the minimum is taken.

     :param f: a distribution of values 
     :type f: `escript.Data`
     :param tol: relative tolerance used to decide if point is on fault 
     :type f: ``tol``
     :return: the fault tag the minimum is taken, and a `Locator` object to collect the value at location of minimum value.
     """
     ref=Lsup(f)*2
     f_min=ref
     t_min=None
     loc_min=None
     x=f.getFunctionSpace().getX()
     for t in self.getTags():
        p,m=self.getParametrization(x,tag=t, tol=tol)
        loc=((m*f)+(1.-m)*ref).minGlobalDataPoint()
        f_t=f.getTupleForGlobalDataPoint(*loc)[0]
        if f_t<f_min:
           f_min=f_t
           t_min=t
           loc_min=loc

     if loc_min == None:
         return None, None
     else:
         return t_min, Locator(x.getFunctionSpace(),x.getTupleForGlobalDataPoint(*loc_min))

  def getParametrization(self,x,tag=None, tol=sqrt(EPSILON), outsider=None):
    """
    returns the parametrization of the fault ``tag`` in the fault system. In fact the values of the parametrization for at given coordinates ``x`` is returned. In addition to the value of the parametrization a mask is returned indicating if the given location is on the fault with given tolerance ``tol``.

    Typical usage of the this method is

    dom=Domain(..)
    x=dom.getX()
    fs=FaultSystem()
    fs.addFault(tag=3,...)
    p, m=fs.getParametrization(x, outsider=0,tag=3)
    saveDataCSV('x.csv',p=p, x=x, mask=m)

    to create a file with the coordinates of the points in ``x`` which are on the fault (as ``mask=m``) together with their location ``p`` in the fault coordinate system.

    :param x: location(s)
    :type x: `escript.Data` object or `numpy.ndarray`
    :param tag: the tag of the fault
    :param tol: relative tolerance to check if location is on fault.
    :type tol: ``float``
    :param outsider: value used for parametrization values outside the fault. If not present an appropriate value is choosen.
    :type outsider: ``float``
    :return: the coordinates ``x`` in the coordinate system of the fault and a mask indicating coordinates in the fault by 1 (0 elsewhere)
    :rtype: `escript.Data` object or `numpy.ndarray`
    """
    offsets=self.getW0Offsets(tag)
    w1_range=self.getW1Range(tag)
    w0_range=self.getW0Range(tag)[1]-self.getW0Range(tag)[0]
    if outsider == None:
       outsider=min(self.getW0Range(tag)[0],self.getW0Range(tag)[1])-abs(w0_range)/sqrt(EPSILON)
        
    if isinstance(x,list): x=numpy.array(x, numpy.double)
    updated=x[0]*0 

    if self.getDim()==2:
        #
        #
        p=x[0]*0 + outsider
        top=self.getTopPolyline(tag)
        for i in xrange(1,len(top)):
           d=top[i]-top[i-1]
           h=x-top[i-1]
           h_l=length(h)
           d_l=length(d)
           s=inner(h,d)/d_l**2
           s=s*whereNonPositive(s-1.-tol)*whereNonNegative(s+tol)
           m=whereNonPositive(length(h-s*d)-tol*maximum(h_l,d_l))*(1.-updated)
           p=(1.-m)*p+m*(offsets[i-1]+(offsets[i]-offsets[i-1])*s)
           updated=wherePositive(updated+m)
    else:
        p=x[:2]*0 + outsider
        top=self.getTopPolyline(tag)
        bottom=self.getBottomPolyline(tag)
        n=self.getSegmentNormals(tag)
        for i in xrange(len(top)-1):
            h=x-top[i]
            R=top[i+1]-top[i]
            r=bottom[i+1]-bottom[i]
            D0=bottom[i]-top[i]
            D1=bottom[i+1]-top[i+1]
            s_upper=matrix_mult(numpy.linalg.pinv(numpy.vstack((R,D1)).T),h)
            s_lower=matrix_mult(numpy.linalg.pinv(numpy.vstack((r,D0)).T),h)
            m_ul=wherePositive(s_upper[0]-s_upper[1])
            s=s_upper*m_ul+s_lower*(1-m_ul)
            s0=s[0]
            s1=s[1]
            m=whereNonNegative(s0+tol)*whereNonPositive(s0-1.-tol)*whereNonNegative(s1+tol)*whereNonPositive(s1-1.-tol)
            s0=s0*m
            s1=s1*m
            atol=tol*maximum(length(h),length(top[i]-bottom[i+1]))
            m=whereNonPositive(length(h-s0*R-s1*D1)*m_ul+(1-m_ul)*length(h-s0*r-s1*D0)-atol)
            p[0]=(1.-m)*p[0]+m*(offsets[i]+(offsets[i+1]-offsets[i])*s0)
            p[1]=(1.-m)*p[1]+m*(w1_range[1]+(w1_range[0]-w1_range[1])*s1)
            updated=wherePositive(updated+m)
    
    return p, updated
 
  def getSideAndDistance(self,x,tag=None):
    """
    returns the side and the distance at ``x`` from the fault ``tag``. 

    :param x: location(s)
    :type x: `escript.Data` object or `numpy.ndarray`
    :param tag: the tag of the fault
    :return: the side of ``x`` (positive means to the right of the fault, negative to the left) and the distance to the fault. Note that a value zero for the side means that that the side is undefined.
    """
    d=None
    side=None
    if self.getDim()==2:
        mat=numpy.array([[0., 1.], [-1., 0.] ])
        s=self.getTopPolyline(tag)
        for i in xrange(1,len(s)):
           q=(s[i]-s[i-1])
           h=x-s[i-1]
           q_l=length(q)
           qt=matrixmult(mat,q)   # orthogonal direction
           t=inner(q,h)/q_l**2
           t=maximum(minimum(t,1,),0.)
           p=h-t*q
           dist=length(p)
           lside=sign(inner(p,qt))
           if d == None:
               d=dist
               side=lside
           else:
               m=whereNegative(d-dist)
               m2=wherePositive(whereZero(abs(lside))+m)
               d=dist*(1-m)+d*m
               side=lside*(1-m2)+side*m2
    else:
        ns=self.getSegmentNormals(tag)
        top=self.getTopPolyline(tag)
        bottom=self.getBottomPolyline(tag)
        for i in xrange(len(top)-1):
            h=x-top[i]
            R=top[i+1]-top[i]
            r=bottom[i+1]-bottom[i]
            D0=bottom[i]-top[i]
            D1=bottom[i+1]-top[i+1]
            s_upper=matrix_mult(numpy.linalg.pinv(numpy.vstack((R,D1)).T),h)
            s_lower=matrix_mult(numpy.linalg.pinv(numpy.vstack((r,D0)).T),h)
            m_ul=wherePositive(s_upper[0]-s_upper[1])
            s=s_upper*m_ul+s_lower*(1-m_ul)
            s=maximum(minimum(s,1.),0)
            p=h-(m_ul*R+(1-m_ul)*r)*s[0]-(m_ul*D1+(1-m_ul)*D0)*s[1]
            dist=length(p)
            lside=sign(inner(p,ns[i]))
            if d == None:
               d=dist
               side=lside
            else:
               m=whereNegative(d-dist)
               m2=wherePositive(whereZero(abs(lside))+m)
               d=dist*(1-m)+d*m
               side=lside*(1-m2)+side*m2

    return side, d
