source: inundation/ga/storm_surge/pyvolution/util.py @ 850

"""This modul contains various auxiliary function used by pyvolution.

It is also a clearing house for function tat may later earn a module
of their own.
"""

def angle(v):
    """Compute angle between e1 (the unit vector in the x-direction)
    and the specified vector
    """

    from math import acos, pi, sqrt
    from Numeric import sum, array

    l = sqrt( sum (array(v)**2))
    v1 = v[0]/l
    v2 = v[1]/l
        
    theta = acos(v1)

    if v2 < 0:
        #Quadrant 3 or 4
        theta = 2*pi-theta

    return theta


def anglediff(v0, v1):
    """Compute difference between angle of vector x0, y0 and x1, y1.
    This is used for determining the ordering of vertices,
    e.g. for checking if they are counter clockwise. 
    
    Always return a positive value
    """
        
    from math import pi
    
    a0 = angle(v0)
    a1 = angle(v1)

    #Ensure that difference will be positive
    if a0 < a1:
        a0 += 2*pi
            
    return a0-a1


def mean(x):
    from Numeric import sum
    return sum(x)/len(x)


def point_on_line(x, y, x0, y0, x1, y1): 
    """Determine whether a point is on a line segment 
   
    Input: x, y, x0, x0, x1, y1: where
        point is given by x, y
        line is given by (x0, y0) and (x1, y1)
        
    """
        
    from Numeric import array, dot, allclose
    from math import sqrt

    a = array([x - x0, y - y0]) 
    a_normal = array([a[1], -a[0]])
                        
    b = array([x1 - x0, y1 - y0])
    
    if dot(a_normal, b) == 0:
        #Point is somewhere on the infinite extension of the line

        len_a = sqrt(sum(a**2))                
        len_b = sqrt(sum(b**2))                                 
        if dot(a, b) >= 0 and len_a <= len_b:
           return True
        else:   
           return False
    else:
      return False  
    

def file_function(filename, domain=None, quantities = None, interpolation_points = None):  
    assert type(filename) == type(''),\
               'First argument to File_function must be a string'

    try:
        fid = open(filename)
    except Exception, e:
        msg = 'File "%s" could not be opened: Error="%s"'\
                  %(filename, e)
        raise msg

    line = fid.readline()
    fid.close()

    if domain is not None:
        quantities = domain.conserved_quantities   
    else:
        quantities = None
        
    #Choose format 
    #FIXME: Maybe these can be merged later on
    if line[:3] == 'CDF':
        return File_function_NetCDF(filename, domain, quantities, interpolation_points)
    else:
        return File_function_ASCII(filename, domain, quantities, interpolation_points)    
           
             
class File_function_NetCDF:
    """Read time history of spatial data from NetCDF sww file and 
    return a callable object f(t,x,y)  
    which will return interpolated values based on the input file.    
    
    x, y may be either scalars or vectors
    
    #FIXME: More about format, interpolation  and order of quantities
    
    The quantities returned by the callable objects are specified by
    the list quantities which must contain the names of the 
    quantities to be returned and also reflect the order, e.g. for
    the shallow water wave equation, on would have 
    quantities = ['stage', 'xmomentum', 'ymomentum']
    
    interpolation_points decides at which points interpolated quantities are to be computed
    If None, return average value
    """
    
    def  __init__(self, filename, domain=None, quantities=None, interpolation_points=None):
        """Initialise callable object from a file.

        If domain is specified, model time (domain.starttime)
        will be checked and possibly modified
        


        All times are assumed to be in UTC
        """

        import time, calendar
        from config import time_format
        from Scientific.IO.NetCDF import NetCDFFile     

        #Open NetCDF file
        fid = NetCDFFile(filename, 'r')

        if quantities is None or len(quantities) < 1:
            msg = 'ERROR: File must contain at least one independent value'
            raise msg

        missing = []
        for quantity in ['x', 'y', 'time'] + quantities:
             if not fid.variables.has_key(quantity):
                 missing.append(quantity)
                 
        if len(missing) > 0:
            msg = 'Quantities %s could not be found in file %s'\
                  %(str(missing), filename)
            raise msg
                 

        #Get first timestep
        try:
            starttime = fid.starttime[0]
        except ValueError:    
            msg = 'Could not read starttime from file %s' %filename
            raise msg

    
        self.number_of_values = len(quantities)
        self.fid = fid
        self.filename = filename
        self.starttime = starttime
        self.quantities = quantities
        self.domain = domain

        if domain is not None:
            msg = 'WARNING: Start time as specified in domain (%s)'\
                  %domain.starttime
            msg += ' is earlier than the starttime of file %s: %s.'\
                     %(self.filename, self.starttime)
            msg += 'Modifying starttime accordingly.'
            if self.starttime > domain.starttime:
                #FIXME: Print depending on some verbosity setting
                #print msg
                domain.starttime = self.starttime #Modifying model time

        #Read all data in and produce values for desired data points at each timestep 
        self.spatial_interpolation(interpolation_points) 
    

    def spatial_interpolation(self, interpolation_points):
        """For each timestep in fid: read surface, interpolate to desired points 
        and store values for use when object is called.
        """
        
        from Numeric import array, zeros, Float, alltrue, concatenate

        from config import time_format
        from least_squares import Interpolation
        import time, calendar
        
        fid = self.fid

        #Get variables
        x = fid.variables['x']
        y = fid.variables['y']
        z = fid.variables['elevation']
        triangles = fid.variables['volumes']
        time = fid.variables['time']
        
        #Check
        msg = 'File %s must list time as a monotonuosly ' %self.filename
        msg += 'increasing sequence'
        assert alltrue( time[1:] - time[:-1] > 0 ), msg 
        

        if interpolation_points is not None: 
        
            try:
                P = array(interpolation_points) 
            except:
                msg = 'Interpolation points must be an N x 2 Numeric array or a list of points\n'
                msg += 'I got: %s.' %( str(interpolation_points)[:60] + '...')
                raise msg
            
            
            ####self.Q = zeros( (len(time),
             
            for i, t in enumerate(time[:]):
    
                #Interpolate quantities at this timestep 
                vertex_coordinates = concatenate((x,y), axis=1) #m x 2 array
                interpol = Interpolation(vertex_coordinates, 
                                         triangles,
                                         point_coordinates = P,
                                         alpha = 0, 
                                         verbose = False)

                for name in self.quantities:                            
                    print t, name, interpol.interpolate(fid.variables[name][i,:])                    

        else:
            pass 

        self.T = time[:]
        
        return
        
        fid = open(self.filename)        
        lines = fid.readlines()
        fid.close()
        
        N = len(lines)
        d = self.number_of_values

        T = zeros(N, Float)       #Time
        Q = zeros((N, d), Float)  #Values
        
        for i, line in enumerate(lines):
            fields = line.split(',')
            realtime = calendar.timegm(time.strptime(fields[0], time_format))

            T[i] = realtime - self.starttime

            for j, value in enumerate(fields[1].split()):
                Q[i, j] = float(value)



        self.T = T     #Time
        self.Q = Q     #Values
        self.index = 0 #Initial index

        
             
class File_function_ASCII:
    """Read time series from file and return a callable object:
    f(t,x,y)
    which will return interpolated values based on the input file.

    The file format is assumed to be either two fields separated by a comma:

        time [DD/MM/YY hh:mm:ss], value0 value1 value2 ...

    or four comma separated fields

        time [DD/MM/YY hh:mm:ss], x, y, value0 value1 value2 ...

    In either case, the callable object will return a tuple of
    interpolated values, one each value stated in the file.

    
    E.g

      31/08/04 00:00:00, 1.328223 0 0
      31/08/04 00:15:00, 1.292912 0 0

    will provide a time dependent function f(t,x=None,y=None),
    ignoring x and y, which returns three values per call.

    
    NOTE: At this stage the function is assumed to depend on
    time only, i.e  no spatial dependency!!!!!
    When that is needed we can use the least_squares interpolation.
    
    #FIXME: This should work with netcdf (e.g. sww) and thus render the 
    #spatio-temporal boundary condition in shallow water fully general
    
    #FIXME: Specified quantites not used here - 
    #always return whatever is in the file
    """

    
    def __init__(self, filename, domain=None, quantities = None, interpolation_points=None):
        """Initialise callable object from a file.
        See docstring for class File_function

        If domain is specified, model time (domain,starttime)
        will be checked and possibly modified

        All times are assumed to be in UTC
        """

        import time, calendar
        from Numeric import array
        from config import time_format

        fid = open(filename)
        line = fid.readline()
        fid.close()
    
        fields = line.split(',')
        msg = 'File %s must have the format date, value0 value1 value2 ...'
        msg += ' or date, x, y, value0 value1 value2 ...'
        mode = len(fields)
        assert mode in [2,4], msg

        try:
            starttime = calendar.timegm(time.strptime(fields[0], time_format))
        except ValueError:    
            msg = 'First field in file %s must be' %filename
            msg += ' date-time with format %s.\n' %time_format
            msg += 'I got %s instead.' %fields[0] 
            raise msg


        #Split values
        values = []
        for value in fields[mode-1].split():
            values.append(float(value))

        q = array(values)
        
        msg = 'ERROR: File must contain at least one independent value'
        assert len(q.shape) == 1, msg
            
        self.number_of_values = len(q)

        self.filename = filename
        self.starttime = starttime
        self.domain = domain

        if domain is not None:
            msg = 'WARNING: Start time as specified in domain (%s)'\
                  %domain.starttime
            msg += ' is earlier than the starttime of file %s: %s.'\
                     %(self.filename, self.starttime)
            msg += 'Modifying starttime accordingly.'
            if self.starttime > domain.starttime:
                #FIXME: Print depending on some verbosity setting
                #print msg
                domain.starttime = self.starttime #Modifying model time
        
            #if domain.starttime is None:
            #    domain.starttime = self.starttime
            #else:
            #    msg = 'WARNING: Start time as specified in domain (%s)'\
            #          %domain.starttime
            #    msg += ' is earlier than the starttime of file %s: %s.'\
            #             %(self.filename, self.starttime)
            #    msg += 'Modifying starttime accordingly.'
            #    if self.starttime > domain.starttime:
            #        #FIXME: Print depending on some verbosity setting
            #        #print msg
            #        domain.starttime = self.starttime #Modifying model time

        if mode == 2:        
            self.read_times() #Now read all times in.
        else:
            raise 'x,y dependency not yet implemented'

        
    def read_times(self):
        """Read time and values 
        """
        from Numeric import zeros, Float, alltrue
        from config import time_format
        import time, calendar
        
        fid = open(self.filename)        
        lines = fid.readlines()
        fid.close()
        
        N = len(lines)
        d = self.number_of_values

        T = zeros(N, Float)       #Time
        Q = zeros((N, d), Float)  #Values
        
        for i, line in enumerate(lines):
            fields = line.split(',')
            realtime = calendar.timegm(time.strptime(fields[0], time_format))

            T[i] = realtime - self.starttime

            for j, value in enumerate(fields[1].split()):
                Q[i, j] = float(value)

        msg = 'File %s must list time as a monotonuosly ' %self.filename
        msg += 'increasing sequence'
        assert alltrue( T[1:] - T[:-1] > 0 ), msg

        self.T = T     #Time
        self.Q = Q     #Values
        self.index = 0 #Initial index

        
    def __repr__(self):
        return 'File function'

        

    def __call__(self, t, x=None, y=None):
        """Evaluate f(t,x,y)

        FIXME: x, y dependency not yet implemented except that
        result is a vector of same length as x and y
        FIXME: Naaaa
        """

        from math import pi, cos, sin, sqrt
        

        #Find time tau such that
        #
        # domain.starttime + t == self.starttime + tau
        
        if self.domain is not None:
            tau = self.domain.starttime-self.starttime+t
        else:
            tau = t
        
                
        msg = 'Time interval derived from file %s (%s:%s) does not match model time: %s'\
              %(self.filename, self.T[0], self.T[1], tau)
        if tau < self.T[0]: raise msg
        if tau > self.T[-1]: raise msg        

        oldindex = self.index

        #Find slot
        while tau > self.T[self.index]: self.index += 1
        while tau < self.T[self.index]: self.index -= 1

        #t is now between index and index+1
        ratio = (tau - self.T[self.index])/\
                (self.T[self.index+1] - self.T[self.index])

        #Compute interpolated values
        q = self.Q[self.index,:] +\
            ratio*(self.Q[self.index+1,:] - self.Q[self.index,:]) 

        #Return vector of interpolated values
        if x == None and y == None:
            return q
        else:
            try:
                N = len(x)
            except:
                return q
            else:
                from Numeric import ones, Float
                #x is a vector - Create one constant column for each value
                N = len(x)
                assert len(y) == N, 'x and y must have same length'
             
                res = []
                for col in q:
                    res.append(col*ones(N, Float))
            
                return res
            
            
#FIXME: TEMP        
class File_function_copy:
    """Read time series from file and return a callable object:
    f(t,x,y)
    which will return interpolated values based on the input file.

    The file format is assumed to be either two fields separated by a comma:

        time [DD/MM/YY hh:mm:ss], value0 value1 value2 ...

    or four comma separated fields

        time [DD/MM/YY hh:mm:ss], x, y, value0 value1 value2 ...

    In either case, the callable object will return a tuple of
    interpolated values, one each value stated in the file.

    
    E.g

      31/08/04 00:00:00, 1.328223 0 0
      31/08/04 00:15:00, 1.292912 0 0

    will provide a time dependent function f(t,x=None,y=None),
    ignoring x and y, which returns three values per call.

    
    NOTE: At this stage the function is assumed to depend on
    time only, i.e  no spatial dependency!!!!!
    When that is needed we can use the least_squares interpolation.
    
    #FIXME: This should work with netcdf (e.g. sww) and thus render the 
    #spatio-temporal boundary condition in shallow water fully general
    """

    
    def __init__(self, filename, domain=None):
        """Initialise callable object from a file.
        See docstring for class File_function

        If domain is specified, model time (domain,starttime)
        will be checked and possibly modified

        All times are assumed to be in UTC
        """

        import time, calendar
        from Numeric import array
        from config import time_format

        assert type(filename) == type(''),\
               'First argument to File_function must be a string'


        try:
            fid = open(filename)
        except Exception, e:
            msg = 'File "%s" could not be opened: Error="%s"'\
                  %(filename, e)
            raise msg


        line = fid.readline()
        fid.close()
        fields = line.split(',')
        msg = 'File %s must have the format date, value0 value1 value2 ...'
        msg += ' or date, x, y, value0 value1 value2 ...'
        mode = len(fields)
        assert mode in [2,4], msg

        try:
            starttime = calendar.timegm(time.strptime(fields[0], time_format))
        except ValueError:    
            msg = 'First field in file %s must be' %filename
            msg += ' date-time with format %s.\n' %time_format
            msg += 'I got %s instead.' %fields[0] 
            raise msg


        #Split values
        values = []
        for value in fields[mode-1].split():
            values.append(float(value))

        q = array(values)
        
        msg = 'ERROR: File must contain at least one independent value'
        assert len(q.shape) == 1, msg
            
        self.number_of_values = len(q)

        self.filename = filename
        self.starttime = starttime
        self.domain = domain

        if domain is not None:
            if domain.starttime is None:
                domain.starttime = self.starttime
            else:
                msg = 'WARNING: Start time as specified in domain (%s)'\
                      %domain.starttime
                msg += ' is earlier than the starttime of file %s: %s.'\
                         %(self.filename, self.starttime)
                msg += 'Modifying starttime accordingly.'
                if self.starttime > domain.starttime:
                    #FIXME: Print depending on some verbosity setting
                    #print msg
                    domain.starttime = self.starttime #Modifying model time

        if mode == 2:        
            self.read_times() #Now read all times in.
        else:
            raise 'x,y dependency not yet implemented'

        
    def read_times(self):
        """Read time and values 
        """
        from Numeric import zeros, Float, alltrue
        from config import time_format
        import time, calendar
        
        fid = open(self.filename)        
        lines = fid.readlines()
        fid.close()
        
        N = len(lines)
        d = self.number_of_values

        T = zeros(N, Float)       #Time
        Q = zeros((N, d), Float)  #Values
        
        for i, line in enumerate(lines):
            fields = line.split(',')
            realtime = calendar.timegm(time.strptime(fields[0], time_format))

            T[i] = realtime - self.starttime

            for j, value in enumerate(fields[1].split()):
                Q[i, j] = float(value)

        msg = 'File %s must list time as a monotonuosly ' %self.filename
        msg += 'increasing sequence'
        assert alltrue( T[1:] - T[:-1] > 0 ), msg

        self.T = T     #Time
        self.Q = Q     #Values
        self.index = 0 #Initial index

        
    def __repr__(self):
        return 'File function'

        

    def __call__(self, t, x=None, y=None):
        """Evaluate f(t,x,y)

        FIXME: x, y dependency not yet implemented except that
        result is a vector of same length as x and y
        FIXME: Naaaa
        """

        from math import pi, cos, sin, sqrt
        

        #Find time tau such that
        #
        # domain.starttime + t == self.starttime + tau
        
        if self.domain is not None:
            tau = self.domain.starttime-self.starttime+t
        else:
            tau = t
        
                
        msg = 'Time interval derived from file %s (%s:%s) does not match model time: %s'\
              %(self.filename, self.T[0], self.T[1], tau)
        if tau < self.T[0]: raise msg
        if tau > self.T[-1]: raise msg        

        oldindex = self.index

        #Find slot
        while tau > self.T[self.index]: self.index += 1
        while tau < self.T[self.index]: self.index -= 1

        #t is now between index and index+1
        ratio = (tau - self.T[self.index])/\
                (self.T[self.index+1] - self.T[self.index])

        #Compute interpolated values
        q = self.Q[self.index,:] +\
            ratio*(self.Q[self.index+1,:] - self.Q[self.index,:]) 

        #Return vector of interpolated values
        if x == None and y == None:
            return q
        else:
            try:
                N = len(x)
            except:
                return q
            else:
                from Numeric import ones, Float
                #x is a vector - Create one constant column for each value
                N = len(x)
                assert len(y) == N, 'x and y must have same length'
             
                res = []
                for col in q:
                    res.append(col*ones(N, Float))
            
                return res
            

def read_xya(filename, format = 'netcdf'):
    """Read simple xya file, possibly with a header in the first line, just
    x y [attributes]
    separated by whitespace

    Format can be either ASCII or NetCDF
   
    Return list of points, list of attributes and
    attribute names if present otherwise None
    """
    #FIXME: Probably obsoleted by similar function in load_ASCII
    
    from Scientific.IO.NetCDF import NetCDFFile

    if format.lower() == 'netcdf': 
        #Get NetCDF
        
        fid = NetCDFFile(filename, 'r') 
      
        # Get the variables
        points = fid.variables['points']
        keys = fid.variables.keys()
        attributes = {}
        for key in keys:
            attributes[key] = fid.variables[key]
        #Don't close - arrays are needed outside this function,
        #alternatively take a copy here
    else:    
        #Read as ASCII file assuming that it is separated by whitespace
        fid = open(filename)
        lines = fid.readlines()
        fid.close()

        #Check if there is a header line
        fields = lines[0].strip().split()
        try:
            float(fields[0])
        except:
            #This must be a header line
            attribute_names = fields
            lines = lines[1:]
        else:
            attribute_names = ['elevation']  #HACK

        attributes = {}    
        for key in attribute_names:
            attributes[key] = []

        points = []
        for line in lines:
            fields = line.strip().split()
            points.append( (float(fields[0]), float(fields[1])) )
            for i, key in enumerate(attribute_names):
                attributes[key].append( float(fields[2+i]) )
        
    return points, attributes
    

#####################################
#POLYGON STUFF
#
#FIXME: ALl these should be put into new module polygon.py

def inside_polygon(point, polygon, closed = True):
    """Determine whether points are inside or outside a polygon
    
    Input:
       point - Tuple of (x, y) coordinates, or list of tuples
       polygon - list of vertices of polygon
       closed - (optional) determine whether points on boundary should be 
       regarded as belonging to the polygon (closed = True) 
       or not (closed = False) 
    
    Output:
       If one point is considered, True or False is returned.
       If multiple points are passed in, the function returns indices 
       of those points that fall inside the polygon     
       
    Examples:
       inside_polygon( [0.5, 0.5], [[0,0], [1,0], [1,1], [0,1]] )
       will evaluate to True as the point 0.5, 0.5 is inside the unit square 
       
       inside_polygon( [[0.5, 0.5], [1, -0.5], [0.3, 0.2]] )
       will return the indices [0, 2] as only the first and the last point 
       is inside the unit square
       
    Remarks:
       The vertices may be listed clockwise or counterclockwise and
       the first point may optionally be repeated.    
       Polygons do not need to be convex.
       Polygons can have holes in them and points inside a hole is 
       regarded as being outside the polygon.          
               
       
    Algorithm is based on work by Darel Finley, 
    http://www.alienryderflex.com/polygon/ 
    
    """    

    from Numeric import array, Float, reshape
    
    
    #Input checks
    try:
        point = array(point).astype(Float)         
    except:
        msg = 'Point %s could not be converted to Numeric array' %point
        raise msg        
        
    try:
        polygon = array(polygon).astype(Float)             
    except:
        msg = 'Polygon %s could not be converted to Numeric array' %polygon
        raise msg               
    
    assert len(polygon.shape) == 2,\
       'Polygon array must be a 2d array of vertices: %s' %polygon

        
    assert polygon.shape[1] == 2,\
       'Polygon array must have two columns: %s' %polygon    


    if len(point.shape) == 1:
        one_point = True
        points = reshape(point, (1,2))
    else:       
        one_point = False
        points = point

    N = polygon.shape[0] #Number of vertices in polygon 

    px = polygon[:,0]
    py = polygon[:,1]   

    #Begin algorithm
    indices = []
    for k in range(points.shape[0]):
        #for each point   
        x = points[k, 0]
        y = points[k, 1]        

        inside = False
        for i in range(N):
            j = (i+1)%N
            
            #Check for case where point is contained in line segment    
            if point_on_line(x, y, px[i], py[i], px[j], py[j]):
                if closed:
                    inside = True
                else:        
                    inside = False
                break
            else:        
                #Check if truly inside polygon              
                if py[i] < y and py[j] >= y or\
                   py[j] < y and py[i] >= y:
                    if px[i] + (y-py[i])/(py[j]-py[i])*(px[j]-px[i]) < x:
                        inside = not inside
                    
        if inside: indices.append(k)

    if one_point: 
        return inside
    else:
        return indices
             

class Polygon_function:
    """Create callable object f: x,y -> z, where a,y,z are vectors and 
    where f will return different values depending on whether x,y belongs 
    to specified polygons.
    
    To instantiate:
      
       Polygon_function(polygons)
       
    where polygons is a dictionary of the form
    
      {P0: v0, P1: v1, ...}
      
      with Pi being lists of vertices defining polygons and vi either 
      constants or functions of x,y to be applied to points with the polygon.
      
    The function takes an optional argument, default which is the value 
    (or function) to used for points not belonging to any polygon.
    For example:
    
       Polygon_function(polygons, default = 0.03)       
      
    If omitted the default value will be 0.0  
    
    Note: If two polygons overlap, the one last in the list takes precedence

    """
    
    def __init__(self, regions, default = 0.0):
        
        try:
            len(regions)
        except:
            msg = 'Polygon_function takes a list of pairs (polygon, value). Got %s' %polygons           
            raise msg


        T = regions[0]                                   
        try:
            a = len(T)
        except:    
            msg = 'Polygon_function takes a list of pairs (polygon, value). Got %s' %polygons           
            raise msg   
                   
        assert a == 2, 'Must have two component each: %s' %T       

        self.regions = regions             
        self.default = default
         
         
    def __call__(self, x, y):
        from util import inside_polygon
        from Numeric import ones, Float, concatenate, array, reshape, choose
        
        x = array(x).astype(Float)
        y = array(y).astype(Float)      
        
        N = len(x)
        assert len(y) == N
        
        points = concatenate( (reshape(x, (N, 1)), 
                               reshape(y, (N, 1))), axis=1 )

        if callable(self.default):
            z = self.default(x,y)
        else:                   
            z = ones(N, Float) * self.default
            
        for polygon, value in self.regions:
            indices = inside_polygon(points, polygon)
            
            #FIXME: This needs to be vectorised 
            if callable(value):
                for i in indices:
                    xx = array([x[i]])
                    yy = array([y[i]])
                    z[i] = value(xx, yy)[0]
            else:    
                for i in indices:
                    z[i] = value 

        return z                 

def read_polygon(filename):
    """Read points assumed to form a polygon
       There must be exactly two numbers in each line
    """              
    
    #Get polygon
    fid = open(filename)
    lines = fid.readlines()
    fid.close()
    polygon = []
    for line in lines:
        fields = line.split(',')
        polygon.append( [float(fields[0]), float(fields[1])] )

    return polygon      
    
def populate_polygon(polygon, number_of_points, seed = None):
    """Populate given polygon with uniformly distributed points.

    Input:
       polygon - list of vertices of polygon
       number_of_points - (optional) number of points 
       seed - seed for random number generator (default=None)
       
    Output:
       points - list of points inside polygon
       
    Examples:
       populate_polygon( [[0,0], [1,0], [1,1], [0,1]], 5 )
       will return five randomly sleected points inside the unit square 
    """

    from random import uniform, seed

    seed(seed)

    points = []

    #Find outer extent of polygon
    max_x = min_x = polygon[0][0]
    max_y = min_y = polygon[0][1]
    for point in polygon[1:]:
        x = point[0] 
        if x > max_x: max_x = x
        if x < min_x: min_x = x           
        y = point[1] 
        if y > max_y: max_y = y
        if y < min_y: min_y = y           


    while len(points) < number_of_points:     
        x = uniform(min_x, max_x)
        y = uniform(min_y, max_y)        

        if inside_polygon( [x,y], polygon ):
            points.append([x,y])

    return points

####################################################################
#Python versions of function that are also implemented in util_gateway.c
#

def gradient_python(x0, y0, x1, y1, x2, y2, q0, q1, q2):
    """
    """
    
    det = (y2-y0)*(x1-x0) - (y1-y0)*(x2-x0)            
    a = (y2-y0)*(q1-q0) - (y1-y0)*(q2-q0)
    a /= det

    b = (x1-x0)*(q2-q0) - (x2-x0)*(q1-q0)
    b /= det            

    return a, b





##############################################
#Initialise module

import compile
if compile.can_use_C_extension('util_ext.c'):
    from util_ext import gradient, point_on_line 
else:
    gradient = gradient_python


if __name__ == "__main__":
    pass