underworld.function.shape module

This module includes shape type functions. Shape functions generally define some geometric object, and return boolean values to indicate whether the queried locations are inside or outside the shape.

Module Summary

classes:

underworld.function.shape.input	This class generates a function which simply passes through its input.
underworld.function.shape.Polygon	This function creates a polygon shape.

Module Details

classes:

class underworld.function.shape.input(*args, **kwargs)

Bases: underworld.function._function.Function

This class generates a function which simply passes through its input. It is the identity function. It is often useful when construct functions where the input itself needs to be accessed, such as to extract a particular component.

For example, you may wish to use this function when you wish to extract a particular coordinate component for manipulation. For this reason, we also provide an alias to this class called ‘coord’.

Returns:fn.input Return type:the input function

Examples

Here we see the input function simply passing through its input.

>>> infunc = input()
>>> np.allclose( infunc.evaluate( (1.,2.,3.) ), [ 1., 2., 3.] )
True

Often this behaviour is useful when we want to construct a function which operates on only a particular coordinate, such as a depth dependent density. We may wish to extract the z coordinate (in 2d):

>>> zcoord = input()[1]
>>> baseDensity = 1.
>>> density = baseDensity - 0.01*zcoord
>>> testCoord1 = (0.1,0.4)
>>> testCoord2 = (0.9,0.4)
>>> np.allclose( density.evaluate( testCoord1 ), density.evaluate( testCoord2 ) )
True

class underworld.function.shape.Polygon(vertices, fn=None, *args, **kwargs)

Bases: underworld.function._function.Function

This function creates a polygon shape. Note that this is strictly a 2d shape, and the third dimension of any query will be ignored. You may create a box type function if you wish to limit the shape extent in the third dimension.

You will need to use rotations to orient the polygon in other directions. Rotations functions will be available shortly (hopefully!).

Parameters:

• vertices (np.ndarray) – This array provides the vertices for the polygon. Note that the order of the vertices is important. The polygon is defined by a piecewise linear edge joining the vertices in the order provided by the array. The final vertex and the initial vertex are joined to complete the polygon.
• fn (underworld.function.Function, default=None) – This is the input function. Generally it will not be required, but you may need to use (for example) to transform the incoming coordinates.

Example

In this example we will create a triangle shape and test some points.

>>> import underworld as uw
>>> import numpy as np

Create the array to define the triangle, and the function

>>> vertex_array = np.array( [(0.0,0.0),(0.5,1.0),(1.0,0.0)] )
>>> polyfn = uw.function.shape.Polygon(vertex_array)

Create some test points, and do a test evaluation

>>> test_array = np.array( [(0.0,0.9),(0.5,0.5),(0.9,0.2)] )
>>> polyfn.evaluate(test_array)
array([[False],
       [ True],
       [False]], dtype=bool)