25. geometry — A generic interface to the Coords transformation methods

This module defines a generic Geometry superclass which adds all the possibilities of coordinate transformations offered by the Coords class to the derived classes.

class geometry.Geometry

A virtual base class for all geometry classes in pyFormex.

The Geometry class is a generic parent class for all geometry classes in pyFormex. It is not intended to be used directly, but only through derived classes. Examples of derived classes are Formex, Mesh, TriSurface, PolyLine, BezierSpline, Polygons.

The basic entity of geometry is the point, defined by its coordinates. The Geometry class expects these to be stored in a Coords object assigned to the coords attribute (it is the responsability of the derived class object initialisation to do this).

The Geometry class exposes the following attributes of the coords attribute, so that they can be directly used on the Geometry object: xyz, x, y, z, xy, yz, xz.

The Geometry class exposes a large set of Coords methods for direct use on the derived class objects. These methods are automatically executed on the coords attribute of the object. One set of such methods are those returning some information about the Coords: points(), bbox(), center(), bboxPoint(), centroid(), sizes(), dsize(), bsphere(), bboxes(), inertia(), principalCS(), principalSizes(), distanceFromPlane(), distanceFromLine(), distanceFromPoint(), directionalSize(), directionalWidth(), directionalExtremes(). Thus, if F is an instance of class Formex, then one can use F.center() as a convenient shorthand for F.coords.center().

Likewise, most of the transformation methods of the :class:~coords.Coords` class are exported through the Geometry class to the derived classes. When called, they will return a new object identical to the original, except for the coordinates, which are transformed by the specified method. Refer to the correponding Coords method for the precise arguments of these methods: scale(), adjust(), translate(), centered(), align(), rotate(), shear(), reflect(), affine(), toCS(), fromCS(), transformCS(), position(), cylindrical(), hyperCylindrical(), toCylindrical(), spherical(), superSpherical(), toSpherical(), circulize(), bump(), flare(), map(), map1(), mapd(), copyAxes(), swapAxes(), permuteAxes(), rollAxes(), projectOnPlane(), projectOnSphere(), projectOnCylinder(), isopar(), addNoise(), rot(), trl().

Geometry is a lot more than points however. Therefore the Geometry and its derived classes can represent higher level entities, such as lines, planes, circles, triangles, cubes,… These entities are often represented by multiple points: a line segment would e.g. need two points, a triangle three. Geometry subclasses can implement collections of many such entities, just like the Coords can hold many points. We call these geometric entities ‘elements’. The subclass must at least define a method nelems() returning the number of elements in the object, even if there is only one.

The Geometry class allows the attribution of a property number per element. This is an integer number that can be used as the subclass or user wants. It could be just the element number, or a key into a database with lots of more element attributes. The Geometry class provides methods to handle these property numbers.

The Geometry class provides a separate mechanism to store attributes related to how the geometry should be rendered. For this purpose the class defines an attrib attribute which is an object of class Attributes. This attribute is callable to set any key/value pairs in its dict. For example, F.attrib(color=yellow) will make the object F always be drawn in yellow.

The Geometry class provides for adding fields to instances of the derived classes. Fields are numerical data (scalar or vectorial) that are defined over the geometry. For example, if the geometry represents a surface, the gaussian curvature of that surface is a field defined over the surface. Field data are stored in Field objects and the Geometry object stores them internally in a dict object with the field name as key. The dict is kept in an attribute fields that is only created when the first Field is added to the object.

Finally, the Geometry class also provides the interface for storing the Geometry object on a file in pyFormex’s own ‘pgf’ format.

Note

When subclassing the Geometry class, care should be taken to obey some rules in order for all the above to work properly. See UserGuide.

setAttrib(**kargs)

Set attributes on the Geometry.

While the attributes can be directly set by calling self.attrib, using this function returns the parent object and can thus be chained in a sequence of calls:

M = Mesh(...)
M.attrib(**kargs)
M = M.transform(...)

can thus be replaced by:

M = Mesh(...).setAttrib(**kargs).transform(...)

property xyz

Return the xyz property of the coords attribute of the Geometry object.

See coords.Coords.xyz for details.

property x

Return the x property of the coords attribute of the Geometry object.

See coords.Coords.x for details.

property y

Return the y property of the coords attribute of the Geometry object.

See coords.Coords.y for details.

property z

Return the z property of the coords attribute of the Geometry object.

See coords.Coords.z for details.

property xy

Return the xy property of the coords attribute of the Geometry object.

See coords.Coords.xy for details.

property yz

Return the yz property of the coords attribute of the Geometry object.

See coords.Coords.yz for details.

property xz

Return the xz property of the coords attribute of the Geometry object.

See coords.Coords.xz for details.

abstract nelems()

Return the number of elements in the Geometry.

Returns:

int – The number of elements in the Geometry. This is an abstract method that should be reimplemented by the derived class.

level()

Return the dimensionality of the Geometry

The level of a Geometry is the dimensionality of the geometric object(s) represented:

• 0: points

• 1: line objects

• 2: surface objects

• 3: volume objects

Returns:

int – The level of the Geometry, or -1 if it is unknown. This should be implemented by the derived class. The Geometry base class always returns -1.

info()

Return a short string representation about the object

points(*args, **kargs)

Call Coords.points method on the Geometry object’s coords.

See coords.Coords.points() for details.

bbox(*args, **kargs)

Call Coords.bbox method on the Geometry object’s coords.

See coords.Coords.bbox() for details.

center(*args, **kargs)

Call Coords.center method on the Geometry object’s coords.

See coords.Coords.center() for details.

bboxPoint(*args, **kargs)

Call Coords.bboxPoint method on the Geometry object’s coords.

See coords.Coords.bboxPoint() for details.

centroid(*args, **kargs)

Call Coords.centroid method on the Geometry object’s coords.

See coords.Coords.centroid() for details.

sizes(*args, **kargs)

Call Coords.sizes method on the Geometry object’s coords.

See coords.Coords.sizes() for details.

dsize(*args, **kargs)

Call Coords.dsize method on the Geometry object’s coords.

See coords.Coords.dsize() for details.

bsphere(*args, **kargs)

Call Coords.bsphere method on the Geometry object’s coords.

See coords.Coords.bsphere() for details.

bboxes(*args, **kargs)

Call Coords.bboxes method on the Geometry object’s coords.

See coords.Coords.bboxes() for details.

inertia(*args, **kargs)

Call Coords.inertia method on the Geometry object’s coords.

See coords.Coords.inertia() for details.

principalCS(*args, **kargs)

Call Coords.principalCS method on the Geometry object’s coords.

See coords.Coords.principalCS() for details.

principalSizes(*args, **kargs)

Call Coords.principalSizes method on the Geometry object’s coords.

See coords.Coords.principalSizes() for details.

distanceFromPlane(*args, **kargs)

Call Coords.distanceFromPlane method on the Geometry object’s coords.

See coords.Coords.distanceFromPlane() for details.

distanceFromLine(*args, **kargs)

Call Coords.distanceFromLine method on the Geometry object’s coords.

See coords.Coords.distanceFromLine() for details.

distanceFromPoint(*args, **kargs)

Call Coords.distanceFromPoint method on the Geometry object’s coords.

See coords.Coords.distanceFromPoint() for details.

directionalSize(*args, **kargs)

Call Coords.directionalSize method on the Geometry object’s coords.

See coords.Coords.directionalSize() for details.

directionalWidth(*args, **kargs)

Call Coords.directionalWidth method on the Geometry object’s coords.

See coords.Coords.directionalWidth() for details.

directionalExtremes(*args, **kargs)

Call Coords.directionalExtremes method on the Geometry object’s coords.

See coords.Coords.directionalExtremes() for details.

convexHull(dir=None, return_mesh=True)

Return the convex hull of a Geometry.

This is the convexHull() applied to the coords attribute, but it has return_mesh=True as default.

Returns:

Mesh – The convex hull of the geometry.

testPlane(p, n, atol=0.0)

Test what parts of a Formex or Mesh are at either side of a plane.

Parameters:

• p (array_like (3,)) – A point in the testing plane

• n (array_like (3,)) – The positive normal on the plane

• atol (float) – Tolerance value to be added to the tests. Specifying a small positive value will make sure that elements located at one side of the plane, but having one or more points inside the plane, will be considered completely at one side. A negative value will include these elements with the ones vut by the plane.

Returns:

• tp (bool array (nelems,)) – True for the elements that are completely at the positive side of the plane

• tc (bool array (nelems,)) – True for the elements that are cut by the plane

• tn (bool array (nelems,)) – True for the elements that are completely at the negative side

testBbox(bb, dirs=(0, 1, 2), nodes='any', atol=0.0)

Test which part of a Formex or Mesh is inside a given bbox.

The Geometry object needs to have a test() method, This is the case for the Formex and Mesh classes. The test can be applied in 1, 2 or 3 viewing directions.

Parameters:

• bb (Coords (2,3) or alike) – The bounding box to test for.

• dirs (tuple of ints (0,1,2)) – The viewing directions in which to check the bbox bounds.

• nodes – Same as in formex.Formex.test() or mesh.Mesh.test().

Returns:

bool array – The array flags the elements that are inside the given bounding box.

scale(*args, **kargs)

Apply the scale transformation to the Geometry object.

See coords.Coords.scale() for details.

resized(size=1.0, tol=1e-05)

Return a copy of the Geometry scaled to the given size.

size can be a single value or a list of three values for the three coordinate directions. If it is a single value, all directions are scaled to the same size. Directions for which the geometry has a size smaller than tol times the maximum size are not rescaled.

adjust(*args, **kargs)

Apply the adjust transformation to the Geometry object.

See coords.Coords.adjust() for details.

translate(*args, **kargs)

Apply the translate transformation to the Geometry object.

See coords.Coords.translate() for details.

centered(*args, **kargs)

Apply the centered transformation to the Geometry object.

See coords.Coords.centered() for details.

align(*args, **kargs)

Apply the align transformation to the Geometry object.

See coords.Coords.align() for details.

rotate(*args, **kargs)

Apply the rotate transformation to the Geometry object.

See coords.Coords.rotate() for details.

shear(*args, **kargs)

Apply the shear transformation to the Geometry object.

See coords.Coords.shear() for details.

reflect(*args, **kargs)

Apply the reflect transformation to the Geometry object.

See coords.Coords.reflect() for details.

affine(*args, **kargs)

Apply the affine transformation to the Geometry object.

See coords.Coords.affine() for details.

toCS(*args, **kargs)

Apply the toCS transformation to the Geometry object.

See coords.Coords.toCS() for details.

fromCS(*args, **kargs)

Apply the fromCS transformation to the Geometry object.

See coords.Coords.fromCS() for details.

transformCS(*args, **kargs)

Apply the transformCS transformation to the Geometry object.

See coords.Coords.transformCS() for details.

position(*args, **kargs)

Apply the position transformation to the Geometry object.

See coords.Coords.position() for details.

cylindrical(*args, **kargs)

Apply the cylindrical transformation to the Geometry object.

See coords.Coords.cylindrical() for details.

hyperCylindrical(*args, **kargs)

Apply the hyperCylindrical transformation to the Geometry object.

See coords.Coords.hyperCylindrical() for details.

toCylindrical(*args, **kargs)

Apply the toCylindrical transformation to the Geometry object.

See coords.Coords.toCylindrical() for details.

spherical(*args, **kargs)

Apply the spherical transformation to the Geometry object.

See coords.Coords.spherical() for details.

superSpherical(*args, **kargs)

Apply the superSpherical transformation to the Geometry object.

See coords.Coords.superSpherical() for details.

toSpherical(*args, **kargs)

Apply the toSpherical transformation to the Geometry object.

See coords.Coords.toSpherical() for details.

circulize(*args, **kargs)

Apply the circulize transformation to the Geometry object.

See coords.Coords.circulize() for details.

bump(*args, **kargs)

Apply the bump transformation to the Geometry object.

See coords.Coords.bump() for details.

flare(*args, **kargs)

Apply the flare transformation to the Geometry object.

See coords.Coords.flare() for details.

map(*args, **kargs)

Apply the map transformation to the Geometry object.

See coords.Coords.map() for details.

map1(*args, **kargs)

Apply the map1 transformation to the Geometry object.

See coords.Coords.map1() for details.

mapd(*args, **kargs)

Apply the mapd transformation to the Geometry object.

See coords.Coords.mapd() for details.

copyAxes(*args, **kargs)

Apply the copyAxes transformation to the Geometry object.

See coords.Coords.copyAxes() for details.

swapAxes(*args, **kargs)

Apply the swapAxes transformation to the Geometry object.

See coords.Coords.swapAxes() for details.

permuteAxes(*args, **kargs)

Apply the permuteAxes transformation to the Geometry object.

See coords.Coords.permuteAxes() for details.

rollAxes(*args, **kargs)

Apply the rollAxes transformation to the Geometry object.

See coords.Coords.rollAxes() for details.

projectOnPlane(*args, **kargs)

Apply the projectOnPlane transformation to the Geometry object.

See coords.Coords.projectOnPlane() for details.

projectOnSphere(*args, **kargs)

Apply the projectOnSphere transformation to the Geometry object.

See coords.Coords.projectOnSphere() for details.

projectOnCylinder(*args, **kargs)

Apply the projectOnCylinder transformation to the Geometry object.

See coords.Coords.projectOnCylinder() for details.

isopar(*args, **kargs)

Apply the isopar transformation to the Geometry object.

See coords.Coords.isopar() for details.

addNoise(*args, **kargs)

Apply the addNoise transformation to the Geometry object.

See coords.Coords.addNoise() for details.

rot(*args, **kargs)

Apply the rotate transformation to the Geometry object.

See coords.Coords.rotate() for details.

trl(*args, **kargs)

Apply the translate transformation to the Geometry object.

See coords.Coords.translate() for details.

setProp(prop=None)

Create or destroy the property array for the Geometry.

A property array is a 1-dim integer array with length equal to the number of elements in the Geometry. Each element thus has its own property number. These numbers can be used for any purpose. In derived classes like Formex and :class`~mesh.Mesh` they play an import role when creating new geometry: new elements inherit the property number of their parent element. Properties are also preserved on pure coordinate transformations.

Because elements with different property numbers can be drawn in different colors, the property numbers are also often used to impose color.

Parameters:

prop (int, int array_like or ‘range’) –

The property number(s) to assign to the elements. If a single int, all elements get the same property value. If the number of passed values is less than the number of elements, the list will be repeated. If more values are passed than the number of elements, the excess ones are ignored.

A special value 'range' may be given to set the property numbers equal to the element number. This is equivalent to passing arange(self.nelems()).

A value None (default) removes the properties from the Geometry.

Returns:

• The calling object self, with the new properties inserted

• or with the properties deleted if argument is None.

Note

This is one of the few operations that change the object in-place. It still returns the object itself, so that this operation can be used in a chain with other operations.

See also

toProp

Create a valid set of properties for the object

whereProp

Find the elements having some property value

toProp(prop)

Create a valid set of properties for the object.

Parameters:

prop (int or int array_like) – The property values to turn into a valid set for the object. If a single int, all elements get the same property value. If the number of passed values is less than the number of elements, the list will be repeated. If more values are passed than the number of elements, the excess ones are ignored.

Returns:

int array – A 1-dim int array that is valid as a property array for the Geometry object. The length of the array will is self.nelems() and the dtype is Int.

See also

setProp

Set the properties for the object

whereProp

Find the elements having some property value

Note

When you set the properties (using setProp()) you do not need to call this method to validate the properties. It is implicitely called from setProp().

maxProp()

Return the highest property value used.

Returns:

int – The highest value used in the properties array, or -1 if there are no properties.

propSet()

Return a list with unique property values in use.

Returns:

int array – The unique values in the properties array. If no properties are defined, an empty array is returned.

propDict()

Return a dict with the elements grouped per prop value.

Returns:

dict – A dict where the keys are the unique prop values and the values are the lists of element numbers having that prop value. The dict is empty if the object doen’t have prop numbers.

whereProp(prop)

Find the elements having some property value.

Parameters:

prop (int or int array_like) – The property value(s) to be found.

Returns:

int array – A 1-dim int array with the indices of all the elements that have the property value prop, or one of the values in prop.

If the object has no properties, an empty array is returned.

See also

setProp

Set the properties for the object

toProp

Create a valid set of properties for the object

selectProp

Return a Geometry object with only the matching elements

copy()

Return a deep copy of the Geometry object.

Returns:

Geometry (or subclass) object – An object of the same class as the caller, having all the same data (for coords, prop, attrib, fields, and any other attributes possibly set by the subclass), but not sharing any data with the original object.

Note

This is seldomly used, because it may cause wildly superfluous copying of data. Only used it if you absolutely require data that are independent of those of the caller.

select(sel, compact=False)

Select some element(s) from a Geometry.

Parameters:

• sel (index-like) –

  The index of element(s) to be selected. This can be anything that can be used as an index in an array:

  • a single element number

  • a list, or array, of element numbers

  • a bool list, or array, of length self.nelems(), where True values flag the elements to be selected

• compact (bool, optional) – This option is only useful for subclasses that have a compact method, such as mesh.Mesh and its subclasses. If True, the returned object will be compacted, i.e. unused nodes are removed and the nodes are renumbered from zero. If False (default), the node set and numbers are returned unchanged.

Returns:

Geometry (or subclass) object – An object of the same class as the caller, but only containing the selected elements.

See also

cselect

Return all but the selected elements.

clip

Like select, but with compact=True as default.

cselect(sel, compact=False)

Return the Geometry with the selected elements removed.

Parameters:

• sel (index-like) –

  The index of element(s) to be selected. This can be anything that can be used as an index in an array:

  • a single element number

  • a list, or array, of element numbers

  • a bool list, or array, of length self.nelems(), where True values flag the elements to be selected

• compact (bool, optional) – This option is only useful for subclasses that have a compact method, such as mesh.Mesh and its subclasses. If True, the returned object will be compacted, i.e. unused nodes are removed and the nodes are renumbered from zero. If False (default), the node set and numbers are returned unchanged.

Returns:

Geometry (or subclass) object – An object of the same class as the caller, but containing all but the selected elements.

See also

select

Return a Geometry with only the selected elements.

cclip

Like cselect, but with compact=True as default.

clip(sel)

Return a Geometry only containing the selected elements.

This is equivalent to select() with compact=True.

See also

select

Return a Geometry with only the selected elements.

cclip

The complement of clip, returning all but the selected elements.

cclip(sel)

Return a Geometry with the selected elements removed.

This is equivalent to select() with compact=True.

See also

cselect

Return a Geometry with only the selected elements.

clip

The complement of cclip, returning only the selected elements.

selectProp(prop, compact=False)

Select elements by their property value.

Parameters:

prop (int or int array_like) – The property value(s) for which the elements should be selected.

Returns:

Geometry (or subclass) object – An object of the same class as the caller, but only containing the elements that have a property value equal to prop, or one of the values in prop. If the input object has no properties, a copy containing all elements is returned.

See also

cselectProp

Return all but the elements with property prop.

whereProp

Get the numbers of the elements having a specified property.

select

Select the elements with the specified indices.

cselectProp(prop, compact=False)

Return an object without the elements with property val.

Parameters:

prop (int or int array_like) – The property value(s) of the elements that should be left out.

Returns:

Geometry (or subclass) object – An object of the same class as the caller, with all but the elements that have a property value equal to prop, or one of the values in prop. If the input object has no properties, a copy containing all elements is returned.

See also

selectProp

Return only the elements with property prop.

whereProp

Get the numbers of the elements having a specified property.

cselect

Remove elements by their index.

splitProp(prop=None, compact=True)

Partition a Geometry according to the values in prop.

Parameters:

prop (int array_like, optional) – A 1-dim int array with length self.nelems() to be used in place of the objects own prop attribute. If None (default), the latter will be used.

Returns:

List of Geometry objects – A list of objects of the same class as the caller. Each object in the list contains all the elements having the same value of prop. The number of objects in the list is equal to the number of unique values in prop. The list is sorted in ascending order of the prop value.

If prop is None and the the object has no prop attribute, an empty list is returned.

addField(fldtype, data, fldname)

Add Field data to the Geometry.

Field data are scalar or vectorial data defined over the Geometry. This convenience function creates a Field object with the specified data and adds it to the Geometry object’s fields dict.

Parameters:

• fldtype (str) – The field type. See Field for details.

• data (array_like) – The field data. See Field for details.

• fldname (str) – The field name. See Field for details. This name is also used as key to store the Field in the fields dict.

Returns:

Field – The constructed and stored Field object.

Note

Whenever a Geometry object is exported to a PGF file, all Fields stored inside the Geometry object are included in the PGF file.

See also

fields

Return a dict with all Fields on the Geometry.

getField

Retrieve a Field by its name.

delField

Deleted a Field.

convertField

Convert the Field to another Field type.

fieldReport

Return a short overview of the stored Fields

Examples

>>> from pyformex.mesh import Mesh
>>> M = Mesh(eltype='quad4').subdivide(2)
>>> fld1 = M.addField('elemc', np.asarray([0,1,1,2]), 'elemnr')
>>> print(fld1)
Field 'elemnr', type 'elemc', shape (4,), nnodes=9, nelems=4, nplex=4
[0 1 1 2]
>>> fld2 = M.convertField('elemnr', 'node', 'onnodes')
>>> fld3 = M.getField('onnodes')
>>> print(fld3)
Field 'onnodes', type 'node', shape (9, 1), nnodes=9, nelems=4, nplex=4
[[0. ]
 [0.5]
 [1. ]
 [0.5]
 [1. ]
 [1.5]
 [1. ]
 [1.5]
 [2. ]]
>>> print(M.fieldReport())
Field 'elemnr', fldtype 'elemc', dtype int64, shape (4,)
Field 'onnodes', fldtype 'node', dtype float64, shape (9, 1)

property fields

Return the Fields dict of the Geometry.

Returns:

dict – A dict with the term:`Field objects that were attached to the Geometry. The keys are the Field names. If the Geometry has no Fields, an empty dict is returned.

getField(fldname)

Get the data field with the specified name.

Parameters:

fldname (str) – The name of the Field to retrieve.

Returns:

Field – The data field with the specified name, if it exists in the Geometry object’s fields. Returns None if no such key exists.

Examples

See addFields().

delField(fldname)

Delete the Field with the specified name.

Parameters:

fldname (str) – The name of the Field to delete from the Geometry object. A nonexisting name is silently ignored.

convertField(fldname, totype, toname)

Convert the data field with the specified name to another type.

Parameters:

• fldname (str) – The name of the data Field to convert to another type. A nonexisting name is silently ignored.

• totype (str) – The field type to convert to. See Field for details.

• toname (str) – The name of the new (converted) Field (and key to store it). If the same name is specified as the old Field, that one will be overwritten by the new. Otherwise, both will be kept in the Geometry object’s fields dict.

Returns:

Field – The converted and stored data field. Returns None if the original data field does not exist.

Examples

See addFields().

fieldReport()

Return a short report of the stored fields

Returns:

str – A multiline string with the stored Fields’ attributes: name, type, dtype and shape.

write(filename, sep=' ', mode='w', **kargs)

Write a Geometry object to a PGF file

classmethod read(filename)

Read a single Geometry object from a PGF file

pzf_dict()

Construct common part of all Geometry pzf dicts