18. 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
[source]¶ A generic geometry class allowing manipulation of large coordinate sets.
The Geometry class is a generic parent class for all geometry classes. It is not intended to be used directly, but only through derived classes. Examples of derived classes are
Formex
,Mesh
and its subclassTriSurface
,Curve
.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 thecoords
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 used 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 classFormex
, then one can useF.center()
as a convenient shorthand forF.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()
,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 methodnelems()
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 classAttributes
. 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 attributefields
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.

coords
¶ A Coords object that holds the coordinates of the points required to describe the type of geometry.
Type: Coords

prop
¶ Element property numbers. This is a 1dim int array with length
nelems()
. Each element of the Geometry can thus be assigned an integer value. It is up the the subclass to define if and how its instances are divided into elements, and how to use this element property number.Type: int array

attrib
¶ An Attributes object that is primarily used to define persisting drawing attributes (like color) for the Geometry object.
Type: Attributes

fields
¶ A dict with the Fields defined on the object. This atribute only exists when at least one Field has been defined. See
addField()
.Type: OrderedDict

xyz
¶ Return the
xyz
property of thecoords
attribute of the Geometry object.See
coords.Coords.xyz
for details.

x
¶ Return the
x
property of thecoords
attribute of the Geometry object.See
coords.Coords.x
for details.

y
¶ Return the
y
property of thecoords
attribute of the Geometry object.See
coords.Coords.y
for details.

z
¶ Return the
z
property of thecoords
attribute of the Geometry object.See
coords.Coords.z
for details.

xy
¶ Return the
xy
property of thecoords
attribute of the Geometry object.See
coords.Coords.xy
for details.

yz
¶ Return the
yz
property of thecoords
attribute of the Geometry object.See
coords.Coords.yz
for details.

xz
¶ Return the
xz
property of thecoords
attribute of the Geometry object.See
coords.Coords.xz
for details.

nelems
()[source]¶ 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
()[source]¶ 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.

points
(*args, **kargs)[source]¶ Call Coords.points method on the Geometry object’s coords.
See
coords.Coords.points()
for details.

bbox
(*args, **kargs)[source]¶ Call Coords.bbox method on the Geometry object’s coords.
See
coords.Coords.bbox()
for details.

center
(*args, **kargs)[source]¶ Call Coords.center method on the Geometry object’s coords.
See
coords.Coords.center()
for details.

bboxPoint
(*args, **kargs)[source]¶ Call Coords.bboxPoint method on the Geometry object’s coords.
See
coords.Coords.bboxPoint()
for details.

centroid
(*args, **kargs)[source]¶ Call Coords.centroid method on the Geometry object’s coords.
See
coords.Coords.centroid()
for details.

sizes
(*args, **kargs)[source]¶ Call Coords.sizes method on the Geometry object’s coords.
See
coords.Coords.sizes()
for details.

dsize
(*args, **kargs)[source]¶ Call Coords.dsize method on the Geometry object’s coords.
See
coords.Coords.dsize()
for details.

bsphere
(*args, **kargs)[source]¶ Call Coords.bsphere method on the Geometry object’s coords.
See
coords.Coords.bsphere()
for details.

bboxes
(*args, **kargs)[source]¶ Call Coords.bboxes method on the Geometry object’s coords.
See
coords.Coords.bboxes()
for details.

inertia
(*args, **kargs)[source]¶ Call Coords.inertia method on the Geometry object’s coords.
See
coords.Coords.inertia()
for details.

principalCS
(*args, **kargs)[source]¶ Call Coords.principalCS method on the Geometry object’s coords.
See
coords.Coords.principalCS()
for details.

principalSizes
(*args, **kargs)[source]¶ Call Coords.principalSizes method on the Geometry object’s coords.
See
coords.Coords.principalSizes()
for details.

distanceFromPlane
(*args, **kargs)[source]¶ Call Coords.distanceFromPlane method on the Geometry object’s coords.
See
coords.Coords.distanceFromPlane()
for details.

distanceFromLine
(*args, **kargs)[source]¶ Call Coords.distanceFromLine method on the Geometry object’s coords.
See
coords.Coords.distanceFromLine()
for details.

distanceFromPoint
(*args, **kargs)[source]¶ Call Coords.distanceFromPoint method on the Geometry object’s coords.
See
coords.Coords.distanceFromPoint()
for details.

directionalSize
(*args, **kargs)[source]¶ Call Coords.directionalSize method on the Geometry object’s coords.
See
coords.Coords.directionalSize()
for details.

directionalWidth
(*args, **kargs)[source]¶ Call Coords.directionalWidth method on the Geometry object’s coords.
See
coords.Coords.directionalWidth()
for details.

directionalExtremes
(*args, **kargs)[source]¶ Call Coords.directionalExtremes method on the Geometry object’s coords.
See
coords.Coords.directionalExtremes()
for details.

convexHull
(dir=None, return_mesh=True)[source]¶ Return the convex hull of a Geometry.
This is the
convexHull()
applied to thecoords
attribute, but it hasreturn_mesh=True
as default.Returns: Mesh – The convex hull of the geometry.

testBbox
(bb, dirs=(0, 1, 2), nodes='any', atol=0.0)[source]¶ 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 theFormex
andMesh
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()
ormesh.Mesh.test()
.
Returns: bool array – The array flags the elements that are inside the given bounding box.

scale
(*args, **kargs)[source]¶ Apply the
scale
transformation to the Geometry object.See
coords.Coords.scale()
for details.

resized
(size=1.0, tol=1e05)[source]¶ 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)[source]¶ Apply the
adjust
transformation to the Geometry object.See
coords.Coords.adjust()
for details.

translate
(*args, **kargs)[source]¶ Apply the
translate
transformation to the Geometry object.See
coords.Coords.translate()
for details.

centered
(*args, **kargs)[source]¶ Apply the
centered
transformation to the Geometry object.See
coords.Coords.centered()
for details.

align
(*args, **kargs)[source]¶ Apply the
align
transformation to the Geometry object.See
coords.Coords.align()
for details.

rotate
(*args, **kargs)[source]¶ Apply the
rotate
transformation to the Geometry object.See
coords.Coords.rotate()
for details.

shear
(*args, **kargs)[source]¶ Apply the
shear
transformation to the Geometry object.See
coords.Coords.shear()
for details.

reflect
(*args, **kargs)[source]¶ Apply the
reflect
transformation to the Geometry object.See
coords.Coords.reflect()
for details.

affine
(*args, **kargs)[source]¶ Apply the
affine
transformation to the Geometry object.See
coords.Coords.affine()
for details.

toCS
(*args, **kargs)[source]¶ Apply the
toCS
transformation to the Geometry object.See
coords.Coords.toCS()
for details.

fromCS
(*args, **kargs)[source]¶ Apply the
fromCS
transformation to the Geometry object.See
coords.Coords.fromCS()
for details.

transformCS
(*args, **kargs)[source]¶ Apply the
transformCS
transformation to the Geometry object.See
coords.Coords.transformCS()
for details.

position
(*args, **kargs)[source]¶ Apply the
position
transformation to the Geometry object.See
coords.Coords.position()
for details.

cylindrical
(*args, **kargs)[source]¶ Apply the
cylindrical
transformation to the Geometry object.See
coords.Coords.cylindrical()
for details.

hyperCylindrical
(*args, **kargs)[source]¶ Apply the
hyperCylindrical
transformation to the Geometry object.See
coords.Coords.hyperCylindrical()
for details.

toCylindrical
(*args, **kargs)[source]¶ Apply the
toCylindrical
transformation to the Geometry object.See
coords.Coords.toCylindrical()
for details.

spherical
(*args, **kargs)[source]¶ Apply the
spherical
transformation to the Geometry object.See
coords.Coords.spherical()
for details.

superSpherical
(*args, **kargs)[source]¶ Apply the
superSpherical
transformation to the Geometry object.See
coords.Coords.superSpherical()
for details.

toSpherical
(*args, **kargs)[source]¶ Apply the
toSpherical
transformation to the Geometry object.See
coords.Coords.toSpherical()
for details.

circulize
(*args, **kargs)[source]¶ Apply the
circulize
transformation to the Geometry object.See
coords.Coords.circulize()
for details.

bump
(*args, **kargs)[source]¶ Apply the
bump
transformation to the Geometry object.See
coords.Coords.bump()
for details.

flare
(*args, **kargs)[source]¶ Apply the
flare
transformation to the Geometry object.See
coords.Coords.flare()
for details.

map
(*args, **kargs)[source]¶ Apply the
map
transformation to the Geometry object.See
coords.Coords.map()
for details.

map1
(*args, **kargs)[source]¶ Apply the
map1
transformation to the Geometry object.See
coords.Coords.map1()
for details.

mapd
(*args, **kargs)[source]¶ Apply the
mapd
transformation to the Geometry object.See
coords.Coords.mapd()
for details.

copyAxes
(*args, **kargs)[source]¶ Apply the
copyAxes
transformation to the Geometry object.See
coords.Coords.copyAxes()
for details.

swapAxes
(*args, **kargs)[source]¶ Apply the
swapAxes
transformation to the Geometry object.See
coords.Coords.swapAxes()
for details.

rollAxes
(*args, **kargs)[source]¶ Apply the
rollAxes
transformation to the Geometry object.See
coords.Coords.rollAxes()
for details.

projectOnPlane
(*args, **kargs)[source]¶ Apply the
projectOnPlane
transformation to the Geometry object.See
coords.Coords.projectOnPlane()
for details.

projectOnSphere
(*args, **kargs)[source]¶ Apply the
projectOnSphere
transformation to the Geometry object.See
coords.Coords.projectOnSphere()
for details.

projectOnCylinder
(*args, **kargs)[source]¶ Apply the
projectOnCylinder
transformation to the Geometry object.See
coords.Coords.projectOnCylinder()
for details.

isopar
(*args, **kargs)[source]¶ Apply the
isopar
transformation to the Geometry object.See
coords.Coords.isopar()
for details.

addNoise
(*args, **kargs)[source]¶ 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)[source]¶ Create or destroy the property array for the Geometry.
A property array is a 1dim 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 passingarange(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 inplace. 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
 The calling object

toProp
(prop)[source]¶ 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 1dim 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 isInt
.See also
setProp()
 Set the properties for the object
whereProp()
 Find the elements having some property value

maxProp
()[source]¶ Return the highest property value used.
Returns: int – The highest value used in the properties array, or 1 if there are no properties.

propSet
()[source]¶ 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.

whereProp
(prop)[source]¶ 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 1dim int array with the indices of all the elements that have the property value prop
, or one of the values inprop
.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
()[source]¶ 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)[source]¶ Select some element(s) from a Geometry.
Parameters:  sel (indexlike) –
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 asmesh.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.
 sel (indexlike) –

cselect
(sel, compact=False)[source]¶ Return the Geometry with the selected elements removed.
Parameters:  sel (indexlike) –
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 asmesh.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.
 sel (indexlike) –

clip
(sel)[source]¶ Return a Geometry only containing the selected elements.
This is equivalent with
select()
but havingcompact=True
as default.

cclip
(sel)[source]¶ Return a Geometry with the selected elements removed.
This is equivalent with
select()
but havingcompact=True
as default.

selectProp
(prop, compact=False)[source]¶ 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 inprop
. 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)[source]¶ 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 inprop
. 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)[source]¶ Partition a Geometry according to the values in prop.
Parameters: prop (int array_like, optional) – A 1dim int array with length self.nelems()
to be used in place of the objects ownprop
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.

fields
Return the Fields dict of the Geometry.
If the Geometry has no Fields, an empty dict is returned.

addField
(fldtype, data, fldname)[source]¶ Add
Field
data to theGeometry
.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’sfields
dict.Parameters: 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
getField()
 Retrieve a Field by its name.
delField()
 Deleted a Field.
convertField()
 Convert the Field to another Field type.
fieldReport()
 Return a short report of the stored Fields

getField
(fldname)[source]¶ 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’sfields
. Returns None if no such key exists.

delField
(fldname)[source]¶ 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. Returns: None

convertField
(fldname, totype, toname)[source]¶ 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.

fieldReport
()[source]¶ 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)[source]¶ Write a Geometry to a PGF file.
This writes the Geometry to a pyFormex Geometry File (PGF) with the specified name.
It is a convenient shorthand for:
writeGeomFile(filename, self, sep=sep, mode=mode, **kargs)
See
writeGeomFile()
for details.

classmethod
read
(filename)[source]¶ Read a Geometry from a PGF file.
This reads a single object (the object) from a PGF file and returns it.
It is a convenient shorthand for:
next(readGeomFile(filename, 1).values())
See
readGeomFile()
for details.
