Modeling Geometry with pyFormex

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Abstract

This chapter explains the different geometrical models in pyFormex, how and when to use them, how to convert between them, how to import and export them in various formats.

Introduction

Everything is geometry

In everyday life, geometry is ubiquitous. Just look around you: all the things you see, whether objects or living organisms or natural phenomena like clouds, they all have a shape or geometry. This holds for all concrete things, even if they are ungraspable, like a rainbow, or have no defined or fixed shape, like water. The latter evidently takes the shape of its container. Only abstract concepts do not have a geometry. Any material thing has though [1], hence our claim: everything is geometry.

Since geometry is such an important aspect of everybody’s life, one would expect that it would take an important place in education (base as well as higher). Yet we see that in the educational system of many developed countries, attention for geometry has vaned during the last decades. Important for craftsmen, technician, engineer, designer, artist

We will give some general ideas about geometry, but do not pretend to be a full geometry course. Only concepts needed for or related to modleing with pyFormex.

We could define the geometry of an object as the space it occupies. In our three-dimensional world, any object is also 3D. Some objects however have very small dimensions in one or more directions (e.g. a thin wire or a sheet of paper). It may be convenient then to model these only in one or two dimensions. [2]

Concrete things also have a material. THIngs going wrong is mostly mechanical: geometry/materail

[1]	We obviously look here at matter in the way we observe it with our senses (visual, tactile) and not in a quantum-mechanics way.

[2]	Mathematically we can also define geometry with higher dimensionality than 3, but this is of little practical use.

The Formex model

The Mesh model

The TriSurface model

The Curve model

Subclassing Geometry

The __init__ method of the derived class should at least call Geometry.__init__(self) and then assign a Coords to self.coords. Furthermore, the class should override the nelems() method. Then a newly created instance of the subclass will at least have these attributes:

Derived classes can (and in most cases should) declare a method _set_coords(coords) returning an object that is identical to the original, except for its coords being replaced by new ones with the same array shape.

The Geometry class provides two possible default implementations:

• _set_coords_inplace sets the coords attribute to the provided new coords, thus changing the object itself, and returns itself,
• _set_coords_copy creates a deep copy of the object before setting the coords attribute. The original object is unchanged, the returned one is the changed copy.

When using the first method, a statement like B = A.scale(0.5) will result in both A and B pointing to the same scaled object, while with the second method, A would still be the untransformed object. Since the latter is in line with the design philosophy of pyFormex, it is set as the default _set_coords method. Many derived classes that are part of pyFormex override this default and implement a more efficient copy method.

Derviced classes should immplement the _select method

def _select(self,selected,**kargs):

“”“Return a Formex only holding the selected elements.

The kargs can hold optional arguments: compact = True/False

if the Coords modell can hold unused points that can be removed by compacyion (the case with Mesh)

Analytical models