=Paper=
{{Paper
|id=Vol-2050/shapes-paper1
|storemode=property
|title=The Interplay between Shape and Feature Representation
|pdfUrl=https://ceur-ws.org/Vol-2050/SHAPES_paper_1.pdf
|volume=Vol-2050
|authors=Emilio M. Sanfilippo,Ferruccio Mandorli,Claudio Masolo,Matteo Ragni
|dblpUrl=https://dblp.org/rec/conf/jowo/SanfilippoMMR17
}}
==The Interplay between Shape and Feature Representation==
https://ceur-ws.org/Vol-2050/SHAPES_paper_1.pdf
The Interplay between Shape and Feature
Representation
Emilio M. SANFILIPPO a,1 Ferruccio MANDORLI b Claudio MASOLO a and
Matteo RAGNI c
a ISTC-CNR Laboratory for Applied Ontology, Trento, Italy
b Polytechnic University of Marche, Ancona, Italy
c University of Trento, Department of Industrial Engineering, Trento, Italy
Abstract.
When we approach shape representation, we need to choose which modeling
constructs to adopt, e.g., low-level geometric elements like edges and (sur)faces,
or more general elements like protrusions, bumps and holes, among others. The
latter can be described as spatial configurations of the former satisfying unity and,
possibly, identity criteria. However, once these are brought into the picture, we need
to understand what they are, how they relate to their shape, as well as how complex
shapes result from the combination of simpler ones. We address in the paper these
issues and sketch an initial approach based on patterns.
Keywords. Shape modeling, feature, CAD systems
1. Introduction
When we model shapes, we need to choose which modeling elements to adopt. Con-
sider, e.g., the three-dimensional object (partially showed) in Fig. 1. We can describe it
as being characterised by a U-shape or by referring to more functional elements, e.g.,
two protrusions, a slot, etc. This scenario is typical of what happens in the context of
Computer-Aided Design (CAD) where we can rely on different approaches for shape
representation, e.g., by considering pure shapes or by including features.
These representational alternatives are all viable but we need to recognise (i) that
they capture different information and perspectives about the object and (ii) that they
have a technical impact on the choice of the modeling language. For instance, once we
explicitly use protrusions or slots, we can characterise them by means of functional prop-
erties but we also need to add them into our domain and to understand what they are.
We take here a knowledge engineering stance and focus on the choice of which
elements to adopt for shape modeling. In Sect. 2 we introduce two approaches for shape
representation that are common in CAD contexts. These approaches provide the basic
concepts which are further discussed in Sect. 3 where a notion of ‘structured shape’ is
proposed. Sect. 4 analyses the notions of protrusion, hole, slot, etc. from an ontological
1 Corresponding Author: Emilio M. Sanfilippo, ISTC-CNR Laboratory for Applied Ontology, via alla cascata
56/c, Povo, Trento, 38123; E-mail: sanfilippo@loa.istc.cnr.it
perspective, sketching what are the advantages of having these entities in the domain of
discourse but also highlighting what are the difficulties to properly account for them.
Figure 1. Sketch of the section of a 3D object
2. Representing Shapes in CAD Systems
The wing rib showed in Fig. 2, a structural element of the skeleton of an airplane wing, is
a more realistic case of the U-shaped object in Fig. 1. From an engineering perspective,
CAD systems for mechanical design (MCAD) allow to represent the wing rib by means
of basic elements such as faces, edges and vertexes, as well as geometric and topological
constraints. The resulting morphology is then mapped into an appropriated data structure
called boundary representation (B-rep) [9].
Figure 2. 3D model of wing rib
However, even in MCAD systems, the final B-rep of the wing rib can be obtained
in different manners, e.g., by means of low-level modeling constructs (faces, edges, ver-
texes, etc.), or by composing various and possibly simpler shapes, which can recursively
result from other constructs. In the latter case, the choice of which shapes to adopt is
not straightforward and different modelers may easily come to the same final shape by
means of different (simpler) ones.
Pure morphological (B-rep based) approaches run the risk of not making explicit
relevant information. Looking at Fig. 2, for example, we may want to acknowledge for
holes and mid ribs. As suggested in Jowers and Earl [5], this means that we identify
in the wing rib those (generally speaking) structural aspects that are relevant for some
reasons. The recognition of holes and the like however presupposes that certain modeling
constructs are given some kind of unity and are identified as entities of certain types,
therefore satisfying identity criteria. On the other hand, this knowledge is not necessarily
represented in morphological approaches and needs to be explicitly taken into account.
In engineering, feature-based approaches have been proposed with the purpose of
developing product models by abstracting from low-level geometric elements and re-
lying, instead, on features (e.g., things like holes and ribs, among others) [9]. Accord-
ingly, features are whole entities that can be associated with disparate properties—e.g.,
shape or functional properties—and are commonly understood as modeling constructs to
represent “the engineering significance of the geometry of a part” [2].2
The introduction of feature-based approaches has been an important improvement of
engineering 3D modeling. MCAD systems, however, only include macro-modeling ele-
ments to ease model creation but neither provide explicit feature definitions, nor their ge-
ometric/topological properties are preserved along the overall modeling process. More-
over, CAD systems are not per se helpful to decide whether the representation of some
features should be preferred over the others. Feature representation is indeed context-
dependent and different experts recognize the presence of different features in the same
model [5]. For example, looking again at Fig. 2, from a mechanical perspective the trade-
off between deformation and weight explains a section shape that minimizes the defor-
mation on a prescribed axis, therefore the presence of the mid ribs, as well as the several
holes on the lateral surface and the one at the center. From a manufacturing perspective,
the object is machined from a blank, therefore by removing material until reaching the
described product. It becomes clear that the two interpretations specify different features:
structural features in the first case, machined features in the second one.
Understanding (i) how a complex shape results from the composition of other, sim-
pler, shapes, (ii) what are the ontological properties that these shapes carry, especially
when they are looked from a feature perspective, and (iii) how to make sense of multiple-
perspectives on the same shapes/features are problems that are not restricted to the engi-
neering domain, but more generally apply to the overall context of shape representation.
We shall address the first two issues in the remaining sections, while leaving the third
one to future work.
3. Structured Shapes
In cognitive science, the model of geons of Biederman [1] and the hierarchical model of
cylinders of Marr and Nishihara [6] have been widely used to specify complex shapes.
In these approaches, the overall shape of an object is approximated by a primitive shape
(e.g., a cylinder or a parametric volume) that can be decomposed into smaller ones—
approximating the shape of some relevant parts of the whole—structured in a given way.
The decomposition process can be recursively applied.3 One could think to apply this
idea to shape modeling in general, i.e., complex shapes could be represented by consid-
ering the way in which basic shapes are recursively (geometrically, topologically, mere-
ologically, etc.) structured. For instance, one could think that the shapes of the objects
represented in Fig. 1–2 are complex, and therefore structured in simpler (basic) ones.
Hence shapes could be understood as sorts of distributional properties [8], e.g., in the
case of colors, being polka-dotted.
As observed by Jowers [5], the way the designers build complex shapes starting from
simple ones is important for the understanding of the design itself since it may reflect, for
2 ‘Part’ is synonym of ‘product’ in this sentence.
3 Approximation and granularity play a central role in the process of recognizing and representing shapes.
instance, functional requirements or the way in which designers think about the shapes
themselves.
B B B B B B C B
A A A A
(a) (b) (c) (d) (e)
Figure 3. Different shapes for the object in Fig. 1
Let us consider the object in Fig. 1. Fig. 3 shows different shapes that describe the
morphology of this object. As in the case of the hierachical model of Marr and Nishi-
hara, we assume that, at a given level of granularity, the shape of the whole object is
‘approximated’ by a basic one, which we assume to be a B-rep. In Fig. 3.a one has a
single basic (unstructured) shape, a single level of granularity, i.e., a single B-rep (dots
represent edges, while lines represent faces). Vice versa, Fig. 3.b depicts the case of a
complex shape obtained by structuring the basic shapes Ab 4 and Bb according to a given
geometrical pattern represented by the dotted line. First, note that the shape Bb is used
two times in Fig. 3.b, i.e., the spatial pattern requires the same shape Bb to be linked in
two different ways to Ab . In terms of colors, one can think to the pattern of red/blue/red
strips, where red occurs twice. Second, the existence of the shape does not necessarily
implies the existence of an object with this shape, i.e., the designed product may be still
atomic (i.e., without any component), hence the existence of a component for each basic
shapes is not mandatory. Third, the shape in Fig. 3.b is intended to capture two levels of
granularity. The finer one is given in terms of the spatial distribution of the shapes Ab
and Bb . The coarser one is just a basic shape that is implicit in the picture, and which
corresponds to the B-rep in Fig. 3.a. One can thus think that the shape in Fig. 3.b is
a refinement of the one in Fig. 3.a because it adds some structural information that Aa
discards. Clearly, Aa can be refined in alternative ways, e.g., in Fig. 3.c one starts from
different shapes and a different pattern. Note that the shapes in Fig. 3.b and Fig. 3.c are
different even though at the coarser level they coincide with Aa . We can re-iterate the
process of decomposition introducing more refined shapes distributions.
Considering features, one can think that, e.g., a parallelepipedic protuberance or a
parallelepipedic hole are specific kinds of shapes that differ from other parallelepipedic
shapes, because of the way in which they are related to other shapes. Following this
reasoning, a parallelepipedic protuberance can be defined as a parallelepipedic shape
plus a pattern specifying how the shape must be linked to another one. Fig. 3.d shows the
graphical notation for a protuberance where the depicted pattern means that the lower
face of Bd must be connected (in a certain way) to a face of the host-shape. Holes are
more complex than protuberances, since to obtain the B-rep that approximates a complex
shape with a hole the B-rep of the hole has to be discarded from the whole. In Fig. 3.e,
we represent (basic) holes with grey edges and surfaces. If the design explicitly refers to
holes, the shape Aa can be refined as in Fig. 3.e, where Ce is a (basic) parallelepipedic
4A
x denotes the basic shape indicated with A in Fig. 3.x. In general Ax and Ay are different in case x 6= y.
hole. Accordingly, the upper face of Ce is not part of the B-rep in Aa . Furthermore, the
pattern that specifies the hole includes also constraints on the way the three shapes it
plugs-in are connected.
In this view, shapes do not reduce to B-reps; they are rather recursively structured
into simpler ‘building blocks’ linked according to given patterns. However, once we
bring these building blocks into the picture, we want to make sense of their differences
in terms of a reference ontology for objects’ representation. Especially when we move
from the specification of abstract shapes to engineering modeling, we are interested in
making explicit the distinctions, e.g., between a shape construct referring to a material
product, and one referring to a (physical) hole or a protrusion. For instance, looking
again at Fig. 3.e, one may wonder why a shape for a hole must be necessarily related
to a shape referring to some (material) object. We shall see in the next section that this
choice, enforced by means of a suitable pattern, relies on the ontological assumptions
about what holes are.
4. An Ontological Framework for Feature Representation
For our purposes, we adopt a minimal ontology distinguishing between objects, parasitic
objects (parasite, for short) and qualities. Objects are extended in space and are possibly
made of some material; an example is the physical counterpart of the wing rib showed
in Fig. 2. Parasitic objects are objects that ultimately depend on non-parasites, i.e., they
cannot exist if detached from the latter, e.g., the head of a bolt.5 Qualities are objects
characteristics, e.g., the weight of a wing rib, or the pitch of a threaded screw.
In terms of this framework, (physical) holes or protrusions fit well with the notion
of parasite. E.g., to be a protrusion (or a hole) means to be a protrusion in something
else. By ‘objectifying’ features, we have the possibility of representing them along with
their characterising qualities without however reducing them to qualities themselves.
Additionally, we reflect engineering theories treating features as objects satisfying unity
and possibly even identity criteria. We will therefore adopt this approach from now on.
Looking at the ontological dependence of parasites, it can be understood as being
either specific or generic. In the first case, a feature f depends on a specific individual o,
so that if o ceases to exist, then f ceases to exist, too. In the second case, f depends on
some entity (of a certain type), so that f can survive the replacement of its host.6
Despite this distinction finds its place in ontology [7], it is not straightforward to
establish the kind of dependence that a parasite satisfies. Consider, for instance, the hole
at the centre of the wing rib in Fig. 2, call it h. On the one hand, we can assume that as
far as h maintains its identity, it keeps existing although the radical changes that its host
may undergo. For example, assume that persistence conditions of the wing rib are given
in functional terms, so that it ceases to exist when it cannot exhibit its functionality. If
generic dependence is adopted, then h may continue to exist when the wing rib ‘passes
away’. On the other hand, if specific dependence is adopted, then h stops existing along
with the wing rib. Since from an ontological perspective both views are well motivated,
the choice of which kind of dependence to adopt relies on background domain assump-
5 For the sake of the example, we assume that when the head of a bolt is detached from the bolt, it stops
existing as ‘the head of the bolt’. In this sense, the head is a ‘parasitic part’ of the bolt.
6 We call host the entity upon which a parasite depends.
tions. In the case of CAD modeling, for instance, specific dependence may be better
suited, since each feature is intentionally attached to individual products.
We now need to make sense of the fact that some features are ascribed with mate-
riality. We therefore introduce the notion of material parasite, that is, a parasitic object
made of some material. Conversely, an immaterial parasite lacks material constitution.
Consider now holes:7 are they material or immaterial parasites? Both views are found
in philosophical ontology [3], as well as in engineering. On the one hand, it is indeed
common to refer to holes as voids, which are often ascribed with the functionality of
accommodating some other entity, e.g., screws.8 On the other hand, a hole in an object
is understood as set of surfaces with a characterising shape. Take again the hole h in the
wing rib. From the latter perspective, h is the cylindrical surface of the wing rib located
in a certain spatial position (within the spatial system relative to the wing rib). From the
former perspective, h is the cavity which is (topologically) connected to some of the wing
rib surfaces. It is hard to discard one of these views, since—looking at a hole—one may
need to represent both a cavity (e.g., in which something can be accommodated) and a
surface (possibly made of some material) to which the cavity connects. From an ontolog-
ical stance, these are however two different entities. We therefore propose to distinguish
between cavity-like (or void-like) features as immaterial parasites and the (material) ob-
jects to which they connect.
Admittedly, this ontological framework is still general and more specific constraints
should be added, e.g., to characterize features with respect to functional properties. The
introduced distinctions are however helpful to shed some light on the high-level proper-
ties that features satisfy, and to support the development of patterns for shape modeling
that are coherent with these properties. For instance, if we consider components as prod-
ucts intentionally designed to be possibly related to some other product, then features
cannot be components. Indeed, it is reasonably to assume that a component can exist on
its own, whereas—as we saw—the existence of features depends on other entities.9
5. Conclusions
We addressed some general issues concerning shape modeling. In particular, we saw that
shapes can be represented by means of different modeling constructs at different repre-
sentational layers. B-rep models can be taken as the lowest representational level since
they provide a precise specification of morphological properties in terms of vertexes and
other low-level geometric constructs. We saw that this approach comes with its own
costs, e.g., it does not allow to refer to a certain portion of the shape at stake to attribute
it some functional property. Following cognitive science theories and engineering mod-
eling approaches, we considered how to build a more strctured, coarse-grained represen-
tational level on the top of B-rep constructs. Accordingly, an overall shape results from
the composition of multiple (simpler) shapes, which are spatially arranged according to
given patterns. In other words, in this second level structured collections of B-rep ele-
7 The same considerations can be done for features like slots, pockets, etc.
8 See the modeling element IfcFeatureElementSubtraction in the Industry Foundation Classes (IFC);
http://www.buildingsmart-tech.org/ifc/IFC4/Add1/html/, last access on July 2017.
9 We assume here a rigid [4] notion of component. This means that an object is a component for the entire
duration of its life, independently from the fact that it is not attached to some other product at a certain time.
ments are explicitly selected and composed. On the top of structured shapes, we built an
ontological level to characterise the ontological nature of features in the scope of a larger
ontology for objects’ representation. In particular, we sketched a way to distinguish pro-
trusions and holes, which are usually considered in CAD-based design.
Even though the choice of which building blocks to adopt is up to modelers and their
use may rely on different requirements such as the optimisation of the design process, or
the specification of functional properties, by explicitly representing this choice and the
way the object under design is structured, we think that the proposed approach may fa-
cilitate the integration between different designs as well as their conceptual clarification.
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