Noname manuscript No.
(will be inserted by the editor)
Topology Reconstruction for Reverse Engineering
Roseline Bénière · Gérard Subsol · Gilles Gesquière · François Le
Breton · William Puech
Received: date / Accepted: date
Abstract In a previous work, we proposed to reconstruct 3D primitives from a mesh using extracted point
areas. In this paper, we present a new method to determine the topology of this 3D primitive set. This topology definition is based on both continuous informations
from primitives and discrete informations from point
areas.
Keywords Topology · Primitives · CAD · Reverse
engineering · B-Rep model
1 Introduction
In reverse engineering, the aim is to reconstruct a continuous model of an object (B-Rep model for example)
from a discretized representation (as 3D mesh). Several
methods have been proposed these last years (see for example the method of Lavva et al [3]); they often focused
on the algorithm of detection of geometric primitives
(as planes, spheres, cones, torus ...). But, a key-point is
to define the adjacency relations and the boundaries between these primitives in order to obtain a B-Rep representation. The informations stored in the B-Rep model
for each surface are: the primitive type, the parameters
and the references of the wires (which form the boundR. Bénière
LIRMM, Univ Montpellier 2, CNRS, France /
C4W, Montpellier France
E-mail: roseline.beniere@lirmm.fr
G. Subsol and W. Puech
LIRMM, Univ Montpellier 2, CNRS, France
G. Gesquière
LSIS, Univ Aix-Marseille, CNRS, France
F. Le Breton
C4W, Montpellier France
aries of the primitives). If two surfaces are neighbors,
they must reference the same wire, so the adjacency
informations between the surfaces are needed. Hence
after a first step to extract simple primitives, a second
one lead to reconstruct the topology, determining the
neighbor primitives to others primitives. The intersections between the neighbor primitives define the surface
boundaries and allow to reconstruct the B-Rep model.
Our proposed method reconstructs the topology using
both the parameterized representation of the extracted
primitives and their corresponding point areas. After
a presentation of existing methods and the explication
of the primitive extraction based on the previous work
[1] in Section 2. In Section 3, we describe the topology
reconstruction which is the novelty of this paper. Then
we conclude Section 4.
2 Previous Work
Methods defining a process to reconstruct a topology
from a mesh have already presented in previous papers
[2, 4]. Benkõ et al [2] describe a complete process to
reconstruct a B-Rep model. They use a segmentation
and many approximation tests to reconstruct the primitives. Then, using the edges of the triangulation and
the intersections between the primitives, they compute
a topology. This method can give good results, but only
if the mesh is dense and accurate; because it is very dependent of the mesh edges.
Sunil and Pande [4], propose another method to extract the topology information from CAD meshes. The
first step of their proposed approach is a segmentation followed by a primitive type attribution to each
sub-mesh. This method does not reconstruct the primitives, but defines only the topology. Furthermore, it
2
Roseline Bénière et al.
Fig. 1 Original 3D mesh(a), Point areas(b), Extracted primitives(c), Adjacency graph and intersection curves(d), B-Rep
model(e).
uses many a priori, which are only valid on the CAD
meshes.
The method to extract geometric primitive has been
presented in [1]. This method used the curvature features (principal curvatures and directions) to label the
mesh vertices and extract point areas, to define the
primitive type for each area and to compute the primitive parameters.
3 Reconstructing the Topology
With our previous work, the mesh vertices, Figure 1.(a),
corresponding to a primitive are labeled (one color by
primitive type in the Figure 1.(b)). Then, primitive parameters are approximated for each point area (Figure
1.(c)). But, in order to get a B-Rep representation, each
geometric primitive has to be trimmed, according to its
intersections with the other ones.
So, a new method step is defined to create a complete reconstruction pipeline. For this purpose, an adjacency graph containing the relationship between the
primitives, is computed using the points areas. A vertex can be common to several point areas. Using these
vertices, labeled in blue Figure 1.(b), adjacency graph
is defined. This graph guides the computation, in the
parametric way, of the intersections between two adjacent primitives. These intersection curves can be not
significant, as for example the intersection between the
cylinder and the top of the sphere 1 (the biggest), illustrated Figure 1.(c). So, to verify this, each intersection curve is compared with the points shared by the
two primitives which have generated this intersection.
If they are not close enough, the intersection curve will
not be taken into account in the B-Rep reconstruction.
In Figure 1.(d), only the intersection curves in green
are used and the red one between the sphere 1 and the
cylinder is rejected. Once the intersections have been
checked; these intersection curves, the primitives and
the adjacency relations are used to reconstruct the BRep model (Figure 1.(e)).
4 Conclusion
The novelty proposed in this paper is the topology
reconstruction from discretized mesh and continuous
primitives, extracted in a previous step. It completes
our pipeline of B-Rep model reconstruction from a mesh.
This method has been tested on combination of primitives and gives interesting preliminary results.
Acknowledgements The authors want to thank the C4W1
company and the Association Nationale de la Recherche et de
la Technologie (ANRT) for their financial support.
References
1. Bénière, R., Subsol, G., Gesquière, G., Le Breton, F.,
Puech, W.: Recovering Primitives in 3D CAD meshes.
SPIE Electronic Imaging 2011, 3D Imaging, Interaction
and Measurement 7864, 7864 0R–1–9 (2011)
2. Benkõ, P., Martin, R., Várady, T.: Algorithms for reverse
engineering boundary representation models. ComputerAided Design 33(11), 839–851 (2001)
3. Lavva, I., Hameiri, E., Shimshoni, I.: Robust methods for
geometric primitive recovery and estimation from range
images. IEEE Trans. Systems, Man and Cybernetics
37(3), 826–845 (2007)
4. Sunil, V.B., Pande, S.S.: Automatic recognition of features
from freeform surface CAD models. Computer-Aided Design 40(4), 502–517 (2008)
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