Triangle Mesh Completer by Alexander Emelyanov - Mesh Repairing Tools

Triangle Mesh Completer


RHINOCEROS® plug-in & standalone program

Advanced Mesh Repairing. Theory

Alexander Emelyanov,
Institute of Computing for Physics and Technology
Protvino, Moscow region, Russia
ae@ae3d.ru
(Updated version of the paper presented on Graphicon 2010)

2. Formalization of damaged cad-models

Consider a CAD-model that is an unsuccessful result of work of some surface reconstruction algorithm and has the following properties: the model contains a partially reconstructed surface (A), with condition that each part of this surface represents the corresponding part of the original object; the remaining part of the model surface (A) is missing; the model can contain unused sampled points (free points). Let’s call such model an incomplete CAD-model (ICADM). In general case, to obtain it, we need to apply a proper filtering procedure that removes all parts of A which don’t represent the original object surface. Just an ICADM is the assumed input in our works.

In an ICADM A can be represented by one or several isolated coherent regions. Let’s call such regions islands.

Any ICADM contains one or several closed boundaries which separate A and A. Each boundary has connection with one and only one region of A. If this region is connected only with the same boundary let’s call such boundary a hole boundary or a complex boundary (CB) otherwise. As a consequence, the aggregate of a hole boundary and the region of A that is connected with the boundary is called a hole.

Let’s call a hole a trivial hole (TH) if its region of A can be reconstructed by an existing not so complicated algorithm or a complicated hole (CH) otherwise. A boundary that is not the boundary of a trivial hole will be called a non-trivial boundary.

Using the terms defined above the following classification of ICADMs is made: class

num. of islands

CB

CH

TH

ICM3

>1

y

y/n

y/n

ICM2

1

n

y

y/n

ICM1

1

n

n

y

ICMT

1

y

y/n

y/n

© Alexander Emelyanov, 2011-2016     
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