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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**)

From the contents of the previous section it follows that obtaining a correct CAD-model from an ICADM of class ICM1 is not a problem. So, in general case we need a way to reduce an ICADM of class ICM3 to an ICADM of class ICM1 via intermediate ICADMs of classes ICMT (if this class is possible) and ICM2. To make it, it is enough to reconstruct **A** only in properly chosen strip-like regions connecting the corresponding boundaries of **A**(F3.1).

Diminishing the width of such strip region to 0 we obtain a curve connecting the two corresponding boundary points of **A**; at each internal point of the curve the normal vector to **A** is defined (F3.2). Letâ€™s call such curve a *bridge*.

Figure F3.1 illustrates how the concept of bridges works. In the left there is a beginning ICADM of class ICM3 representing a ball-like object. Initially, using bridges we reduce it to an ICADM of class ICM2 (middle). This ICADM contains only holes, each hole boundary is formed by the corresponding bridges and fragments of island boundaries. Then using bridges again each complicated hole of the ICADM is recursively decomposed until a set of only trivial holes is obtained (right).

In this way bridges create an irregular mesh approximating **A**, inside each cell of the mesh **A** can be reconstructed by a simple existing method (see F3.3).

Considering that a bridge approximates the corresponding surface strip of a finite width (the width depends on a specified approximation precision) we can conclude that using the concept of bridges a major share of **A** is reconstructed the simple method. So, using the concept significantly reduces the total repairing cost.