## Modeling of Standard Teeth

There are many commercial dental CAD/CAM systems for automating the dental design process as reviewed previously. In these systems the basic models of teeth are available in their own libraries. However, general forms of teeth geometry provided by these CAD/CAM systems can only give raw shapes. There are always some manual alterations and modifications required as every patient is unique and every tooth has its own topological features.

The procedure based on the work of Song et al. (2005) can assist developing a system to form such a library with standard teeth models. It formulates a way of modeling a standard tooth based on the special topological features pertaining to that tooth. In this method, the data points are extracted from the surface of a tooth using a 3D digitizer as shown in the Fig. 8.22(a).

The digital data can be used to create a standard prosthetic crown using a B-spline surface. For an array of (m+1) by («+1) control points, the equation of the surface is

Fig. 8.22 (a) Point cloud data; (b) B-Spline surface mesh; (c) the surface in shaded image; (d) feature-based curves (Song et al., 2005)

Fig. 8.22 (a) Point cloud data; (b) B-Spline surface mesh; (c) the surface in shaded image; (d) feature-based curves (Song et al., 2005)

where P(u, v) is a point on the B-spline surface, Pij are the control points, and Ni,k(u) and Nj,l(v) are polynomial functions. The values of m, n, k and l were selected by Song et al. (2005) as 30, 33, 4 and 4, respectively. These values imply that there are 29 x 32 control points and the B-spline function is a bi-cubic surface in the form

30 33

The B-spline surface generated based on these control points is shown in Fig. 8.22(b) and (c). Adjustment of the control points affects a local area, and it may be a tedious job for the user to adjust the entire area using this adjustment. To facilitate an easier and more effective adjustment, some of the feature points can be put together to form a feature curve so that editing the curve automatically changes the feature points. The feature curve can be represented by a cubic B-spline function as follows:

Thus a feature curve can be modified by adjusting its feature points, and this modification results in the global modification of the tooth surface. In this way the topological features of the B-spline curves remain unchanged while the points are moved to customize the tooth design. The feature curves of the discussed tooth model are shown in Fig. 8.22(d). With the above technique a set of 28 standard teeth as shown in Fig. 8.23 were modeled by Song et al. (2005). These models can be stored in the library and retrieved later for any customized design.

Fig. 8.23 Feature based models of teeth (Song et al., 2005)

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