## Surface Reconstruction Techniques

The digital data acquired through various techniques and instruments discussed in the previous section are converted into standard format so that the data can be processed utilizing the capabilities of a CAD/CAM system. This section discusses how the extracted data is processed into useful information and format for digital design and manufacturing.

Most of data acquisition methods, no matter using contact or non-contact devices, give the x, y and z coordinates of data points in a point cloud. Techniques like CT and MRI produce 2D cross sections of the solid, which are broken down into lines and points. A fundamental issue is how to connect these points to form the boundary surface of the 3D solid represented by a triangular mesh. If the points are taken in parallel planar slices, one way to reconstruct the surface is to first connect them into contours in planar slices and then tile these contours into triangular facets as illustrated in Fig. 8.18.

The conversion of a set of points into triangular facets is generally based on four steps (Fabio, 2003):

1. Pre-processing: Any data acquisition technique registers some noise or data that is not desired. In the preprocessing stage, the outliers and noise are filtered to trim the point cloud. This involves sampling of scanning data, noise filtering, outlier rejection, and filling of gaps in the point cloud data.

2. Determination of global topology: This derives relations between adjacent portions of a surface. It requires some global sorting techniques like fuzzy logic and curve of best fit to apply topological constraints and maintain special features.

3. Generation of triangular mesh: This is the main part of surface reconstruction. Based on some technique these points are connected into triangular facets representing the boundary surface.

4. Post-processing: The last phase of surface reconstruction typically involves refining the model created through the above three phases. The created triangular mesh may need some refinements to correct imperfections and errors in the surface.

Fig. 8.18 Parallel planar contours connected to form triangular facets (Asam, 2006)

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