**4.3.1** *Geomagic Studio v.11*

*Geomagic* demonstrates an excellent surface construction capability with a high level of automation. Based on our evaluations, excellent NURB surface models can be created for all five examples from their respective scanned data in less than 30 minutes. In addition, *Geomagic* offers interactive capabilities that allow users to manually edit or create geometric entities. For examples, *Point Phase* of *Geomagic* supports users to edit points, reduce data noise, and adjust sampling to reduce number of point data. After point editing operations, polygon meshes are created by using *Wrap*. In *Mesh Phase,* self-intersecting, highly creased edges (edge with sharp angle between the normal vectors of the two neighboring polygonal faces), spikes and small clusters of polygons (a group of small isolated polygon meshes) can be detected and repaired automatically by *Mesh Doctor*. Mesh editing tools; such as smooth polygon mesh, define sharp edges, defeature and fill holes; are also provided to support users to create quality polygon meshes conveniently. Once a quality mesh is generated, *Shape Phase* is employed to create NURB surfaces best fit to the polygon mesh.

*Auto Surface* consists of a set of steps that automatically construct surface models. The steps include *Detect Contour*, *Construct Patches*, *Construct Grids* and *Fit Surfaces*. Before using *Auto Surface*, users only have to consider the quality of the surface model (for example, specifying required tolerance) and the method (for example, with or without mesh segmentation). For the *block* example, we set *surface tolerance* to 0.01 inch and construct NURB surface model with *Detect Contours* option (which performs mesh segmentation) using *Auto Surface*. A complete NURB surface model was created in 5 minutes (Fig. 8). Average deviation of the NURB model is 0.0 inch and the standard deviation is 0.0003 inch. The deviation is defined as the shortest distance (a signed distance) between the polygon mesh and the NURB surfaces. Note that in Figure 8d, green area indicates deviation close to 0 and red spot indicates the max deviation, which is about 0.017 inch in this case.

Fig. 8. Results of the *block* example tested using *Geomagic*, (a) point cloud model (634,957 points), (b) polygon mesh (1,271,924 triangles), (c) NURB surface model, and (d) deviation analysis

Two more examples, *tubing* and *sheetmetal*, are processed following the same steps. Results are shown in Figs. 9 and 10, respectively. These examples demonstrate that *Auto surface* of *Geomagic* offers reliable, viable and extremely efficient capability for automated surface reconstruction.

Fig. 9. Results of the *tubing* example tested using *Geomagic*, (a) polygon mesh (589,693 triangles), (b) NURB model (1,107 patches), and (c) deviation analysis

Fig. 10. Results of the sheet metal example tested using *Geomagic*, (a) polygon mesh (126,492 triangles), (b) NURB model (91 patches), and (c) deviation analysis
