**A Review on Shape Engineering and Design Parameterization in Reverse Engineering**

Kuang-Hua Chang

*The University of Oklahoma Norman, OK USA* 

#### **1. Introduction**

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3D scanning technology has made enormous progress in the past 25 years (Blais, 2004); especially, the non-contact optical surface digitizers. These scanners or digitizers become more portable, affordable; and yet capturing points faster and more accurately. A hand-held laser scanner captures tens of thousands points per second with a level of accuracy around 40 m, and can cost as low as fifty thousand dollars, such as *ZScanner 800* (ZCorp). Such technical advancement makes the scanners become largely accepted and widely used in industry and academia for a broad range of engineering assignments. As a result, demand on geometric modeling technology and software tools that support efficiently processing large amount of data points (scattered points acquired from a 3D scanning, also called point cloud) and converting them into useful forms, such as NURB (non-uniform rational Bspline) surfaces, become increasingly higher.

Auto surfacing technology that automatically converts point clouds into NURB surface models has been developed and implemented into commercial tools, such as *Geomagic*  (Geomagic), *Rapidform* (INUS Technology, Inc.), *PolyWorks* (innovMetric), *SolidWorks/Scan to 3D (*SolidWorks, Inc.), among many others. These software tools have been routinely employed to create NURB surface models with excellent accuracy, saving significant time and effort. The NURB surface models are furnished with geometric information that is sufficient to support certain types of engineering assignments in maintenance, repair, and overhaul (MRO) industry, such as part inspection and fixture calibration. The surface models support 3D modeling for bioengineering and medical applications, such as (Chang et al., 2003; Sun et al., 2002; Liu et al., 2010; Lv et al., 2009). They also support automotive industry and aerospace design (Raja & Fernades 2008). NURB surface models converted from point clouds have made tremendous contributions to wide range of engineering applications. However, these models contain only surface patches without the additional semantics and topology inherent in feature-based parametric representation. Therefore, they are not suitable for design changes, feature-based NC toolpath generations, and technical data package preparation. Part re-engineering that involves design changes also requires parametric solid models.

On the other hand, shape engineering and design parameterization aims at creating fully parametric solid models from scanned data points and exporting them into mainstream

A Review on Shape Engineering and Design Parameterization in Reverse Engineering 163

Fig. 1. A single-piston engineexploded view, (a) bore diameter 1.2", and (b) bore diameter

The overall process of shape engineering and parametric solid modeling is shown in Fig. 2, in which four main phases are involved. They are (1) triangulation that converts data points to a polygon mesh, (2) mesh segmentation that separates a polygon mesh into regions based on the characteristics of the surface geometry they respectively represent, (3) solid modeling that converts segmented regions into parametric solid models, and (4) model translation that exports solid models constructed to mainstream CAD systems. Note that it is desired to have the entire process fully automated; except for Phase 3. This is because that, as stated earlier, Phase 3 requires designer's interaction mainly to recover original design intents.

Fig. 2. General process of shape engineering and parametric solid model construction

The mathematic theory and computational algorithms for triangulation have been well developed in the past few decades. A polygon mesh can be automatically and efficiently created for a given set of data points. The fundamental concept in triangulation is Delaunay triangulation. In addition to Delaunay triangulation, there are several well-known mathematic algorithms for triangulation, including marching cubes (Lorensen et al., 1987), alpha shapes (Edelsbrunner et al., 1983), ball pivoting algorithm (BPA) (Bernardini et al., 1999), Poisson surface reconstruction (Kazhdan et al., 2006), moving least squares (Cuccuru et al., 2009), etc. A few high profile projects yield very good results, such as sections of Michelangelo's Florentine

These four phases are briefly discussed in the following subsections.

1.6"

**3. Shape engineering** 

**3.1 Triangulation** 

CAD packages that support part re-engineering, feature-based NC toolpath generations, and technical data package preparation. Although, converting data points into NURB surface models has been automated, creating parametric solid models from data points cannot and will not be fully automated. This is because that, despite technical challenges in implementation, the original design intent embedded in the data points must be recovered and realized in the parametric solid model. Modeling decisions have to be made by the designer in order to recover the original design intents. However, designers must be relieved from dealing with tedious point data manipulations and primitive geometric entity constructions. Therefore, the ideal scenario is having software tools that take care of labor intensive tasks, such as managing point cloud, triangulation, etc., in an automated fashion; and offer adequate capabilities to allow designers to interactively recover design intents. Such an ideal scenario has been investigated for many years. After these many years, what can be done with the technology and tools developed at this point? Many technical articles already address auto surfacing. In this chapter, in addition to auto surfacing, we will focus on solid modeling and design parameterization.

We will present a brief review and technical advancement in 3D shape engineering and design parameterization for reverse engineering, in which discrete point clouds are converted into feature-based parametric solid models. Numerous efforts have been devoted to developing technology that automatically creates NURB surface models from point clouds. Only very recently, the development was extended to support parametric solid modeling that allows significant expansion on the scope of engineering assignments. In this chapter, underlying technology that enables such advancement in 3D shape engineering and design parameterization is presented. Major commercial software that offers such capabilities is evaluated using practical examples. Observations are presented to conclude this study. Next, we will present a more precise discussion on design parameterization to set the tone for later discussion in this chapter.
