# T-Spline Based Unifying Registration Procedure for Free-Form Surface Workpieces in Intelligent CMM
## 1 Introduction  
The coordinate measuring machine (CMM) is a powerful tool in the modern manufacturing industry [1; 2]. With the development of modern society, CMMs must be increasingly intelligent, and the next generation of CMMs is the intelligent CMM [1]. Intelligent CMMs should be able to recognize position and orientation, plan safe paths, and evaluate test results. Free-form surface parts that have pleasing appearance and texture have been increasingly used with the development of modern manufacturing. Due to the complex shape and expression of free-form surface, the intelligent detection is still difficult, including finding model rapidly and calculating form error. The study on the intelligent detection free-form surface is significantly important to improve the intelligence of CMMs. A number of previous papers have discussed intelligent CMMs, which are mainly focused on position recognition for conventional parts and path planning. Only a few studies have focused on the position and orientation recognition of free-form surface workpieces. In relevant work on intelligent CMMs [1; 2; 3], a single camera is used to identify the position and orientation of the parts and a path planning method is proposed, but not for free-form surface parts [4]. Various methods, such as the ant colony algorithm and the genetic algorithm, have been proposed for path planning in the literature [5; 6; 7; 8; 9; 10]. A method of path planning for free-form surface scanning has been presented [11]. An intelligent interface for computer aided design (CAD)-CMM [3] and an off-line interactive CMM [12] have been proposed. Free-form surfaces have been detected and the error has been calculated based on non-uniform rational B-spline curve (NURBS) and the CMM [2; 13; 14; 15]. The registration of measured data and the surface model and the recognition of free-form surface parts have similar principles. The registration method can be divided into two categories: one isthe matching of the scanned point cloud and the designed surface point cloud [16; 17; 18; 19; 20; 21; 22]; the other is associating the mathematical formula of the designed surface and the scanned point cloud [2; 13; 14; 15; 23]. Where \"designed surface point cloud\" is the point cloud generated by the design surface model, it is usually generated with the help of the software as Unigraphics NX or NURBS sampling. \"mathematical formula of the designed surface\" is NURBS formula of surface, which can be obtained from CAD files. The point cloud registration is realized based either on local characteristics [16; 17] or global features [19]. A greedy search algorithm has been used for point cloud matching [13]. The fruit fly optimization algorithm has also been used [20]. The iterative closest point (ICP) algorithm and its improved counterpart have also been used [21; 22]. The accuracy of the first matching class is relatively low. If high accuracy matching is realized, the more intensive point cloud must be extracted. This intensive point cloud will occupy a large amount of storage space and is not conducive to the system software model database. The second class can achieve high accuracy [13; 23], but the current literature has generally focused on the NURBS surface and detection point cloud. When a complex free-form surface cannot be fully expressed by NURBS, it is impossible to achieve a unified registration and evaluation. A sub-evaluation must be performed using human intervention. The T-spline has many advantages not afforded by NURBS, such as seamless splicing, a unified formula, allow partial modification and fewer control points. The control points of T-spline no need to be aligned in the entire row of rows as NURBS [24; 25; 26]. Numerous studies [24; 25; 26; 27; 28; 29] have focused on T-spline modeling technology. The concept, rules and seamless splicing method of T-spline modeling have been proposed [24]. A local interpolation and modification method for the T-spline surface has also been proposed [25].