## Info

### Figure 7.17 Parameterizing the extracted NURBS curves of the PP

1. Three extra reference points are added to describe the trough and crest points. These points are used to dimension their respective vertical heights (Ht, Hci, Hc2) from the horizontal base line, which represent their vertical distances from the centre of rotation.
2. The crest points are also used to define the horizontal distance, Wc, based on the respective horizontal distances from the crest points (Wc1, Wc2). The horizontal distance between the two crests, Wc, is important as it determines the separation between the convex PP head of the bi-condylar hinge joint.

After each of the surface feature curves is parameterized, the control points (crest points and trough point) can be used to construct guide curves which in turn are used to reconstruct the bearing surface of the PP head.

7.5.3.2 NURBS curve feature extraction from the PP and MP base

The curve feature extraction procedure for the base of the PP and MP is similar to that for the PP head. The same problem of identification of the PP/MP base also exists.

A reference plane needs to be constructed to identify and isolate the PP/MP base surface from the whole freeform bone surface. Since the width of the PP/MP base is the key parameter of the PP/MP base, the position of the cutting plane is referenced to the width of the PP/MP base. The cutting plane is horizontal which is different from the cutting plane of the PP head. The distance from the cutting plane to the top of the PP/MP base equals the width of the PP/MP base multiplied by a conversion factor, which is defined as a constant value of 0.25 for the PP/MP base in this research. Figure 7.18 shows an example of the cutting plane for the base of the MP. The width of the MP base is 14.40 mm for this specimen. Therefore, the distance from the cutting plane to the top plane is set to 3.60 mm for this MP model.

The following procedure extracts curve features of the MP base as an example. However, it is also applicable to PP base feature extractions. In fact, the same curve feature extraction method can also be used for the head of the metacarpal phalanx (MCP) bone.

Ten equiangular planes over a 180° angle of rotation are inserted into the head of the MP bone. Each curve can be parameterized to obtain the quantitative surface feature of the PP/MP base. The following procedure takes the MP base as an example. However, it is also applicable to quantitative parameter extraction for the PP base.

Figure 7.18 Cutting plane inserted into the bone model of the MP
Figure 7.19 Parameterizing the extracted NURBS curves of the MP

Since there are no distinct properties for the extracted surface curves of MP, such as troughs and crests, ten equiangular lines are inserted to divide the curve into several segments (Figure 7.19). These intersection points are saved as the control points of the surface feature and will be used to reconstruct the bearing surface of the PP/MP base.

### 7.5.3.3 Discussion on curve feature extraction

Different parameterizing methods are used for MP and PP curve extraction. The accuracy of the final reconstructed surfaces varies for different parameterizing methods.

The numbers of reference planes and feature points on each extracted feature curve affect the accuracy of the reconstructed surfaces. Eight analyses were performed on the same MCP bone samples and nine analyses for PP using different numbers of feature curves and control points.

New splines are constructed using the control points, and these are used to loft out the finger joint bone surface. Here, V0 is the volume of the original bone head, which is compared with the volume of the reconstructed bone head, VR. The expression

Vo is used to calculate the volume difference between the original bone head and reconstructed bone head.

For the MCP bone, the number of control points for each spline has more effect on the final reconstructed surface accuracy. The volume difference is less than 2% for 10 control points for each spline. However, with seven and five control points for each spline, the volume difference will not change much. Since the MCP bone head is like a half-sphere, an appropriate number of spline curves and control points can be selected for reconstructing the final surface. Increase in the spline and control point number will not improve the accuracy much.

For the PP bone sample, the parameter of the control points on the spline curves has more effect on the accuracy of the reconstructed surface. For the same number of control points, the final surface accuracy will be greatly improved if the control points are the extreme points of the spline curve. The number of splines and control points also affect the reconstructed surface. Therefore, appropriate positions of control points and an appropriate number of control points and splines should be used according to the required accuracy of the final reconstructed surface.

From the above we can draw the following conclusions: to simplify the feature extraction and ensure accuracy of the final reconstructed surface, appropriate numbers of reference planes and control points should be used for different bone model types.

7.5.4 Automatic surface reconstruction and feature extraction

The above method describes the detailed procedures in finger joint digitalization, surface reconstruction and feature extraction. For each sample, such procedures can be effectively implemented step by step, but, for a large number of finger joint bones, a great deal of data must be analysed and many features extracted. Obviously, it is preferred that such procedures be automated to enhance overall efficiency. An automated implementation of such processes was developed with the application programming interface (API) of the commercial software RapidForm.

RapidForm API is designed for automation. We can access RapidForm objects and reuse codes to develop functions and applications for automation. RapidForm integrates Visual Basic, so we can use macros to automate the curve feature extraction process.

Two macros were developed: one for automated identification of the bearing surface, the other for automated feature extraction.

7.5.4.1 Automated identification of the bearing surface

Automated identification of the bearing surface is implemented using RapidForm API functions. The 3D point cloud data are first imported into RapidForm (Figure 7.20). The macro begins with registration which aligns the scanned shells, followed by a merge operation which combines them into one shell. The final joint model is shown in Figure 7.21. The intersection planes are constructed and corresponding curve features on the surface are derived. Redundant vertices around the lower part of the model are deleted.

### 7.5.4.2 Automated feature extraction

Two methods were used for the finger joint feature extraction. Method I is called the maximum tangential method (MTM) and method II is called the equiangular method (EM). MTM is suitable for the head of the PP while EM is suitable for the PP and MP bases.

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