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One of the main focus of scattered data interpolation is fitting a smooth surface to a set of non-uniformly distributed data points which extends to all positions in a prescribed domain. In this paper, given a set of scattered data V ={(x i ,y i ) , i=1,...,n} R 2 over a polygonal domain and a corresponding set of real numbers n i i z 1 , we wish to construct a surface S which has continuous varying tangent plane everywhere (G 1 ) such that S(x i ,y i ) = z i . Specifically, the polynomial being considered belong to G 1 quartic Bézier functions over a triangulated domain. In order to construct the surface, we need to construct the triangular mesh spanning over the unorganized set of points, V which will then have to be covered with Bézier patches with coefficients satisfying the G 1 continuity between patches and the minimized sum of squares of principal curvatures. Examples are also presented to show the effectiveness of our proposed method.

This paper proposes the reconstruction of craniofacial fracture using rational cubic Ball curve. The idea of choosing Ball curve is based on its robustness of computing efficiency over Bezier curve. The main steps are conversion of Digital Imaging and Communications in Medicine (Dicom) images to binary images, boundary extraction and corner point detection, Ball curve fitting with genetic algorithm and final solution conversion to Dicom format. The last section illustrates a real case of craniofacial reconstruction using the proposed method which clearly indicates the applicability of this method. A Graphical User Interface (GUI) has also been developed for practical application.