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 algor...

The dynamics of all quadratic Newton maps rational functions is completely described. Julia set such a map found to be either Jordan curve or totally disconnected. It proved that no with degree at least three any function conformally conjugate unicritical polynomial (i.e., exactly one finite critical point). However, there are cubic which other polynomials. shown closed curve. whenever the has ...

This article is devoted to the rotation minimizing frames that are associated with spatial curves. Firstly we summarize some results concerning the differential geometry of the sweeping surfaces which are generated by these frames (the so–called profile or moulding surfaces). In the second part of the article we describe a rational approximation scheme. This scheme is based on the use of spatia...

Using the theory of the cubic modular equation we have discovered a remarkably simple class of cubically convergent algebraic iterations for n. In the course of a study of cubic modular equations the following two remarkably simple cubically convergent iterations for n were uncovered. Details of the derivation will appear in [1]. A related but less elegant iteration was discussed in [2]. While ...