Fitting Piecewise Algebraic Curve To Scattered Data In A Plane

The problem of constructing approximations based upon scattered data is encountered in many areas of scientific applications.So many scholars have been researching about this topic and developed many algorithms. We presents an algorithm using the piecewise algebraic curve to approximate the scattered data, and using the least-squares method to calculate the best approximations.RenHong Wang advanced the theory of the muti-spline, and using the classic algebraic geometry to develop the muti- spline in 1975.After that, he and his students gave the base functions of the kinds of spline space. We adopt the spine function of the space:S₃¹(â–³_mn¹). Using the Least-squares to create a objective function. At the same time,we also considered other items, such as the associated normals and tangents, and points constraints, the energy term is also considered in the method. As a result, we get to solve a optimization problem. We can get a better result by fractionizing the partition.Because the piecewise algebraic curve is implicitly defined curves, This method is computational simple, and the main advantage is that the degrees of curves are lower compared with other methods.The numerical examples in this thesis show us these methods are feasible, and the results are satisfying.