We discuss methods for fitting implicitly defined (e.g. piecewise algebraic) curves to scattered data, which may contain problematic regions, such as edges, cusps or vertices. As the main idea, we construct a bivariate function, whose zero contour approximates a given set of points, and whose gradient field simultaneously approximates an estimated normal field. The coefficients of the implicit ...

a systematic way is presented for the construction of multi-step iterative method with frozen jacobian. the inclusion of an auxiliary function is discussed. the presented analysis shows that how to incorporate auxiliary function in a way that we can keep the order of convergence and computational cost of newton multi-step method. the auxiliary function provides us the way to overcome the singul...

With the advent of a simple matrix inversion technique, measurement-based storage ring modeling has made rapid progress in recent years. Using fast computers with large memory, the matrix inversion procedure typically adjusts up to 103 model variables to fit the order of 105 measurements. The results have been surprisingly accurate. Physics aside, one of the next frontiers is to simplify the pr...

Although some of the lÝnear curve fitting techniques provide improvements over the classicalleast squares fit algorithm,most of them cannot globally stabilize majority of data sets, and are not robust enough to handIe moderate levels of noise or missing data. In this paper, we apply "ridge regression regularization" to strengthen the stability and robustness of a linear fitting method, 3L fitti...

We give a piecewise cubic curve fitting algorithm which preserves monotonicity of the data. The algorithm has a higher order of convergence than the Fritsch-Carlson algorithm and is simpler than the Eisenstat-Jackson-Lewis algorithm.

Fractal interpolation provides an efficient way to describe data that have an irregular or self-similar structure. Fractal interpolation literature focuses mainly on functions, i.e. on data points linearly ordered with respect to their abscissa. In practice, however, it is often useful to model curves as well as functions using fractal intepolation techniques. After reviewing existing methods f...

1. An image’s outline cannot be fitted by a single cubic Bézier curve piece if it contains corners. Corners are points In this paper, a new curve-fitting algorithm is presented. This algorithm can automatically fit a set of data points with at which the outline’s directions take a sharp turn, or the piecewise geometrically continuous (G) cubic Bézier curves. outlines have discontinuous tangent ...