Curve and surface optimizations are the processes of constructing a curve and a surface, or mathematical functions, that have the best fit to a series of data points, possibly subject to constraints. Curve and surface optimizations can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a ”smooth” function is constructed that approximately fits the data.

Optimized curves and surfaces can be used as an aid for data visualization, to infer values of a function where no data are available, and to summarize the relationships among two or more variables. The optimization of a curve or a surface through a set of observational data is a recurring problem across numerous disciplines such as applications.

This book is devoted on designing, analysing and applying computational techniques for optimization of curves and surfaces on time scales. The book provides material for typical first course.

This book is an introduction to numerical methods for optimization of curves and surfaces on time scales. The book contains 4 chapters.

In Chapter 1 are introduced the Lagrange, σ -Lagrange, Hermite and σ -Hermite polynomial interpolations. .