Spliniinterpolaation

Spliniinterpolaation is a method used in computer graphics and data analysis to create smooth curves or surfaces that pass through a given set of data points. It is a form of interpolation, meaning it estimates values between known data points. The "spline" part refers to the mathematical function used for the interpolation, which is typically a piecewise polynomial.

Unlike simpler interpolation methods like linear interpolation, which connect points with straight lines, or polynomial interpolation, which uses a single polynomial to fit all points (and can lead to undesirable oscillations), spline interpolation uses multiple, simpler polynomial segments. These segments are joined together at the data points, called knots, in a way that ensures continuity and smoothness. This continuity can be defined at various orders, such as first-order continuity (C1, meaning the slopes match at the knots) or second-order continuity (C2, meaning the curvatures also match).

Common types of splines used in interpolation include cubic splines, which are piecewise cubic polynomials. Cubic splines are widely used because they offer a good balance between smoothness and computational efficiency. The piecewise nature of splines allows for local control over the curve. Adjusting one data point only affects the curve in its immediate vicinity, unlike global interpolation methods where a change can impact the entire curve. This makes spline interpolation a robust and flexible tool for generating realistic shapes and interpolating complex data sets.