Interpoleerimisviise

Interpoleerimisviise are methods used to estimate unknown values that lie between known data points. These techniques are fundamental in various fields, including mathematics, computer graphics, statistics, and engineering, for creating smooth curves or surfaces from discrete data. The core idea is to construct a function that passes through a given set of points and then use this function to predict values at intermediate locations.

Linear interpolation is the simplest method, assuming a straight line connects two consecutive data points. The estimated value is found by proportionally scaling the difference between the known values based on the position of the unknown point. Quadratic interpolation uses a parabola passing through three points to estimate an intermediate value. This generally provides a smoother curve than linear interpolation.

More complex methods include cubic interpolation, which uses a cubic polynomial through four points, offering even greater smoothness and accuracy. Spline interpolation is a generalization that uses piecewise polynomial functions (often cubic) joined together at data points, ensuring continuity of derivatives at these connection points. This approach is widely used in computer-aided design (CAD) and animation.

Other interpolation techniques exist, such as polynomial interpolation (using a single high-degree polynomial for all points, which can be prone to oscillations) and nearest-neighbor interpolation (simply selecting the value of the closest data point, often used in image resizing). The choice of interpolation method depends heavily on the nature of the data, the desired smoothness, and computational efficiency requirements.