Fitting Curves to Data

Numerical Analysis · Axiom Academy

Connecting the dots: from data points to smooth curves Imagine you have experimental measurements at specific points, but you need values in between. Or you need to draw a smooth curve through data points for visualization. Curve fitting is the art of finding functions that match your data! The curve passes exactly through all data points. Perfect when your data is exact (no measurement error). Example: A temperature sensor records values at specific times - we want the exact path between readings. The curve passes near the data points, minimizing overall error. Best when data has noise. Example: Survey data with measurement uncertainty - we want the underlying trend, not the noise. How do we find a polynomial that passes through n points? Is higher degree always better? (Spoiler: No!) What are splines and why are they everywhere in graphics? How do we handle the Runge phenomenon? Computer Graphics: Smooth curves in fonts, animation paths, CAD software Data Science: Predicting values between measurements Engineering: Designing smooth surfaces for aerodynamics Signal Processing: Reconstructing continuous signals from samples

This is the written version of the interactive lesson above. See the full Numerical Analysis course.