GoKawiilTechnical deep-dive explains why bezier curves behave the way they do
A technical article breaks down the mathematics behind bezier curves, showing how repeated linear interpolation between control points produces the compact polynomial formulas used in graphics software. It explains why cubic beziers with four control points are the industry standard, since only the first and last points are guaranteed to lie on the curve, and how longer curves are built by joining multiple cubic segments with matched tangents for smoothness.