A deep dive into the mathematics behind Cubic Bézier curves, starting from linear interpolation and building up through quadratic to cubic forms. Explains how the CSS cubic-bezier() function works, what its four parameters mean (the x/y coordinates of control points P1 and P2), and how the curve shape translates directly into motion speed and feel. Includes JavaScript implementations of the quadratic and cubic formulas, interactive visualizers, and shows how common CSS easing functions (ease-in, ease-out, linear) are all Cubic Bézier curves under the hood. Also covers how Framer Motion's transition ease property accepts the same control point values as an array.
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