Bézier Curves and the logic behind them
Two points define a line (one vector + origin). Three points define a plane (two vectors + origin)<p>Quadratic bezier: constructed by a velocity vector and an acceleration vector -- strictly 2D (planar curve). If you can draw a "V", then you can extend it into a parallelogram.[0]<p>Cubic bezier: constructed by velocity, acceleration, and jerk vector -- generally non-planar 3D curves (since there are three vectors involved), only special cases are planar.<p>[0] <a href="https://www.desmos.com/calculator/enz2qqc2ov" rel="nofollow noreferrer">https://www.desmos.com/calculator/enz2qqc2ov</a><p>IMO Rational Quadratic Beziers are much more interesting since it defines 3D perspective, the entire field of Computer Vision can be derived from it alone.