This shows graphically how a Bezier curve connecting two points is generated.
P1 is called the control point, and its location determines the shape of the generated curve. Beziers are used extensively in computer graphics and in font generation.
Each of the three dots slides along a straight line. At any instant in time, each dot has moved some fraction of the total length of its line, and this fraction is same for each dot.
This is a quadratic Bezier – it has one control point, and one “bend” in the curve. Higher order Beziers have more control points, and more bends.
H/T to for the reference to David Mitchell.
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