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Bézier curve construction
Four controls shape a curved handle. To locate its point at t = 1/2, each little calculation only needs two inputs and the same parameter frame.
Selected result
What remains connected
What is checked, and where this example stops
The six exact reads agree with an independent Bernstein polynomial at nine parameter samples, including endpoints. Tests also cover open, closed, repeated and reversed controls.
The drawn curve is a presentation of the control recipe. The selected sample and its intermediate points are checked Gojo reads. t = 1/2 is not generally halfway along arc length.