Bézier curves · Mathematics

BÉZIER CURVE SIMULATION

▸ Placing the control points P₀…Pₙ…

▸ Building the control polygon

▸ Loading de Casteljau's algorithm (nested interpolation)

▸ Calibrating the Bernstein polynomials Bᵢ(t)

▸ Starting the parameter t sweeping 0 → 1…

▸ Ready — Online. ✅

Interpolation & values

✒️ Bézier curve

de Casteljau · t sweeps 0→1

Curve degree—

Number of control points—

Parameter t—

Point B(t) · x—

Point B(t) · y—

Interpolation stages—

Tip

A Bézier curve is "pulled" toward the control points but only passes through P₀ and Pₙ. The de Casteljau algorithm repeats linear interpolation stage by stage until one point remains — exactly the point on the curve at parameter t. Drag the control points to reshape it.

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Drag the control points to change the curve · drag the t bar to set it by hand · change the Scenario (degree 1/2/3 · spline · high degree · font letter)

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Bernstein weights Bᵢ(t) vs t (the "blending" curves) B₀B₁B₂B₃