Math

Bézier curves and splines

Edit control points and inspect the geometric construction of cubic Bézier curves and clamped cubic B-splines.

Actual application image

Try this

Click a control point, then click its new position. Watch de Casteljau interpolation for a cubic Bézier curve or de Boor interpolation for a clamped cubic B-spline.

Equations used in the module

Equations
B(t) = Σᵢ C(3,i)(1−t)³⁻ⁱ tⁱ Pᵢ
de Casteljau: Pᵢʳ = (1−t)Pᵢʳ⁻¹ + tPᵢ₊₁ʳ⁻¹
de Boor uses local knot-dependent interpolation weights
B-spline knots: 0,0,0,0,⅓,⅔,1,1,1,1

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