🎯 Bézier Curves
Drag control points to shape smooth curves. Watch De Casteljau's algorithm recursively interpolate them step by step — the same math behind fonts, SVG paths, and CAD tools.
De Casteljau Algorithm
A degree-n Bézier curve is defined by n+1 control points P₀, P₁, …, Pₙ. For a parameter t ∈ [0, 1], the curve point B(t) is found by n rounds of linear interpolation: Pᵢʲ = (1−t)·Pᵢʲ⁻¹ + t·Pᵢ₊₁ʲ⁻¹. The construction lines shown in yellow trace these intermediate points, converging to the orange dot on the curve.
Drag any control point (blue circles) to reshape the curve. The algorithm guarantees the curve stays within the convex hull of the control polygon and always passes through P₀ and Pₙ.