De Casteljau's Algorithm

(For quadratic Bézier curves)

Core Algorithm

• Uses de Casteljau's recursive algorithm to evaluate points on the Bézier curve
• Given three control points (P₀, P₁, P₂), it constructs intermediate points and evaluates the curve at parameter t

How It Works

1. Start with 3 control points
2. Calculate 2 intermediate points by linear interpolation at parameter t
3. Calculate 1 final point from those 2 intermediate points
4. This final point lies exactly on the Bézier curve!

Try This

• Drag control points to reshape the curve in real-time
• Adjust the t slider to see how the algorithm works at different positions
• Click Animate to watch the algorithm trace along the curve