Understanding derivations based on Bezier curves
Due September 16th, in lab
This worksheet is intended as a short 30 min exercise to be done in groups of 2-3 people.
Degree-2 Bezier Curve
In class, we derived the Bezier curve for cubic interpolation. For this question, derive the Bezier curve for a degree-2 polynomial.
In class, we saw that the formula for a nth-degree Bezier curve is
1) Derive is the polynomial for a degree-2 Bezier curve
2) How many control points does a degree-2 Bezier curve need?
3) How can we use de Casteljau’s algorithm to interpolate using a degree-2 Bezier curve?
4) Show that de Casteljau’s algorithm reduces to the same equation as the degree-2 Bezier Curve.