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

\[p(t) = \sum_{i=0}^n B_i^n(t) b_i\]

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.