Chapter 8.6, Problem 11E

In Exercises 11 and 12, mark each statement True or False. Justify each answer.

11.

1. a. The cubic Bézier curve is based on four control points.
2. b. Given a quadratic Bezier curve x(t) with control points p₀, p₁, and p₂, the directed line segment p₁ – p₀ (from p₀ to p₁) is the tangent vector to the curve at p₀.
3. c. When two quadratic Bézier curves with control points { p₀, p₁, p₂} and {p₂, p₃, p₄} are joined at p₂, the combined Bézier curve will have C¹ continuity at p₂ if p₂ is the midpoint of the line segment between p₁ and p₃.