Solution Found!
In Exercises 11 and 12, mark each statement
Chapter 8, Problem 11E(choose chapter or problem)
In Exercises 11 and 12, mark each statement True or False. Justify each answer.
a. The cubic Bézier curve is based on four control points.
b. Given a quadratic Bézier curve x(t) with control points \(p_0, p_1\), and \(p_2\), the directed line segment \(p_1-p_0\) (from \(p_0\) to \(p_1\)) is the tangent vector to the curve at \(p_0\).
c. When two quadratic Bézier curves with control points \(\left\{\mathbf{p}_{0}, \mathbf{p}_{1}, \mathbf{p}_{2}\right\}\) and \(\left\{\mathbf{p}_{2}, \mathbf{p}_{3}, \mathbf{p}_{4}\right\}\) are joined at \(p_2\), the combined Bézier curve will have \(C^1\) continuity at \(p_2\) if \(p_2\) is the midpoint of the line segment between \(p_1\) and \(p_3\).
Questions & Answers
QUESTION:
In Exercises 11 and 12, mark each statement True or False. Justify each answer.
a. The cubic Bézier curve is based on four control points.
b. Given a quadratic Bézier curve x(t) with control points \(p_0, p_1\), and \(p_2\), the directed line segment \(p_1-p_0\) (from \(p_0\) to \(p_1\)) is the tangent vector to the curve at \(p_0\).
c. When two quadratic Bézier curves with control points \(\left\{\mathbf{p}_{0}, \mathbf{p}_{1}, \mathbf{p}_{2}\right\}\) and \(\left\{\mathbf{p}_{2}, \mathbf{p}_{3}, \mathbf{p}_{4}\right\}\) are joined at \(p_2\), the combined Bézier curve will have \(C^1\) continuity at \(p_2\) if \(p_2\) is the midpoint of the line segment between \(p_1\) and \(p_3\).
ANSWER:Solution 11E1. the given statement “the cubic Bezi