A Bezier curve P(t) is defined by four control points P0 = (−2, 0), P1 = (−2, 4), P2 = (2, 4), P3 = (2, 0). Which statements are correct? A. P(t) has degree 3. B. P(1/2) = (0, 3). C. The curve may extend outside the convex hull of its control points.
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Correct answer: A. A and B only
Explanation
Four control points give a cubic (degree 3). P(½) = (P0 + 3P1 + 3P2 + P3)/8 = (0, 24/8) = (0, 3). A Bezier curve always stays inside the convex hull of its control points, so C is false.
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