Let g(t) be defined as in Exercise 25. Its graph is called a quadratic Bzier curve, and
Question:
Let g(t) be defined as in Exercise 25. Its graph is called a quadratic Bézier curve, and it is used in some computer graphics designs. The points p0, p1, and p2 are called the control points for the curve. Compute a formula for g(t) that involves only p0, p1, and p2. Then show that g(t) is in conv {p0; p1; p2} for 0 ≤ t ≤ 1.
Data From Exercise 25
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Let Po, P₁, and p2 be points in R", and define fo(t) = (1 t)Po +tP₁, f₁(t) = (1-t)p₁ + tp₂, and g(t) = (1 t)fo(t) + tf₁ (t) for 0 ≤ t ≤ 1. For the points as shown below, draw a picture that shows fo (), f₁ (2), and g (¹).
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Related Book For
Linear Algebra And Its Applications
ISBN: 9781292351216
6th Global Edition
Authors: David Lay, Steven Lay, Judi McDonald
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