If you have used a drawing program on a computer, you have probably worked with a curve known as a curve. 2 Such a curve is defined parametrically by using several control points in the plane to shape the curve. In Exercises 7–12, we discuss various aspects of quadratic curves. These curves are defined by using three fixed control points (x1, y1), (x2, y2), and (x3, y3) and a nonnegative constant w. The curve defined by this information is given by x: [0, 1] → R2, x(t) = (x(t), y(t)), where
Repeat Exercise 7 for the control points (−1,−1), (1, 3), and (4, 1).
Exercise 7 Let the control points be (1,0), (0,1), and (1,1). Use a computer to graph the curve for w = 0, 1/2, 1, 2, 5. What happens as w increases?
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