Let x.t / be a cubic Bzier curve determined by points p 0 , p 1 ,

Let x.t / be a cubic Bézier curve determined by points p₀, p₁, p₂, and p₃.
a. Compute the tangent vector x'(t). Determine how x'(0) and x'(1) are related to the control points, and give geometric descriptions of the directions of these tangent vectors. Is it possible to have x'(1) = 0?
b. Compute the second derivative x'(t) and determine how x'(0) and x''(1) are related to the control points. Draw a figure based on Figure 10, and construct a line segment that points in the direction of x"(0).

Transcribed Image Text:

FIGURE 10 A B-spline segment and a Bézier curve.