Show that the curve has c2 continuity at x(1)

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Let x(t) and y(t) be segments of a B-spline as in Exercise 6. Show that the curve has C2 continuity (as well as C1 continuity) at x(1). That is, show that x"(1) = y"(0). This higher-order continuity is desirable in CAD applications such as automotive body design, since the curves and surfaces appear much smoother. However, B-splines require three times the computation of Bézier curves, for curves of comparable length. For surfaces, B-splines require nine times the computation of Bézier surfaces. Programmers often choose Bézier surfaces for applications (such as an airplane cockpit simulator) that require real-time rendering.

Reference no: EM131074876

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