Continuity is used to make sure that the curves are retaining their position. For geometric continuity parametric derivatives of two sections should be proportional to each other. Parametric continuity is achieved by matching the parametric derivatives of adjoining curves at their common boundary. C0 is zero order parametric continuity which means that the curves meet. C1 is first order parametric continuity which means that first parametric derivatives of coordinate functions for two successive curve sections are equal. G1 is the first order geometric continuity in which the parametric first derivatives are proportional at intersection of two successive sections. C2 is second order parametric continuity is the one in which both first order and second order parametric derivatives of two curve sections are same at intersection. G2 is the first order geometric continuity in which both first and second parametric derivatives of the two curve sections are proportional at their boundary.

In C2 continuity,

r(t) = (t² – 2t, t)

n(t) = (t² + 1, t +1)

C1 and G1 are continuous at r(1) =n(0)

Derivative r(t) = 2t-2, 1

r(1) = 0,1

Derivative n(t) = 2t, 1

n(0) = 0,1

Since r(1) = n(0), two curves are continuous.

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