The single Bezier curve is extended to a composite Bezier curve using parametric continuity. Then the more general geometric continuity is defined, first for order two (G^2), and then for arbitrary order n (G^n). Composite Bezier curves are stitched together with G^1 and G^2 continuity using constraints on the control vertices and using geometric constructions.
The subdivision of Bezier curves is then derived along with a discussion of the associated geometric construction, the deCasseljau Algorithm, and flatness testing.
Then, the Bezier curve is generalized to a tensor-product surface. Finally, the rational Bezier curve and rational tensor-product surface are discussed.