A geometric construction for ensuring C<I>¹</I> continuity of adjacent Bézier patches

Abstract

It is in many cases practical to compose a continuous surface out of some low-degree Bézier surface patches having C¹ (first-order parametric) continuity between the adjacent patches. The paper presents a relatively simple geometric construction of the position of the control points in the neighbourhood of the common boundary curve to ensure the required \@mathrm C^1 continuity. The construction is based on the well-known criteria of the continuous joints of the Bézier surface patches and on a straightforward geometric similarity.