An algorithm for interpolating intersecting curves by recursive subdivision surfaces

Interpolation conditions on recursive subdivision surfaces provide more powerful techniques to manipulate such surfaces. Recently, such conditions were extended to handle interpolation of pre-defined curves by a subdivision surface. Given a curve C_i defined by a control polygon cp₀, this consists of constructing a strip complex P_i as part of the defining polyhedral network M₀ or its first subdivision M₁. By repeated subdivision, M_i converges to a limit surface S which interpolates the curve C_i. We describe an algorithm for constructing strip complexes that interpolate intersecting curves at the boundary of a surface. The algorithm is an important step towards solving the problem of interpolating arbitrary intersecting meshes of curves by subdivision surfaces