Local bases of G2 continuous G-splines Original Research Article

The theory of G-splines (Höllig and Mögerle, 1990; Mögerle, 1992) has emerged a method based on linear spaces for representing G2 surfaces over nearly arbitrary rectangular meshes. The only assumption made is that singular vertices, i.e., vertices where n ≠ 4 edges meet, are separated by at least three edges. Our goal is to obtain surfaces of low degree extending the theory of parametric continuity (C2), which will be used wherever possible in the mesh. Similar to B-spline basis, basis functions for G-splines are constructed, which are convenient for interpolation. We show their existence and their construction. The linear systems arising from G2 smoothness constraints in the construction of local bases are quite large. Computer algebra tools to investigate the solvability of these systems are discussed and evaluated.