On the instability in the dimension of splines spaces over T-meshes

The present paper reveals the instability in the dimension of the spline space S(d1,d2,d1−1,d2−1,T)S(d1,d2,d1−1,d2−1,T) over certain types of T-meshes TT, that is, the dimension is related to not only the topological information of TT but also the geometry of TT. This insight suggests us to pay much attention to the structure of the T-meshes in modeling with splines over T-meshes.

► We study the dimension of spline spaces over T-meshes by the smoothing cofactor method.
► We show that the dimension is instability for the knot of the T-mesh.
► We should be careful about the structure of the T-mesh when modeling with splines over T-meshes.