The Instability in the Dimensions of Spline Spaces Over T-Meshes with Nested T-Cycles

摘要

This paper studies on the dimensions of spline spaces over some given T-meshes.Using the smoothing cofactor-conformality method,we study the instability in the dimensions of the spline spaces over T-meshes with 2-nested and 3-nested T-cycles.We define a singularity factor of each simple T-cycle,the instability and the structure's degeneration are associated with the singularity factors.In order to get a stable dimension formula over T-mesh with a N-nested T-cycle,a constraint on the T-mesh is introduced.Finally,a possible degeneration for a case of parallel T-cycles is illustrated.