Shape Modification of B-Spline Curve with Geometric Constraints

A new physically based model for the shape modification of B-spline curve with geometric constraints is presented. The deformation energy of the B-spline curve is minimized based on finite element method, while geometric constraints can be imposed to control the modified shape. By changing the external force, different methods of modification can be obtained. The method based on least square, which results from applying no force, is local and simpler, but the modified shape seems less smooth. While the method based on global deformation, which is more complicated by adding synthetic spring force, can give more natural and smooth results.