Constrained reconstruction of 3D curves and surfaces using integral spline operators

In the context of direct/reverse engineering processes one of the main problem is the reconstruction of curves and surfaces starting from a cloud of points. Most of the times the (re)constructed curves and surfaces have to satisfy some particular geometric constraints and functional properties related to the desired shapes. In this paper, referring to 3D curves and surfaces, we propose an algorithm based on an interpolatory variation diminishing integral spline operator characterized by the presence of shape parameters. In order to choose the best value for the shape parameters different functionals can be adopted. Some test cases are presented in order to show the effectiveness of the proposed algorithm: both academic and real world test cases are considered.