Thin plate spline surface approximation using Coons' patches (Q1330468)

The paper deals with the problem of thin plate spline surface approximation. Instead of the widespread discrete formulation that leads to a large number of representative surface nodal variables and, as a result, to a slow speed of energy minimization the authors propose a new surface representation method with a minimal energy of overcoming the above-mentioned deficiencies. Third-order Coons' patches are adopted to compose the surface. The energy minimization method with the usage of a conjugate gradient algorithm is stated. The problem of patch allocation is also discussed. Some examples illustrating the authors' technique of surface reconstruction are presented.