An improved version of a high accuracy surface modeling method

Abstract

A method of surface modeling, high accuracy surface modeling (HASM), which is based on the fundamental theorem of surface theory, is modified. The earlier version of HASM is theoretically incomplete and almost performs similar or slightly better than other methods being compared in the practical applications which definitely limit its promotion. According to the fundamental theorem of surface theory, we modify HASM by adding another important nonlinear equation to solve the low accuracy in some cases and make HASM have a complete and solid theory foundation. A numerical test and a real-world example are employed to comparatively validate the effectiveness of this modification. It is found that the accuracy of the simulation result has a great improvement. Another feature of the modified version of HASM is that it is theoretically perfect since it considers the third equation of the surface theory. The modified HASM will be useful with a wide range of spatial interpolation, particularly if the focus on simulation accuracy.