Rational Equation for Simplifying Complex Surfaces

Mesh simplification has become an interesting research area over the past few decades. Some researchers have introduced various new methods while others have made some modifications or improvements to the existing method. However, the modified model tended to lose some of its original shape. Hence, to solve these arising problems, a new mesh simplification algorithm is introduced in this paper. Mesh simplification can be divided into two groups; mesh decimation and mesh refinement. However, in this work, mesh decimation is chosen and a rational equation is used as a cost to select elements as a candidate to be removed. The proposed algorithm also used triangular mesh as the element. The proposed algorithm was tested onto three types of data: the parametric equations, 3D data from standard database and 3D data from 3D scanner. The results clearly demonstrated that the proposed algorithm can preserve the important features of the parametric equations and 3D human shape while the boundary of the models is protected from being removed. In addition, the proposed algorithm also succeeded in simplifying the models without distorting the whole shape of the models even if the sliver triangle test is not applied on it.