Solid modelling based on sixth order partial differential equations

Although solid modelling based on partial differential equations (PDEs) has many advantages, such existing methods can either only deal with simple cases or incur expensive computational overheads. To overcome these shortcomings, in this paper we present an efficient PDE based approach to creating and manipulating solid models. With trivariate partial differential equations, the idea is to formulate an accurate closed form solution to the PDEs subject to various complex boundary constraints. The analytical nature of this solution ensures both high computational efficiency and modelling flexibility. In addition, we will also discuss how different geometric shapes can be produced by making use of controls incorporated in the PDEs and the boundary constraint equations, including the surface functions, tangents and curvature in the boundary constraints, the shape control parameters and the sculpting forces. Two examples are included to demonstrate the applications of the proposed approach and solutions.