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.

Research highlights
► This paper presents a solid modelling method based on sixth order partial differential equations.
► Closed form solution is developed to raise modelling efficiency.
► General boundary constraints and sculpting forces are considered to improve modelling capacity.
► Complicated solid models are created from solid chunks based on partial differential equation.
► The created solid models are effectively manipulated by changing design parameters in partial differential equations and boundary constraints.