Output details

Solid modelling based on sixth order partial differential equations

Originality: Solid modelling is widely used in product design and computer animation. This work develops a new partial differential equation (PDE)-based solid modelling method. It outperforms previous methods in terms of computational efficiency and complexity. Due to the analytical nature of our method, it can create and manipulate complex solid models quickly, making it a very effective design and modelling tool.

Significance: Compared to other solid modelling methods, the PDE-based approach has many advantages, including: (1) naturally achieving the required degree of smoothness between adjacent solid chunks; (2) smaller data size; and (3) the possibility of introducing user-defined functions.

With effective treatment of more general situations, this research is able to deal with more complicated solid modelling problems. Since the second order continuity between the adjacent solid blocks is naturally achieved, no manual stitching operations are required, unlike existing methods. Due to the small data size of the representation, they can be manipulated quickly requiring only minimal computer storage.

Rigour: The mathematical model of solid modelling is built on and extended from the well-recognized PDE fundamentals. The analytical solution is obtained from a strict mathematical derivation. It has also been tested with many numerical examples, including complex shapes.