G1 surface modelling using fourth order geometric flows

We use three fourth order geometric partial differential equations to efficiently solve several surface modelling problems, including surface blending, N-sided hole filling and free-form surface fitting with the G1 boundary continuity. The non-linear equations we use include the surface diffusion flow, the quasi surface diffusion flow and the Willmore flow. These non-linear equations are discretized using a mixed finite element method based on a combination of the Loop's basis and the linear basis. The proposed approach is simple, efficient and gives very desirable results.