Interactive PDE patch-based surface modeling from vertex-frames

Polygon, subdivision, and NURBS are three mainstream modeling techniques widely applied in commercial software packages. They require heavy manual operations, involve a lot of design variables leading to big data, high storage costs slow network transmissions. In this paper, we integrate the strengths boundary-based surface creation partial differential equation (PDE)-based geometric obtain first analytical $$C^0$$ continuous 4-sided PDE patches involving sculpting force-based shape manipulation use them develop an interactive technique for easy quick 3D models with small data from vertex-frames. With technique, vertex frame is defined by eight vertices, patch created vertex-frame through solution vector-valued second-order subjected boundary conditions determined vertices vertex-frame. A user-friendly interface developed obtained solution, which enables users interactively input modify easily create real time. Different tasks carried out test tool compare our proposed method polygon Coons surfaces. The results demonstrate effectiveness its advantages reducing variables, saving costs, effective manipulation.