A new boundary interpolation technique for parameterisation of planar surfaces with four arbitrary boundary curves

This article is concerned with construction of planar parametric surfaces enclosed by four arbitrary boundary curves. The available conventional methods for this purpose are algebraic interpolation method (like the Coons method) and partial differential equation method. These methods usually yield some problems. This article proposes a new method namely boundary interpolation method where the geometric properties of the boundary curves have been taken into account. A technique of simultaneous displacement of the interpolated curves from the opposite boundaries has been adopted. The geometric properties considered for displacement include weighted combination of geometric and linear displacement vectors of the two opposite generating curves. The algorithm has two adjustable parameters that control the characteristics of interpolation of one set of curves from their parents. Case studies show that this algorithm gives reasonably smooth boundary-fitted planar parametric surface compared with the other two conventional methods.