Construction of 2-D parametric surfaces bounded with four irregular curves

摘要

Conventional methods of boundary-conformed 2D surface generation including algebraic interpolation method (like the linear Coons method) usually yield some problems. This paper proposes a new method namely boundary transformation method. This new method applies a mechanism of simultaneous displacement of the interpolated curves from the opposite boundaries to generate the intermediate curves. The geometric properties considered for displacements include weighted combination of geometric and linear displacement vectors of the two opposite generating curves. The algorithm has one adjustable parameter that controls the characteristics of transformation of one set of curves from their parents. Case studies show that this algorithm gives reasonably smooth transformation of the boundaries and manipulation of the surface constructed is quite user friendly. The new algorithm is capable enough to resolve the 2D boundary-conformed parameterisation problems.