Contour blending using warp-guided distance field interpolation

Given (n-1)-dimensional parallel cross-sections of an n-dimensional body, one would like to reconstruct the n-dimensional body. The method based on Distance Field Interpolation (DFI) gives a robust solution to this problem in its ability to deal with any topology in any dimension. Still this method may give undesired solutions to the problem if the changes from one cross-section to the next are significant relative to the size of the details in the cross-sections. We consider the problem of solid reconstruction from contours, which can also be considered as a contour blending or contour morphing problem, where the third dimension is time. The method presented is based on interpolation of the distance field, guided by a warp function which is controlled by a set of corresponding anchor points. Some rules for defining a smooth least-distorting warp function are given. To reduce the distortion of the intermediate shapes, the warp function is decomposed into a rigid rotational part and an elastic part. The distance field interpolation method is modified so that the interpolation is guided by the warp function. The advantage of the new approach is that it is capable of blending between contours having different topological genus, and no correspondence between the geometric primitives should be established. The desired general correspondence is defined by the user in terms of a relatively small number of anchor points.