Gauss map computation for free-form surfaces

摘要

The Gauss map of a smooth doubly-curved surface characterizes the range of variation of the surface normal as an area on the unit sphere. An algorithm to approximate the Gauss map boundary to any desired accuracy is presented, in the context of a tensor-product polynomial surface patch, (u, v) for (u, v) ∈ [0, 1] × [0, 1]. Boundary segments of the gauss map correspond to variations of the normal along the patch boundary or the parabolic lines (loci of vanishing Gaussian curvature) on the surface.