Eliminating extraneous solutions in curve and surface operations

We study exact representations for offset curves and surfaces, for equal-distance curves and surfaces, and for fixedand variable-radius blending surfaces. The representations are myekeme of nonlinear equationn that define the curves and surfaces as natural projections from a bigherdimeneional space into &space. We show that the systems derived by-naively trsnalating the geometric constrainb defming the curves and mufaces can entail degeneracies that result in additional solutions that hawe no geometric aigdicancc. We characterize these extraneous solution points geometrically, and then augment the syetems with auxiliary equations of a uniform structure that exclude all extraneous solutions. Thereby, we arrive at representations that capture the geometric intent of the curve and surface definitions precisely.