MATCHING OF FREEFORM CURVES

Freeform parametric curves are extensively employed in various fields such as computer graphics, computer vision, robotics, and geometric mo deling. While many applications exploit and combine univariate freefor m entities into more complex forms such as sculptured surfaces, the pr oblem of a fair or even optimal relative parameterization of freeforms , under some norm, has been rarely considered. In this work, we presen t a scheme that closely approximates the optimal relative matching bet ween two or even n given freeform curves, under a user's prescribed no rm that is based on differential properties of the curves. This matchi ng is computed as a reparameterization of n-1 of the curves that can b e applied explicitly using composition. The proposed matching algorith m is completely automatic and has been successfully employed in differ ent applications with several demonstrated herein: metamorphosis of fr eeform curves with feature preservations, key frame interpolation for animation, self-intersection free ruled surface construction, and auto matic matching of rail curves of blending surfaces. (C) 1997 Elsevier Science Ltd.