Matching of freeform curves

Freeform parametric curves are extensively employed in various fields such as computer graphics, computer vision, robotics, and geometric modeling. While many applications exploit and combine univariate freeform entities into more complex forms such as sculptured surfaces, the problem of a fair or even optimal relative parameterization of freeforms, under some norm, has been rarely considered. In this work, we present a scheme that closely approximates the optimal relative matching between two or even n given freeform curves, under a user's prescribed norm that is based on differential properties of the curves. This matching is computed as a reparameterization of n-1 of the curves that can be applied explicitly using composition. The proposed matching algorithm is completely automatic and has been successfully employed in different applications with several demonstrated herein: metamorphosis of freeform curves with feature preservations, key frame interpolation for animation, self-intersection free ruled surface construction, and automatic matching of rail curves of blending surfaces. (C) 1997 Elsevier Science Ltd.