Generation of High-Quality Curve and Surface with Smoothly Varying Curvature

Abstract

A method for generating curves and surfaces which satisfy constraints of tangent directions and curvature at arbitrary points and which have smoothly varying curvature is introduced. The method is geometrical determination of a Bezier polygon, and quite different from conventional methods such as minimizing the integral of the square of curvature value or the second derivative. This method enables following things : generation of smooth curves by explicitly indicating the characteristic properties of the curves generation of smooth surfaces having not only smooth boundaries but also cross tangent and curvature which change smoothly along the boundary curve, high accurate approximation of intersection curves of surfaces, by satisfying a tangent direction, an osculating plane. and curvature constrained by the surface equations.