Interpolatory Curve Modeling with Feature Points Control

Abstract

In curve modeling, interpolation allows users to directly control the location of curve features. While previous literatures have focused on generating interpolatory curves with properties of smoothness and locality, they usually have difficulty in controlling over geometric feature points (e.g., cusps, loops, and inflection points) that mark salient intrinsic features of curve shapes. In this paper, we propose an intuitive and efficient method for constructing planar cubic curves that are curvature continuous almost-everywhere and interpolate a sequence of input data points. Our method provides a good control over the location and type of the geometric feature points. In particular, cusps and loops only occur at specified input data points, while inflection points only occur at specified input data points and joints. We refer to such feature points controlled interpolatory curves as FPC-Curves for short. To construct FPC-Curves, we focus on piecewise cubic curves, where the occurrence of loops, cusps and inflection points is mutually exclusive. We also provide a simple yet efficient algorithm for real-time interactive design of cubic FPC-Curves. Various experimental results show the efficacy and flexibility of our new approach for curve modeling.