System, method and computer program product for modeling at least one section of a curve

摘要

A system, method and computer program product are provided for modeling at least one section of a curve. Each section can be modeled by initially providing a pair of positions (f_i, f_i+1) of the section of the curve including associated directions (d_i, d_i+1) and curvatures (kappa_i, kappa_i+1). Then, points b₀, b₁, b₂, b₃ and b₄ can be identified based upon the pair of positions (f_i, f_i+1) and associated directions (d_i, d_i+1) and curvatures (kappa_i, kappa_i+1). Thereafter, a quartic interpolant p(t) can be determined over an interval (i<=t<=i+1) based upon points b₀, b₁, b₂, b₃ and b₄ to thereby model the section of the curve. The quartic interpolant can be determined such that the interpolant p(t) has a position, direction and curvature equal to f_i, d_i and kappa_i, respectively, at t=i, and the interpolant p(t) has a position, direction and curvature equal to f_i+1, d_i+1, and kappa_i+1, respectively, at t=i+1.