Abstract:
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, f) of the section of the curve including associated directions (d, d) and curvatures (κ, κ). Then, points b, b, b, band bcan be identified based upon the pair of positions (f, f) and associated directions (d, d) and curvatures (κ, κ). Thereafter, a quartic interpolant p(t) can be determined over an interval (i≦t≦i+1) based upon points b, b, b, band bto 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, dand κ, respectively, at t=i, and the interpolant p(t) has a position, direction and curvature equal to f, d, and κ, respectively, at t=i+1.