Patent ID: 7333109

Claim:
A method of modeling at least one section of a curve f, wherein modeling a section comprises: providing a pair of positions (f i , f i+1 ) of the section of the curve to be modeled, and additionally providing associated directions (d i , d i+1 ) and curvatures (κ i , κ i+1 ), of the section of the curve, the pair of positions (f i , f i+1 ) and directions (d i , d i+1 ) and curvatures (κ i , κ i+1 ) being related to a structure being designed; identifying points b 0 , b 1 , b 2 , b 3 and b 4 based upon the provided pair of positions (f i , f i+1 ) and the provided directions (d i , d i+1 ) and curvatures (κ i , κ i+1 ) associated with the pair of positions, wherein identifying points b 0 and b 4 includes setting b 0 equal to f i and b 4 equal to f i+1 , wherein identifying points b 1 and b 3 includes defining a control point {tilde over (b)} based upon the pair of positions (f i , f i+1 ) and directions (d i , d i+1 ), identifying point b 1 on a segment b 0 {tilde over (b)} , and identifying point b 3 on a segment b 4 {tilde over (b)} , where points b 1 and b 3 are identified further based upon weights (ρ 0 , ρ 1 ), the weights (ρ 0 , ρ 1 ) being defined such that: (a) each weight approaches a value of one-half as a distance between the pair of positions (f i , f i+1 ) approaches zero, and (b) the weights continuously depend on the positions (f i , f i+1 ), directions (d i , d i+1 ) and curvatures (κ i , κ i+1 ), wherein identifying point b 2 comprises identifying point b 2 based upon points b 1 and b 3 and the curvatures (κ i , κ i+1 ), and wherein the weights (ρ 0 , ρ 1 ) are defined, and the points b 1 and b 3 identified, further such that: (c) point b 2 is disposed within a region bounded by a triangular shape defined by points {tilde over (b)}, b 1 and b 3 ; determining a quartic interpolant p(t) over an interval (i≦t≦i+1) based upon point b 0 , b 1 , b 2 , b 3 and b 4 to thereby model the section of the curve and facilitate design of the structure, wherein the interpolant p(t) has a position, direction and curvature equal to f i , d i and κ i , respectively, at t=i, and wherein the interpolant p(t) has a position, direction and curvature equal to f i+1 , d i+1 and κ i+1 , respectively, at t=i+1; and displaying the model of the section of the curve.