An approximation approach of the clothoid curve defined in the interval [0, π/2] and its offset by free-form curves

Baass, 1984, The use of clothoid templates in highway design, Transportation Forum, 1, 47 Hartman, 1957, The highway spiral for combining curves of different radii, Trans Amer Soc Civil Engin, 122, 389, 10.1061/TACEAT.0007451 Boersma, 1960, Computation of Fresnel integrals, Math Comp, 14, 380, 10.1090/S0025-5718-1960-0121973-3 Cody, 1968, Chebyshev approximation for Fresnel integrals, Math Comp, 22, 450, 10.1090/S0025-5718-68-99871-2 Heald, 1985, Rational approximation for the Fresnel integrals, Mathematics of Computation, 44, 459, 10.1090/S0025-5718-1985-0777277-6 Meek, 1989, The use of Cornu spirals in drawing planar curves of controlled curvature, Journal of Computational and Applied Mathematics, 25, 79, 10.1016/0377-0427(89)90076-9 Stoer, 1982, Curve fitting with clothoid splines, J Res Nat Bureau Standards, 87, 317, 10.6028/jres.087.021 Walton, 1998, Planar G2 curve design with spiral segments, Computer-Aided Design, 30, 529, 10.1016/S0010-4485(98)00007-4 Walton, 1998, G2 curve composed of planar cubic and Pythagorean hodograph quintic spirals, Computer-Aided Geometric Design, 15, 547, 10.1016/S0167-8396(97)00028-9 Walton, 1996, A planar cubic Bézier spiral, Journal of Computational and Applied Mathematics, 72, 85, 10.1016/0377-0427(95)00246-4 Walton, 1996, A Pythagorean hodograph quintic spiral, Computer-Aided Design, 28, 943, 10.1016/0010-4485(96)00030-9 Farouki, 1997, Pythagorean-hodograph quintic transition curves of monotone curvature, Computer-Aided Design, 29, 601, 10.1016/S0010-4485(97)00004-3 Miura, 2000, Unit quaternion integral curve: a new type of fair free-form curves, Computer-Aided Geometric Design, 17, 39, 10.1016/S0167-8396(99)00038-2 Hoscheck, 1988, Optimal approximate conversion of spline curves and spline approximation of offset curves, Computer-Aided Design, 20, 475, 10.1016/0010-4485(88)90006-1 Hoscheck, 1987, Approximate conversion of spline curves, Computer-Aided Geometric Design;, 14, 59, 10.1016/0167-8396(87)90024-0