The boundaries are composed of the outer and inner parametric curves
, respectively, as follows:
Two parametric curves
[C.sub.1], [C.sub.2] represented as [p.sub.1] (u), [p.sub.2] (u), u [member of] [0, 1] are connected with [G.sup.2] continuity at the junction, and it is necessary and sufficient that [p.sub.1](1) = [p.sub.2] (0) for [G.sup.0] continuity, [P'.sub.1] (1) = a[P'.sub.1] (0) for [G.sup.1] continuity, and [p".sub.1] (1) = [a.sup.2][P".sub.2] (0) + b[p'.sub.2](0) for [G.sup.2] continuity, where a and b are arbitrary constants.
In  a method combining parametric curves
of Bezier is presented; the goal is to deal with the general case of trajectory planning (in urban environments), combining this with a speed profile generation based on Model Predictive Control.
We will develop a method for comparing cubic Bezier curves (parametric curves
) and, in particular, curves that result from a transform of other curves by similitude or other transformations such as optical scaling (that is not a linear magnification).
The exploration of the use of parametric curves
and surfaces can be viewed as the origin of Computer Aided Geometric Design (CAGD).
Genetic modeling of daily milk yields using orthogonal polynomials and parametric curves
. Animal Science, n.
(2013) A Geometric Strategy for Computing Intersections of Two Spatial Parametric Curves
. The Visual Computer, 29, 1151-1158.
Goldman, "Implicit representation of parametric curves
and surfaces," Computer Vision, Graphics, and Image Processing, vol.
Lin and Rokne  defined the variable-radius generalized offset parametric curves
 Sederberg, T.W., Degenerate Parametric Curves
, Computer Aided Geometric Design, Vol.
The volume covers such topics as vertex processing, rasterization, illumination and shaders, parametric curves
and surfaces, image texturing, bump mapping and character animation.
The surface is generated by a grid of parametric curves
. The method will be implemented on a computer with interactive graphic facilities for designing and smoothing (fairing) of the surface.