Interface CubicSpline

  • All Superinterfaces:
    CurveSegment, GenericCurve, PolynomialSpline, SplineCurve

    public interface CubicSpline
    extends PolynomialSpline
    Cubic splines. Cubic splines are similar to line strings in that they are a sequence of segments each with its own defining function. A cubic spline uses the control points and a set of derivative parameters to define a piecewise 3rd degree polynomial interpolation. Unlike line-strings, the parameterization by arc length is not necessarily still a polynomial. Splines have two parameterizations that are used in this specification, the defining one (constructive parameter) and the one that has been reparameterized by arc length to satisfy the requirements in GenericCurve.

    The function describing the curve must be C², that is, have a continuous 1st and 2nd derivative at all points, and pass through the control points in the order given. Between the control points, the curve segment is defined by a cubic polynomial. At each control point, the polynomial changes in such a manner that the 1st and 2nd derivative vectors are the same from either side. The control parameters record must contain vectorAtStart, and vectorAtEnd which are the unit tangent vectors at controlPoint[0] and controlPoint[n] where n = controlPoint.length-1.

    GeoAPI 2.0