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4.3 Spatial schema (ISO 19107)
139
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f5(X) !
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cubic spline
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Fig. 4.11. GM _ CubicSpline
Function I: fl(x) = 1101 + all*x + a21*x 2 + a31*x 3
Function 2: f2(x) = 1102 + al2*x + a22*x 2 + a32*x 3
Function 5: fs(x) = IIos + als*x + a2S*x 2 + a3S*x 3
The first and the last segment are apart ofthe functions fl and f5 respectively (Nitschke 2003).
A B-spline (c1ass GM _ BSpline) consists of a sequence of segments each with its
own defining function, similar to the cubic spline. The shape of each segment is controlled by a weighted influence of the four control points next to the segment. The
influence is described through four polynomials, one for each control point. The
definition range of the polynomials is zero to one referring to the length of the segment. The polynomials are called basis or blending functions. A typical set of basis
functions is the Bernstein polynomials in figure 4.12.