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This is the marriage of Weighted splines and Nu splines which can be recovered as special cases discussed later in this chapter. The νi are termed point tension factors because they ‘tighten’ a parametric curve at the ith point in the same way that they do for the ν-splines in [11, 12]. The wi are termed interval weights because they ‘tighten’ the curve on the ith interval in the same way that they do for the weighted splines in . If νi = 0 and all ωi = q, where q is some constant value, then the weighted ν-spline equals the ν-spline in [11, 12] with tension factors νi /q.
Sarfraz, M. (2006), Computer-aided reverse engineering using simulated evolution on NURBS, International Journal of Virtual & Physical Prototyping, Taylor & Francis, New York, 1(4), 494–512. 109. , and Gotsman, C. (1995), Multiresolution control for nonuniform B-spline curve editing, in Pacific Graphics ’95. 110. H. (1994), Multiresolution curves, in Proceedings of SIGGRAPH, pp. 261–268, ACM, New York. References 19 111. , and Blanc, C. (1997), An Hermitian Approach for Multiresolution Splines, Technical Report No.
1. Each component of the parametric weighted ν-spline is a C 1 function in general, but it has second-order geometric continuity at ti if ωi−1 = ωi and the tangent vector at ti is non zero and it is C 2 at ti if ωi−1 = ωi and νi = 0. 1 is the parametric weighted ν-spline interpolant to the points denoted by circles using periodic end conditions. ” The rest of the parameters are taken as ωi = 1 and νi = 0. 3 Freeform Weighted Nu Spline This section is devoted to constructing the freeform weighted Nu spline which has inherent properties of B-spline curves.