Modified basis functions for MPHT-splines

Ni, Qian; Wang, Xuhui

doi:10.1016/j.cam.2020.112817

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Cubic B-spline Interpolation Curves With the Minimum Stretch...1

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2023

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“…, q i,d ) T ∈ R d are control points and N i,3 (t) are the cubic B-spline basis functions defined over the knots T . Note that we double the interior knots instead of setting the multiplicity of each interior knot to be one in (1), as PHT-splines and their variants use double interior knots in 2D cases [17][18][19]. PHT-splines, as one of the locally refinable splines, have numerous applications in geometric modeling and isogeometric analyses (see [17,[20][21][22][23][24] and the references therein).…”

Section: Cubic B-spline Interpolation Curves With the Minimum Stretch...mentioning

confidence: 99%

Stretch-Energy-Minimizing B-Spline Interpolation Curves and Their Applications

Ni,

Xie

2023

Mathematics

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In this paper, we propose a new method to construct energy-minimizing cubic B-spline interpolation curves by minimizing the approximated stretch energy. The construction of a B-spline interpolation curve with a minimal approximated stretch energy can be addressed by solving a sparse linear system. The proof of both the existence and uniqueness of the solution for the linear system is provided. In addition, we analyze the computational cost of cubic B-spline curves with an approximated stretch energy, which is close to that of the ordinary interpolation method with cubic B-splines without the requirement of stretch energy.

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