Shape-preserving interpolants with high smoothness

A survey on shape preserving interpolation

“…Because of the computation complexity of exponential spline, this type of curve is seldom applied to practice. (2) Some take the first derivatives and second derivatives of the end points as shape parameters and obtain shape preserving interpolation curves [13]. But here, a nonlinear system of equations needs to be solved.…”

Shape preserving $$HC^2$$ H C 2 interpolatory subdivision

“…Given the data (3.7) on the interval [u, v], we construct the graph of the C 2 interpolating function λ as the support of a suitable planar parametric curve, see [7],…”

“…The function λ will be referred to as a parametric quintic because its graph is the support of a parametric curve with quintic components. For more details on parametric quintics we refer to [7]. .…”

“…Each step of the proposed subdivision procedure can be regarded as the midpoint evaluation of an interpolating function-and of its first and second derivatives-in a suitable space of smooth functions, the so called parametric quintics [7]. This space depends on a shape parameter λ ∈ (0, 1] and has two fundamental properties:…”

Interpolation Scheme for Planar Cubic G 2 Spline Curves

“…Clearly, not all the solutions are admissible. From (6) it follows that the solution (ρ 0 , ρ 1 ) is admissible iff it lies in the open set…”