Optimal distribution of knots for tensor-product spline approximation

Tensor Product Spline Surface Approximation of a Discrete Point Field

1. Theoretical approach Designing the appropriate surface that approximates a certain point vector is one of the most challenging engineering tasks. Some of the aero and hydrodynamic profiles, materials plastic deformation technological problems are to be approached through surface approximation. Usually, the discrete input is achieved after coordinate measuring of a certain model. The designer...

H∞ Optimal Approximation for Causal Spline Interpolation

In this paper, we give a causal solution to the problem of spline interpolation using H∞ optimal approximation. Generally speaking, spline interpolation requires filtering the whole sampled data, the past and the future, to reconstruct the inter-sample values. This leads to non-causality of the filter, and this becomes a critical issue for real-time applications. Our objective here is to derive...

Spline Curve Approximation and Design by Optimal Control over the Knots Using Genetic Algorithms

In [1] Optimal Control methods over re-parametrization for curve and surface design were introduced. The advantage of Optimal Control over Global Minimization such as in [23] is that it can handle both approximation and interpolation. Moreover a cost function is introduced to implement a design objective (shortest curve, smoothest one etc...). The present work introduces the Optimal Control ove...

Least Squares Cubic Spline Approximation I Fixed Knots

Convexity conditions for parametric tensor-product B-spline surfaces

This paper provides four alternative suucient condition-sets, ensuring that a patch of a parametric tensor-product B-spline surface is locally convex. These conditions are at most tri-quadratic with respect to the control points of the surface.