Extrema detection of bivariate spline functions
The problem of finding the extrema of a two-variable spline function \(x(s,t)\) of degree \(k\geq 3\), in a rectangle \(\mathcal{D}\subset \mathbb{R}^2\), is examined. In this respect, a method is developed which allows to detect the extrema of \(x(s,t)\) as well as of their derivatives. An exception is given by those extrema whose Hessian matrix is singular. The performance of the method is tested by considering an optimal smoothing spline which is designed by sampling the function \(f(s,t)=\sum_{i=1}^6 a_i \exp[-\kappa_i((s-p_i)^2+(t-q_i)^2)] \). Another example is the analysis of deformation of a jellyfish in motion. Some figures and tables are shown.
scientific article; zbMATH DE number 5289082
scientific article