Bohumir Bastl: Hermite interpolation techniques using polynomial and rational PH curves

Predavanje od 10h do 11h

Bohumir Bastl: Hermite interpolation techniques using polynomial and rational PH curves

Povzetek: In this talk, we present an overview of our results related to interpolation techniques by polynomial and rational PH curves. In the first part, we show that all rational hypocycloids and epicycloids are rational PH curves and we formulate efficient algorithms for G^1 and G^2 Hermite interpolation with their arcs and arcs of their convolutions. Then, we focus on G^1 Hermite interpolation by PH cubics and we give a thorough analysis of the number and the quality of the interpolants; particularly if they contain a loop or not. Finally, we propose algorithms for C^1 Hermite interpolation with uniform and non-uniform biarcs of Tschirnhausen cubic, the so-called TC-biarcs. We give a formal proof for approximation order of the conversion of an arbitrary continuous planar curve into C^1 PH cubic spline and demostrate advantages of free shape parameter of non-uniform TC-biarcs for e.g. removing self-intersections of interpolants.