Interpolation is widely used in image analysis, trajectory planning and statistical inference attracting a lot of attention in theoretical studies and applications. This thesis is concerned with some variational curves used in interpolation problems. The curves investigated in this thesis include Riemannian cubics, Riemannian cubics in tension, elastica, relative geodesics and generalised cubic de Casteljau curves. In applications, analyses on relative geodesics used in computer vision and generalised cubic de Casteljau curves used in computer aided geometric design are presented. In theory, the method of left Lie reduction is generalised and applied in several scenarios.
|Qualification||Doctor of Philosophy|
|Award date||27 Mar 2020|
|Publication status||Unpublished - 2020|