Ternary interpolatory subdivision

[摘要] ENGLISH ABSTRACT: Subdivision is an important and e cient tool for rendering smooth curves andsurfaces in computer graphics, by repeatedly applying a subdivision (re ning)scheme to a given set of points. In the literature, attention has been mostlyrestricted to developing binary subdivision schemes. The primary emphasis ofthis thesis is on ternary subdivision, and in particular on the interpolatory case.We will derive a symmetric ternary interpolatory subdivision scheme for therendering of curves, satisfying analogous properties to the Dubuc-Deslauriersbinary scheme. Explicit construction methods, as well as a correspondingconvergence analysis, will be presented. Graphical illustrations of the resultswill also be provided.

[发布机构] Stellenbosch University