English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Many applications of geometry modeling and computer graphics necessiteaccurate curvature estimations of curves on the plane or on manifolds. In thispaper, we define the notion of the discrete geodesic curvature of a geodesicpolygon on a smooth surface. We show that, when a geodesic polygon P is closelyinscribed on a $C^2$-regular curve, the discrete geodesic curvature of Pestimates the geodesic curvature of C. This result allows us to evaluate thegeodesic curvature of discrete curves on surfaces. In particular, we apply suchresult to planar and spherical 4-point angle-based subdivision schemes. We showthat such schemes cannot generate in general $G^2$-continuous curves. We alsogive a novel example of $G^2$-continuous subdivision scheme on the unit sphereusing only points and discrete geodesic curvature called curvature-based6-point spherical scheme.

Approximation of the geodesic curvature and applications for spherical geometric subdivision schemes