Related Experiment Video
Updated: Dec 15, 2025

Intravital Longitudinal Imaging of Vascular Dynamics in the Calvarial Bone Marrow
Published on: April 11, 2025
Smooth polar caps for locally quad-dominant meshes
Kȩstutis Karčiauskas1, Jörg Peters2
1Vilnius University, Lithuania.
Abstract:
A polar configuration is a node surrounded by m triangles. Polar configurations are common to cap off cylinders and spheres. When the triangles, interpreted as quadrilaterals with one edge collapsed, are surrounded by a quad-strip then the extended polar configuration qualifies as part of a locally quad-dominant (lqd) mesh. Recent constructions, referred to as semi-structured splines, can use lqd meshes as control nets: multi-sided configurations that merge parameter directions are covered by G-spline; and T-junctions that transition from coarse and fine are covered by GT-splines. This paper complements existing semi-structured splines by providing the missing component for polar configurations. A spectrum of constructions of differing degree are introduced, tested and compared. Bi-2 C 1 splines are extended to polar configurations covered by C 1 surfaces consisting of (macro-)patches of degree as low as bi-2. Bi-3 C 2 splines are extended to polar configurations covered by surfaces that are C 2 except for a C 1 pole and consist of (macro-)patches of degree as low as bi-3.
Related Concept Videos
Curvilinear Motion: Polar Coordinates
The particle's location is described using a unit vector along the radial direction. Deriving the particle's position...
Polar Coordinates
Polar Equations of Conics
Polar and Cylindrical Coordinates
Mesh Analysis
A fundamental concept in mesh analysis is the definition of meshes and mesh currents. A mesh is a closed...
Potential Due to a Polarized Object

