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We show that the number of extraordinary points of the domain manifold is bounded by the number of segmented components.
We then develop a collocation procedure which correctly accounts for sharp edges and corners, extraordinary points, and T-junctions.
G1 continuity is attained around extraordinary points by properly capping quartic Bézier patches, where a constrained optimization problem is solved.
The paper develops a family of algorithms that allow trading polynomial degree for smoothness near the extraordinary points where more or fewer than four tensor-product patches meet.
As a result, the resultant T-splines of decomposed components are automatically glued and have high-order continuity everywhere except at the extraordinary points.
Furthermore, we study truncated T-splines and local refinement on the general domain (2-manifold) with extraordinary points in the T-mesh.
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As a result, the local subdivision rules near an extraordinary point can be modified such that the resulting Loop subdivision surface exactly interpolates a set of input endpoint interpolating CBSCs meeting at the extraordinary point.
However, here we focus on constructions of a too low degree to be curvature continuous also at the extraordinary point.
This paper presents a new solution for defining a Loop subdivision surface interpolating an arbitrary number of CBSCs meeting at an extraordinary point.
What an extraordinary point - thirty shots, a standing ovation, and Murray wins it after some absolutely incredible Djokovic defence.
A whole church congregation had photos of me saying my vows at the altar but that wasn't the extraordinary point of my wedding day in my eyes.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com