# The Quad Layout Immersion: A Mathematically Equivalent Representation of a Surface Quadrilateral Layout

@article{Shepherd2020TheQL, title={The Quad Layout Immersion: A Mathematically Equivalent Representation of a Surface Quadrilateral Layout}, author={Kendrick M. Shepherd and Ren{\'e} R. Hiemstra and Thomas J. R. Hughes}, journal={ArXiv}, year={2020}, volume={abs/2012.09368} }

Quadrilateral layouts on surfaces are valuable in texture mapping, and essential in generation of quadrilateral meshes and in fitting splines. Previous work has characterized such layouts as a special metric on a surface or as a meromorphic quartic differential with finite trajectories. In this work, a surface quadrilateral layout is alternatively characterized as a special immersion of a cut representation of the surface into the Euclidean plane. We call this a quad layout immersion. This…

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