• Corpus ID: 229297570

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

  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},
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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