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Hormann_2023_Wiley_CompGraphForum_Maximum likelihood
Journal article

Maximum likelihood coordinates

  • 2023
Published in:
  • Computer graphics forum. - 2023, vol. 42, no. 5
Computing methodologies
Parametric curve and surface models
Mathematics of computing
Convex optimization
English Any point inside a d-dimensional simplex can be expressed in a unique way as a convex combination of the simplex's vertices, and the coefficients of this combination are called the barycentric coordinates of the point. The idea of barycentric coordinates extends to general polytopes with n vertices, but they are no longer unique if n > d+1. Several constructions of such generalized barycentric coordinates have been proposed, in particular for polygons and polyhedra, but most approaches cannot guarantee the non-negativity of the coordinates, which is important for applications like image warping and mesh deformation. We present a novel construction of non-negative and smooth generalized barycentric coordinates for arbitrary simple polygons, which extends to higher dimensions and can include isolated interior points. Our approach is inspired by maximum entropy coordinates, as it also uses a statistical model to define coordinates for convex polygons, but our generalization to non-convex shapes is different and based instead on the project-and-smooth idea of iterative coordinates. We show that our coordinates and their gradients can be evaluated efficiently and provide several examples that illustrate their advantages over previous constructions.
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Language
  • English
Classification
Computer science and technology
License
CC BY-NC-ND
Open access status
hybrid
Identifiers
Persistent URL
https://n2t.net/ark:/12658/srd1330313
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