Anisotropic polygonal remeshing
ACM SIGGRAPH 2003 Papers
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
A finite element method for three-dimensional unstructured grid smoothing
Journal of Computational Physics
Discrete conformal mappings via circle patterns
ACM Transactions on Graphics (TOG)
Periodic global parameterization
ACM Transactions on Graphics (TOG)
Designing quadrangulations with discrete harmonic forms
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Global parametrization by incremental flattening
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Controlled-distortion constrained global parametrization
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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A continuum description of unstructured meshes in two dimensions, both for planar and curved surface domains, is proposed. The meshes described are those which, in the limit of an increasingly finer mesh (smaller cells), and away from irregular vertices, have ideally-shaped cells (squares or equilateral triangles), and can therefore be completely described by two local properties: local cell size and local edge directions. The connection between the two properties is derived by defining a Riemannian manifold whose geodesics trace the edges of the mesh. A function @f, proportional to the logarithm of the cell size, is shown to obey the Poisson equation, with localized charges corresponding to irregular vertices. The problem of finding a suitable manifold for a given domain is thus shown to exactly reduce to an Inverse Poisson problem on @f, of finding a distribution of localized charges adhering to the conditions derived for boundary alignment. Possible applications to mesh generation are discussed.