Computer Aided Geometric Design
Mean value coordinates for closed triangular meshes
ACM SIGGRAPH 2005 Papers
Mean value coordinates for arbitrary planar polygons
ACM Transactions on Graphics (TOG)
A geometric construction of coordinates for convex polyhedra using polar duals
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Spherical barycentric coordinates
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
On transfinite barycentric coordinates
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
GPU-assisted positive mean value coordinates for mesh deformations
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Barycentric rational interpolation with no poles and high rates of approximation
Numerische Mathematik
A unified, integral construction for coordinates over closed curves
Computer Aided Geometric Design
Transfinite mean value interpolation
Computer Aided Geometric Design
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
On transfinite interpolations with respect to convex domains
Computer Aided Geometric Design
Transfinite surface interpolation over irregular n-sided domains
Computer-Aided Design
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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In this paper we propose a new kind of Hermite interpolation on arbitrary domains, matching derivative data of arbitrary order on the boundary. The basic idea stems from an interpretation of mean value interpolation as the pointwise minimization of a radial energy function involving first derivatives of linear polynomials. We generalize this and minimize over derivatives of polynomials of arbitrary odd degree. We analyze the cubic case, which assumes first derivative boundary data and show that the minimization has a unique, infinitely smooth solution with cubic precision. We have not been able to prove that the solution satisfies the Hermite interpolation conditions but numerical examples strongly indicate that it does for a wide variety of planar domains and that it behaves nicely.