Interpolants within Convex Polygons: Wachspress' Shape Functions

By G. Dasgupta. 2003

108 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design, Industrial and Manufacturing Engineering

View Paper: https://www.semanticscholar.org/paper/e646a0cc77fc21c17f07aadac47b8de622e78444

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Alessandro Russo
2. Gianmarco Manzini
3. Glaucio H. Paulino
4. Natarajan Sukumar
5. Cameron Talischi
6. L. Beirão da Veiga
7. Chau H. Le
8. R. Easter

In Computer Graphics and Computer-Aided Design

1. Natarajan Sukumar
2. Glaucio H. Paulino
3. Gianmarco Manzini
4. Alessandro Russo
5. Cameron Talischi
6. Rida T. Farouki
7. T. Pick
8. Peter Milbradt

In Industrial and Manufacturing Engineering

1. Natarajan Sukumar
2. Rida T. Farouki
3. T. Pick
4. Glaucio H. Paulino
5. Peter Milbradt

Citations in the corpus

• Honeycomb Wachspress finite elements for structural topology optimization (2009, background): “Alternatively, it is possible to compute the coefficients of the numerator and the denominator of Wachspress functions symbolically (Dasgupta 2003) or numerically (Dalton 1985).”
• Numerical integration over arbitrary polygonal domains based on Schwarz–Christoffel conformal mapping (2009, unknown): “Recently, Dasgupta [33] used symbolic computations to compute theWachspress basis functions.”
• New perspectives on polygonal and polyhedral finite element methods (2014, background): “Along with the advances of barycentric coordinates in graphics, there has been a parallel development of barycentric finite element and boundary element methods on polygons and polyhedra [5, 39, 40, 41, 17, 42, 43, 44, 45, 46, 47, 48, 49, 50], with recent applications in fracture modeling [51, 52, 5”
• The Bernstein polynomial basis: A centennial retrospective (2012, methodology): “The first construction of such a system was performed by Wachspress [207] in the context of constructing a finite element basis for convex polygons — see also [45, 208].”
• The DOE E3SM Coupled Model Version 1: Overview and Evaluation at Standard Resolution (2019, methodology): “Instead of the bilinear basis functions used by CICE, MPAS-Seaice uses Wachspress basis functions (Dasgupta, 2003), which are integrated with the quadrature rules of Dunavant (1985).”
• Polytope finite elements (2008, background): “In the recent work of Dasgputa, it was shown how Wachspress’s explicit formula appears when calculated for a five-point polygon [9].”