The Mathematica Journal
Volume 9, Issue 3


In This Issue
Tricks of the Trade
In and Out
Trott's Corner
New Products
New Publications
News Bulletins
New Resources

Download This Issue 

About the Journal
Editorial Policy
Staff and Contributors
Back Issues
Contact Information

Algebraic Construction of Smooth Interpolants on Polygonal Domains
Elisabeth Anna Malsch
Gautam Dasgupta

Concave Polygons with Linearity on the Sides

The perim[a,b,c] function is replaced with perimLin[d,a,b,c,e]. Similarly the varPerim[x,y] function is modified so that four vertices define the behavior of the minimum along a line. The constructed interpolants on the quadrilateral and pentagon are linear on the sides.

The interpolants for a quadrilateral can be constructed as follows.

Figure 6. Interpolants that are smooth and linear on the sides of a concave polygon.

The formulation for a concave element applies to any shape. For linearity on a side the area function must be modified.

Otherwise, the side node would cause singular behavior along the boundary.

Figure 7. Linearity on the sides.

This works even with multiple side nodes.

Figure 8. Side node interpolants that are smooth and linear on the sides.

About Mathematica | Download Mathematica Player
© Wolfram Media, Inc. All rights reserved.