A Quadtree decomposition of heterogeneous materials in NURBS boundary representation

Consider a two-dimensional domain given by a simple closed polygonal chain and a non-uniform rational B-spline (NURBS) curve, see Figure (a). The polygonal chain correspond to the outer boundary of the two-dimensional domain and the NURBS curve represents the boundary of a hole or and inclusion.

The Figures (a) - (f) illustrate the Quadtree subdivision of a two-dimensional domain in boundary representation. The subdomain enclosed by the NURBS curve can represent a hole or an inclusion. The corresponding finite element meshes are shown in Figures (g) and (h).

(a)	(b)	(c)
(d)	(e)	(f)
(g)	(h)

Table of contents

1. Examples
2. Dependencies
3. Acknowledgments
4. Contact

Dependencies

• matlab-tree ¹ - A MATLAB class. to represent the tree data structure

Examples

Two-dimensional domain	Quadtree decomposition

Acknowledgments

The financial support of the DFG (German Research Foundation) under project number 433734847 is gratefully acknowledged.

Contact

Rainer Reichel M.Sc.
LBB - Lehrstuhl für Baustatik und Baudynamik
RWTH Aachen University email: reichel@lbb.rwth-aaachen.de

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Footnotes

1. Jean-Yves Tinevez (2023). Tree data structure as a MATLAB class (https://github.com/tinevez/matlab-tree), GitHub. Retrieved February 23, 2023. ↩