Voronoi diagram for multiply-connected polygonal domains 1: algorithm
IBM Journal of Research and Development
Voronoi diagram for multiply-connected polygonal domains 11: implementation and application
IBM Journal of Research and Development
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Constructing 3-D discrete medial axis
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Continuous skeletons of discrete objects
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Proceedings of the third ARO workshop on Adaptive methods for partial differential equations
Medial axis transform to boundary representation conversion
Medial axis transform to boundary representation conversion
Differential and topological properties of medial axis transforms
Graphical Models and Image Processing
Handbook of mathematics (3rd ed.)
Handbook of mathematics (3rd ed.)
Proceedings of the fifth ACM symposium on Solid modeling and applications
The finite element method using MATLAB (2nd ed.)
The finite element method using MATLAB (2nd ed.)
Finite element solution of boundary value problems: theory and computation
Finite element solution of boundary value problems: theory and computation
Linear onesided stability of MAT for weakly injective 3D domain
Proceedings of the seventh ACM symposium on Solid modeling and applications
Approximate medial axis as a voronoi subcomplex
Proceedings of the seventh ACM symposium on Solid modeling and applications
Homotopy-preserving medial axis simplification
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Graphical Models
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Stability and homotopy of a subset of the medial axis
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Curve-Skeleton Properties, Applications, and Algorithms
IEEE Transactions on Visualization and Computer Graphics
Distance functions and skeletal representations of rigid and non-rigid planar shapes
Computer-Aided Design
Algebraic reduction of beams for CAD-integrated analysis
Computer-Aided Design
Fast iterative solvers for thin structures
Finite Elements in Analysis and Design
A family of skeletons for motion planning and geometric reasoning applications
Artificial Intelligence for Engineering Design, Analysis and Manufacturing - Representing and Reasoning About Three-Dimensional Space
Medial zones: Formulation and applications
Computer-Aided Design
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Dimensional reduction is a simplification technique that eliminates one or more dimensions from a boundary value problem. It results in significant computational savings with minimal loss in accuracy. Existing dimensional reduction methods rely on a lower-dimensional geometric entity called the mid-element that is unfortunately ill defined for irregular thin solids.The main objective of this paper is to propose a new theory of 'skeletal dimensional reduction' that is superior to existing mid-element based methods in that it unambiguous and can be easily automated. The proposed method is based on a popular skeletal representation of geometry that is well defined for all thin solids. By exploiting the unique properties of a skeletal representation it is shown how boundary value problems, specifically 2-D Laplacian problems, over complex 'beam-like' solids can be systematically reduced to lower-dimensional problems over the skeleton. Further, in the special case of a regular thin solid, the skeletal reduction simplifies, as expected, into a mid-element based dimensional reduction.