Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
Area optimization of simple polygons
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
The NURBS book
The Voronoi diagram of curved objects
Proceedings of the eleventh annual symposium on Computational geometry
Computing the visibility graph via pseudo-triangulations
Proceedings of the eleventh annual symposium on Computational geometry
Computer Vision and Image Understanding
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
The convex Hull of Rational Plane Curves
Graphical Models
Computational Geometry in C
Voronoi Diagrams for Planar Shapes
IEEE Computer Graphics and Applications
Heuristics for the Generation of Random Polygons
Proceedings of the 8th Canadian Conference on Computational Geometry
Precise Voronoi cell extraction of free-form rational planar closed curves
Proceedings of the 2005 ACM symposium on Solid and physical modeling
The convex hull of freeform surfaces
Computing - Geometric modelling dagstuhl 2002
Geometric Modeling
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Generating a Simple Polygonalizations
IV '11 Proceedings of the 2011 15th International Conference on Information Visualisation
What is the region occupied by a set of points?
GIScience'06 Proceedings of the 4th international conference on Geographic Information Science
On the shape of a set of points in the plane
IEEE Transactions on Information Theory
Coarse filters for shape matching
IEEE Computer Graphics and Applications
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Of late, researchers appear to be intrigued with the question; Given a set of points, what is the region occupied by them? The answer appears to be neither straight forward nor unique. Convex hull, which gives a convex enclosure of the given set, concave hull, which generates non-convex polygons and other variants such as @a-hull, poly hull, r-shape and s-shape etc. have been proposed. In this paper, we extend the question of finding a minimum area enclosure (MAE) to a set of closed planar freeform curves, not resorting to sampling them. An algorithm to compute MAE has also been presented. The curves are represented as NURBS (non-uniform rational B-splines). We also extend the notion of @a-hull of a point set to the set of closed curves and explore the relation between alpha hull (using negative alpha) and the MAE.