Convex hull (InstanceTopic, 3)
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The '''convex hull''' of a [[shape]] is a shape with the same [[vertices]] but with all other [[hypercell]]s altered in the following way (the convex hull of multiple shapes is that of their [[union]]), where ''n'' is the dimensionality of the shape: | The '''convex hull''' of a [[shape]] is a shape with the same [[vertices]] but with all other [[hypercell]]s altered in the following way (the convex hull of multiple shapes is that of their [[union]]), where ''n'' is the dimensionality of the shape: | ||
#Create (''n''-2)-[[simplices]] over every appropriate set of vertices in the shape | #Create (''n''-2)-[[simplices]] over every appropriate set of vertices in the shape | ||
#Shrink a (''n''-1)-[[hypersurface]] over the shape, blocked by the simplices, until its [[hypervolume]] is a minimum. This is now the convex hull of the original shape. | #Shrink a (''n''-1)-[[hypersurface]] over the shape, blocked by the simplices, until its [[hypervolume]] is a minimum. This is now the convex hull of the original shape. | ||
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Latest revision as of 22:56, 11 February 2014
The convex hull of a shape is a shape with the same vertices but with all other hypercells altered in the following way (the convex hull of multiple shapes is that of their union), where n is the dimensionality of the shape:
- Create (n-2)-simplices over every appropriate set of vertices in the shape
- Shrink a (n-1)-hypersurface over the shape, blocked by the simplices, until its hypervolume is a minimum. This is now the convex hull of the original shape.
