All Questions
Tagged with sumsets convex-geometry
3
questions
7
votes
2
answers
502
views
Do Minkowski sums have anything like calculus?
Is there anything resembling differential calculus over the space of (nicely behaved) regions in $\mathbb{R}^d$, where addition is interpreted in terms of Minkowski sums? For example, it is known ...
- 71
6
votes
1
answer
885
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Minkowski sum of polytopes from their facet normals and volumes
By Minkowski's work in the early 1900s, every polytope $P\subset\mathbb R^n$ is determined up to translation by its unit facet normals $u_1,\dots,u_k$ and facet volumes $\alpha_1,\dots,\alpha_k$. ...
- 363
2
votes
4
answers
609
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Show that the Minkowski sum of two triangles in 3D is the union of Minkowski sums of each triangle along the other's edges?
I'd like to show (or disprove) the claim that the Minkowski sum of two triangles with vertices in $\mathbb{R}^3$, $A+B$, is equal to the union of the unions of the Minkowski sums of $A$ along all ...
- 703