For two polytopes $A$ and $B$, when can we find $C$ such that $A=B+C$?
$Asubsetmathbb{R}^d$ is a polytope if $A$ equals the convex hull of some finite set.
For any two sets $B$ and $C$, $B+Cequiv{x+y:xin B,yin C}$.
My question:
Let $A$ and $B$ be polytopes in $mathbb{R}^d$. When can we find a polytope $C$ such that $A=B+C$?
Such $C$ always exists? I guess not, right?
convex-analysis convex-geometry
asked Nov 26 '18 at 6:42
Yi-Hsuan Lin
30817
add a comment |
$Asubsetmathbb{R}^d$ is a polytope if $A$ equals the convex hull of some finite set.
For any two sets $B$ and $C$, $B+Cequiv{x+y:xin B,yin C}$.
My question:
Let $A$ and $B$ be polytopes in $mathbb{R}^d$. When can we find a polytope $C$ such that $A=B+C$?
Such $C$ always exists? I guess not, right?
convex-analysis convex-geometry
asked Nov 26 '18 at 6:42
Yi-Hsuan Lin
30817
Its the Minkowski sum.
– Wuestenfux
Nov 26 '18 at 7:53
Yes, here, the sum of two sets is defined as Minkowski sum.
– Yi-Hsuan Lin
Nov 26 '18 at 17:49
add a comment |
$Asubsetmathbb{R}^d$ is a polytope if $A$ equals the convex hull of some finite set.
For any two sets $B$ and $C$, $B+Cequiv{x+y:xin B,yin C}$.
My question:
Let $A$ and $B$ be polytopes in $mathbb{R}^d$. When can we find a polytope $C$ such that $A=B+C$?
Such $C$ always exists? I guess not, right?
convex-analysis convex-geometry
asked Nov 26 '18 at 6:42
Yi-Hsuan Lin
30817
$Asubsetmathbb{R}^d$ is a polytope if $A$ equals the convex hull of some finite set.
For any two sets $B$ and $C$, $B+Cequiv{x+y:xin B,yin C}$.
My question:
Let $A$ and $B$ be polytopes in $mathbb{R}^d$. When can we find a polytope $C$ such that $A=B+C$?
Such $C$ always exists? I guess not, right?
convex-analysis convex-geometry
convex-analysis convex-geometry
asked Nov 26 '18 at 6:42
Yi-Hsuan Lin
30817
asked Nov 26 '18 at 6:42
Yi-Hsuan Lin
30817
asked Nov 26 '18 at 6:42
Yi-Hsuan Lin
30817
asked Nov 26 '18 at 6:42
Yi-Hsuan Lin
30817
asked Nov 26 '18 at 6:42
Yi-Hsuan Lin
30817
30817
Its the Minkowski sum.
– Wuestenfux
Nov 26 '18 at 7:53
Yes, here, the sum of two sets is defined as Minkowski sum.
– Yi-Hsuan Lin
Nov 26 '18 at 17:49
add a comment |
Its the Minkowski sum.
– Wuestenfux
Nov 26 '18 at 7:53
Yes, here, the sum of two sets is defined as Minkowski sum.
– Yi-Hsuan Lin
Nov 26 '18 at 17:49
Its the Minkowski sum.
– Wuestenfux
Nov 26 '18 at 7:53
Its the Minkowski sum.
– Wuestenfux
Nov 26 '18 at 7:53
Yes, here, the sum of two sets is defined as Minkowski sum.
– Yi-Hsuan Lin
Nov 26 '18 at 17:49
Yes, here, the sum of two sets is defined as Minkowski sum.
– Yi-Hsuan Lin
Nov 26 '18 at 17:49
add a comment |
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Its the Minkowski sum.
– Wuestenfux
Nov 26 '18 at 7:53
Yes, here, the sum of two sets is defined as Minkowski sum.
– Yi-Hsuan Lin
Nov 26 '18 at 17:49