Skip to main content
MathOverflow

Return to Question

deleted 69 characters in body
Source Link
Sam Hopkins
Sam Hopkins
  • 24.2k
  • 5
  • 97
  • 171

Let $P$ and $Q$ be polyhedra in ${\mathbb R}^m$ with a non-empty intersection. I believe there should exist a constant $C_{PQ}>0$ such that for any point $x\in {\mathbb R}^m$ the following inequality holds: $$d(x,P\cap Q)\leq C_{PQ}\cdot {\rm max} ( d(x,P),d(x,Q)).$$ Here $d(x,Y)$ denotes the Euclidean distance between $x$ and a subset $Y\subset {\mathbb R}^m$. Any suggestions about how to prove this? (A related question: Bounding distance to a polyhedron Bounding distance to a polyhedron)

Let $P$ and $Q$ be polyhedra in ${\mathbb R}^m$ with a non-empty intersection. I believe there should exist a constant $C_{PQ}>0$ such that for any point $x\in {\mathbb R}^m$ the following inequality holds: $$d(x,P\cap Q)\leq C_{PQ}\cdot {\rm max} ( d(x,P),d(x,Q)).$$ Here $d(x,Y)$ denotes the Euclidean distance between $x$ and a subset $Y\subset {\mathbb R}^m$. Any suggestions about how to prove this? (A related question: Bounding distance to a polyhedron )

Let $P$ and $Q$ be polyhedra in ${\mathbb R}^m$ with a non-empty intersection. I believe there should exist a constant $C_{PQ}>0$ such that for any point $x\in {\mathbb R}^m$ the following inequality holds: $$d(x,P\cap Q)\leq C_{PQ}\cdot {\rm max} ( d(x,P),d(x,Q)).$$ Here $d(x,Y)$ denotes the Euclidean distance between $x$ and a subset $Y\subset {\mathbb R}^m$. Any suggestions about how to prove this? (A related question: Bounding distance to a polyhedron)

added 135 characters in body
Source Link
Anton Kapustin
Anton Kapustin
  • 1.6k
  • 7
  • 20

Let $P$ and $Q$ be polyhedra in ${\mathbb R}^m$ with a non-empty intersection. I believe there should exist a constant $C_{PQ}>0$ such that for any point $x\in {\mathbb R}^m$ the following inequality holds: $$d(x,P\cap Q)\leq C_{PQ}\cdot {\rm max} ( d(x,P),d(x,Q)).$$ Here $d(x,Y)$ denotes the Euclidean distance between $x$ and a subset $Y\subset {\mathbb R}^m$. Any suggestions about how to prove this? (A related question: Bounding distance to a polyhedron )

Let $P$ and $Q$ be polyhedra in ${\mathbb R}^m$ with a non-empty intersection. I believe there should exist a constant $C_{PQ}>0$ such that for any point $x\in {\mathbb R}^m$ the following inequality holds: $$d(x,P\cap Q)\leq C_{PQ}\cdot {\rm max} ( d(x,P),d(x,Q)).$$ Here $d(x,Y)$ denotes the Euclidean distance between $x$ and a subset $Y\subset {\mathbb R}^m$. Any suggestions about how to prove this?

Let $P$ and $Q$ be polyhedra in ${\mathbb R}^m$ with a non-empty intersection. I believe there should exist a constant $C_{PQ}>0$ such that for any point $x\in {\mathbb R}^m$ the following inequality holds: $$d(x,P\cap Q)\leq C_{PQ}\cdot {\rm max} ( d(x,P),d(x,Q)).$$ Here $d(x,Y)$ denotes the Euclidean distance between $x$ and a subset $Y\subset {\mathbb R}^m$. Any suggestions about how to prove this? (A related question: Bounding distance to a polyhedron )

Source Link
Anton Kapustin
Anton Kapustin
  • 1.6k
  • 7
  • 20

Bounding distance to an intersection of polyhedra

Let $P$ and $Q$ be polyhedra in ${\mathbb R}^m$ with a non-empty intersection. I believe there should exist a constant $C_{PQ}>0$ such that for any point $x\in {\mathbb R}^m$ the following inequality holds: $$d(x,P\cap Q)\leq C_{PQ}\cdot {\rm max} ( d(x,P),d(x,Q)).$$ Here $d(x,Y)$ denotes the Euclidean distance between $x$ and a subset $Y\subset {\mathbb R}^m$. Any suggestions about how to prove this?