Lucian Maddox

2022-07-15

Find the intersection of two or more polygons in terms of linear inequalities

Given two or more closed polygons each defined by a system of linear inequalities, is there any method by which their intersection polygon may be determined, also in terms of a system of linear inequalities?

Given two or more closed polygons each defined by a system of linear inequalities, is there any method by which their intersection polygon may be determined, also in terms of a system of linear inequalities?

diamondogsaz

Beginner2022-07-16Added 12 answers

In general, the number of inequalities used to describe one convex polytope (high dimensional polygon) may not equal the number needed to describe another, even if they share the same dimension.

Consider a triangle, which in ${\mathbb{R}}^{2}$ requires 3, while a pentagon requires 5.

If $A$ is the set of linear inequalities for one polygon and $B$ is the set of linear inequalities for another, you could consider $A\cup B$ to describe their intersection.

Consider a triangle, which in ${\mathbb{R}}^{2}$ requires 3, while a pentagon requires 5.

If $A$ is the set of linear inequalities for one polygon and $B$ is the set of linear inequalities for another, you could consider $A\cup B$ to describe their intersection.

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V=??

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?

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