Given an arbitrary set
T in the Euc
lidean space whose e
lements are ca
lled sites, and a particu
lar site
s, the Voronoi ce
ll of
s , denoted by
lsi1" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516300891&_mathId=si1.gif&_user=111111111&_pii=S0024379516300891&_rdoc=1&_issn=00243795&md5=c1fa4e3abd58e57aec2d1b65b486384f" title="Click to view the MathML source">VT(s)lass="mathContainer hidden">lass="mathCode">, consists of a
ll points c
loser to
s than to any other site. The Voronoi mapping of
s , denoted by
lsi2" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516300891&_mathId=si2.gif&_user=111111111&_pii=S0024379516300891&_rdoc=1&_issn=00243795&md5=2701c26a8ea1d2fe392475e979d91990" title="Click to view the MathML source">ψslass="mathContainer hidden">lass="mathCode">, associates to each set
lsi3" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516300891&_mathId=si3.gif&_user=111111111&_pii=S0024379516300891&_rdoc=1&_issn=00243795&md5=35f266e0625b1c3c5e2217fb1416cdbb" title="Click to view the MathML source">T∋slass="mathContainer hidden">lass="mathCode"> the Voronoi ce
ll lsi1" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516300891&_mathId=si1.gif&_user=111111111&_pii=S0024379516300891&_rdoc=1&_issn=00243795&md5=c1fa4e3abd58e57aec2d1b65b486384f" title="Click to view the MathML source">VT(s)lass="mathContainer hidden">lass="mathCode"> of
s w.r.t.
T . These Voronoi ce
lls are so
lution sets of
linear inequa
lity systems, so they are c
losed convex sets. In this paper we study the Voronoi inverse prob
lem consisting in computing, for a given c
losed convex set
lsi5" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516300891&_mathId=si5.gif&_user=111111111&_pii=S0024379516300891&_rdoc=1&_issn=00243795&md5=3f2d7321cc63c0d3d3dbae36282152ac" title="Click to view the MathML source">F∋slass="mathContainer hidden">lass="mathCode">, the fami
ly of sets
lsi3" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516300891&_mathId=si3.gif&_user=111111111&_pii=S0024379516300891&_rdoc=1&_issn=00243795&md5=35f266e0625b1c3c5e2217fb1416cdbb" title="Click to view the MathML source">T∋slass="mathContainer hidden">lass="mathCode"> such that
lsi6" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516300891&_mathId=si6.gif&_user=111111111&_pii=S0024379516300891&_rdoc=1&_issn=00243795&md5=12d515e10e2b47c4a31dca81bb2f5738" title="Click to view the MathML source">ψs(T)=Flass="mathContainer hidden">lass="mathCode">. More in detai
l, the paper ana
lyzes re
lationships between the e
lements of this fami
ly,
lsi342" class="mathmlsrc">le="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516300891&_mathId=si342.gif&_user=111111111&_pii=S0024379516300891&_rdoc=1&_issn=00243795&md5=dd41572013a959c17e3366240021040c">
lass="imgLazyJSB inlineImage" height="18" width="57" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0024379516300891-si342.gif">lass="mathContainer hidden">lass="mathCode">, and the
linear representations of
F , provides exp
licit formu
las for maxima
l and minima
l e
lements of
lsi342" class="mathmlsrc">le="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516300891&_mathId=si342.gif&_user=111111111&_pii=S0024379516300891&_rdoc=1&_issn=00243795&md5=dd41572013a959c17e3366240021040c">
lass="imgLazyJSB inlineImage" height="18" width="57" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0024379516300891-si342.gif">lass="mathContainer hidden">lass="mathCode">, and studies the c
losure operator that assigns, to each c
losed set
T containing
s , the
largest e
lement of
lsi342" class="mathmlsrc">le="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516300891&_mathId=si342.gif&_user=111111111&_pii=S0024379516300891&_rdoc=1&_issn=00243795&md5=dd41572013a959c17e3366240021040c">
lass="imgLazyJSB inlineImage" height="18" width="57" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0024379516300891-si342.gif">lass="mathContainer hidden">lass="mathCode">, where
lsi9" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0024379516300891&_mathId=si9.gif&_user=111111111&_pii=S0024379516300891&_rdoc=1&_issn=00243795&md5=8e70a73017a44b84d616489f378e0ea1" title="Click to view the MathML source">F=VT(s)lass="mathContainer hidden">lass="mathCode">.