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Mathematics Mathematica Geometry Wolfram Language

RegionDistance and SignedRegionDistance do not work with Polyhedron objects

Ali Hashmi

Ali Hashmi, University of Helsinki

Posted 4 years ago

Consider this simple example (tested in Mathematica 12.0 and 12.1): triangulatedfaces = {{{0.96061304173482298107700216860393993556`10., 0.45331546030854047435454390324593987316`10., 0.49359205573796699484390160250768531114`10.}, \ {0.73084004010743375268077670625643804669`10., 0.74870596934463617966315496232709847391`10., 0.42952723572831885689993214327841997147`10.}, \ {0.43334606124448857077024372405987991524`10., 0.41689319196522271064517626870821878672`10., 0.45817105631011349367408683026466271084`10.}}, \ {{0.73084004010743375268077670625643804669`10., 0.74870596934463617966315496232709847391`10., 0.42952723572831885689993214327841997147`10.}, \ {0.15756394918966518114977759523753775284`10., 0.89301676609471791756789116334402933717`10., 0.4037575264860177037817834388988558203`10.}, \ {0.43334606124448857077024372405987991524`10., 0.41689319196522271064517626870821878672`10., 0.45817105631011349367408683026466271084`10.}}, \ {{0.15756394918966518114977759523753775284`10., 0.89301676609471791756789116334402933717`10., 0.4037575264860177037817834388988558203`10.}, \ {-0.01645930097046247042591460285620996729`10., 0.43252280089173278376790676702512428164`10., 0.41271457151521584449938018224202096462`10.}, \ {0.43334606124448857077024372405987991524`10., 0.41689319196522271064517626870821878672`10., 0.45817105631011349367408683026466271084`10.}}, \ {{-0.01645930097046247042591460285620996729`10., 0.43252280089173278376790676702512428164`10., 0.41271457151521584449938018224202096462`10.}, \ {0.14379330009296495407333793536963639781`10., 0.02310394547537703360817751274680631468`10., 0.58101409060754916069413411605637520552`10.}, \ {0.43334606124448857077024372405987991524`10., 0.41689319196522271064517626870821878672`10., 0.45817105631011349367408683026466271084`10.}}, \ {{0.14379330009296495407333793536963639781`10., 0.02310394547537703360817751274680631468`10., 0.58101409060754916069413411605637520552`10.}, \ {0.62068324671781538448556148068746551871`10., \ -0.04109172049086395883676914309035055339`10., 0.43668220311461170002331755313207395375`10.}, \ {0.43334606124448857077024372405987991524`10., 0.41689319196522271064517626870821878672`10., 0.45817105631011349367408683026466271084`10.}}, \ {{0.62068324671781538448556148068746551871`10., \ -0.04109172049086395883676914309035055339`10., 0.43668220311461170002331755313207395375`10.}, \ {0.96061304173482298107700216860393993556`10., 0.45331546030854047435454390324593987316`10., 0.49359205573796699484390160250768531114`10.}, \ {0.43334606124448857077024372405987991524`10., 0.41689319196522271064517626870821878672`10., 0.45817105631011349367408683026466271084`10.}}, \ {{0.90339887001981922232118904503295198083`10., 0.39780535114134973895261282450519502163`10., \ -0.49767982164323409932649155962280929089`10.}, \ {0.67343203811032026351313106715679168701`10., \ -0.00722531137087333019675128298331401311`10., \ -0.50724543215112882776907099469099193811`10.}, \ {0.45426437662895290009900361709085829827`10., 0.40378644682349356267746071075992878195`10., \ -0.51720634068240571283482954794751634587`10.}}, \ {{0.67343203811032026351313106715679168701`10., \ -0.00722531137087333019675128298331401311`10., \ -0.50724543215112882776907099469099193811`10.}, \ {0.22606705517260500259979494330764282495`10., \ -0.03684675096394777332742265230081102345`10., \ -0.54603854328090140057838652865029871464`10.}, \ {0.45426437662895290009900361709085829827`10., 0.40378644682349356267746071075992878195`10., \ -0.51720634068240571283482954794751634587`10.}}, \ {{0.22606705517260500259979494330764282495`10., \ -0.03684675096394777332742265230081102345`10., \ -0.54603854328090140057838652865029871464`10.}, \ {0.03823756877052398445160363849026907701`10., 0.53807966207547353043594284827122464776`10., \ -0.4918195240731523809607494968076935038`10.}, \ {0.45426437662895290009900361709085829827`10., 0.40378644682349356267746071075992878195`10., \ -0.51720634068240571283482954794751634587`10.}}, \ {{0.03823756877052398445160363849026907701`10., 0.53807966207547353043594284827122464776`10., \ -0.4918195240731523809607494968076935038`10.}, \ {0.23068196447687261407821779357618652284`10., 0.82936478255809309434454235088196583092`10., \ -0.49236745013861882291905658348696306348`10.}, \ {0.45426437662895290009900361709085829827`10., 0.40378644682349356267746071075992878195`10., \ -0.51720634068240571283482954794751634587`10.}}, \ {{0.23068196447687261407821779357618652284`10., 0.82936478255809309434454235088196583092`10., \ -0.49236745013861882291905658348696306348`10.}, \ {0.63673291554919675405699308612383902073`10., 0.83167834849230060090263805250287987292`10., \ -0.56145887784959491728642433372442610562`10.}, \ {0.45426437662895290009900361709085829827`10., 0.40378644682349356267746071075992878195`10., \ -0.51720634068240571283482954794751634587`10.}}, \ {{0.63673291554919675405699308612383902073`10., 0.83167834849230060090263805250287987292`10., \ -0.56145887784959491728642433372442610562`10.}, \ {0.90339887001981922232118904503295198083`10., 0.39780535114134973895261282450519502163`10., \ -0.49767982164323409932649155962280929089`10.}, \ {0.45426437662895290009900361709085829827`10., 0.40378644682349356267746071075992878195`10., \ -0.51720634068240571283482954794751634587`10.}}, \ {{0.96061304173482298107700216860393993556`10., 0.45331546030854047435454390324593987316`10., 0.49359205573796699484390160250768531114`10.}, \ {0.90339887001981922232118904503295198083`10., 0.39780535114134973895261282450519502163`10., \ -0.49767982164323409932649155962280929089`10.}, \ {0.80595527927073690300953750885886848367`10., 0.60847346983126092536623759112007511912`10., \ -0.05698734323802226018864065147245038359`10.}}, \ {{0.90339887001981922232118904503295198083`10., 0.39780535114134973895261282450519502163`10., \ -0.49767982164323409932649155962280929089`10.}, \ {0.63673291554919675405699308612383902073`10., 0.83167834849230060090263805250287987292`10., \ -0.56145887784959491728642433372442610562`10.}, \ {0.80595527927073690300953750885886848367`10., 0.60847346983126092536623759112007511912`10., \ -0.05698734323802226018864065147245038359`10.}}, \ {{0.63673291554919675405699308612383902073`10., 0.83167834849230060090263805250287987292`10., \ -0.56145887784959491728642433372442610562`10.}, \ {0.73084004010743375268077670625643804669`10., 0.74870596934463617966315496232709847391`10., 0.42952723572831885689993214327841997147`10.}, \ {0.80595527927073690300953750885886848367`10., 0.60847346983126092536623759112007511912`10., \ -0.05698734323802226018864065147245038359`10.}}, \ {{0.73084004010743375268077670625643804669`10., 0.74870596934463617966315496232709847391`10., 0.42952723572831885689993214327841997147`10.}, \ {0.96061304173482298107700216860393993556`10., 0.45331546030854047435454390324593987316`10., 0.49359205573796699484390160250768531114`10.}, \ {0.80595527927073690300953750885886848367`10., 0.60847346983126092536623759112007511912`10., \ -0.05698734323802226018864065147245038359`10.}}, \ {{0.73084004010743375268077670625643804669`10., 0.74870596934463617966315496232709847391`10., 0.42952723572831885689993214327841997147`10.}, \ {0.63673291554919675405699308612383902073`10., 0.83167834849230060090263805250287987292`10., \ -0.56145887784959491728642433372442610562`10.}, \ {0.44750375627034217646135424890508150508`10., 0.82419990224878614722338630170340625964`10., \ -0.02628326583337650328502614760731471431`10.}}, \ {{0.63673291554919675405699308612383902073`10., 0.83167834849230060090263805250287987292`10., \ -0.56145887784959491728642433372442610562`10.}, \ {0.23068196447687261407821779357618652284`10., 0.82936478255809309434454235088196583092`10., \ -0.49236745013861882291905658348696306348`10.}, \ {0.44750375627034217646135424890508150508`10., 0.82419990224878614722338630170340625964`10., \ -0.02628326583337650328502614760731471431`10.}}, \ {{0.23068196447687261407821779357618652284`10., 0.82936478255809309434454235088196583092`10., \ -0.49236745013861882291905658348696306348`10.}, \ {0.15756394918966518114977759523753775284`10., 0.89301676609471791756789116334402933717`10., 0.4037575264860177037817834388988558203`10.}, \ {0.44750375627034217646135424890508150508`10., 0.82419990224878614722338630170340625964`10., \ -0.02628326583337650328502614760731471431`10.}}, \ {{0.15756394918966518114977759523753775284`10., 0.89301676609471791756789116334402933717`10., 0.4037575264860177037817834388988558203`10.}, \ {0.73084004010743375268077670625643804669`10., 0.74870596934463617966315496232709847391`10., 0.42952723572831885689993214327841997147`10.}, \ {0.44750375627034217646135424890508150508`10., 0.82419990224878614722338630170340625964`10., \ -0.02628326583337650328502614760731471431`10.}}, \ {{0.15756394918966518114977759523753775284`10., 0.89301676609471791756789116334402933717`10., 0.4037575264860177037817834388988558203`10.}, \ {0.23068196447687261407821779357618652284`10., 0.82936478255809309434454235088196583092`10., \ -0.49236745013861882291905658348696306348`10.}, \ {0.10040396327093701075588669595812337407`10., 0.67190499440378873685596373849953326928`10., \ -0.01763262562508092381944738006955938542`10.}}, \ {{0.23068196447687261407821779357618652284`10., 0.82936478255809309434454235088196583092`10., \ -0.49236745013861882291905658348696306348`10.}, \ {0.03823756877052398445160363849026907701`10., 0.53807966207547353043594284827122464776`10., \ -0.4918195240731523809607494968076935038`10.}, \ {0.10040396327093701075588669595812337407`10., 0.67190499440378873685596373849953326928`10., \ -0.01763262562508092381944738006955938542`10.}}, \ {{0.03823756877052398445160363849026907701`10., 0.53807966207547353043594284827122464776`10., \ -0.4918195240731523809607494968076935038`10.}, \ {-0.01645930097046247042591460285620996729`10., 0.43252280089173278376790676702512428164`10., 0.41271457151521584449938018224202096462`10.}, \ {0.10040396327093701075588669595812337407`10., 0.67190499440378873685596373849953326928`10., \ -0.01763262562508092381944738006955938542`10.}}, \ {{-0.01645930097046247042591460285620996729`10., 0.43252280089173278376790676702512428164`10., 0.41271457151521584449938018224202096462`10.}, \ {0.15756394918966518114977759523753775284`10., 0.89301676609471791756789116334402933717`10., 0.4037575264860177037817834388988558203`10.}, \ {0.10040396327093701075588669595812337407`10., 0.67190499440378873685596373849953326928`10., \ -0.01763262562508092381944738006955938542`10.}}, \ {{-0.01645930097046247042591460285620996729`10., 0.43252280089173278376790676702512428164`10., 0.41271457151521584449938018224202096462`10.}, \ {0.03823756877052398445160363849026907701`10., 0.53807966207547353043594284827122464776`10., \ -0.4918195240731523809607494968076935038`10.}, \ {0.10552001495081394438994750706155363302`10., 0.22242517263409444008047462276936715858`10., \ -0.03123196218993484001438174680202227369`10.}}, \ {{0.03823756877052398445160363849026907701`10., 0.53807966207547353043594284827122464776`10., \ -0.4918195240731523809607494968076935038`10.}, \ {0.22606705517260500259979494330764282495`10., \ -0.03684675096394777332742265230081102345`10., \ -0.54603854328090140057838652865029871464`10.}, \ {0.10552001495081394438994750706155363302`10., 0.22242517263409444008047462276936715858`10., \ -0.03123196218993484001438174680202227369`10.}}, \ {{0.22606705517260500259979494330764282495`10., \ -0.03684675096394777332742265230081102345`10., \ -0.54603854328090140057838652865029871464`10.}, \ {0.14379330009296495407333793536963639781`10., 0.02310394547537703360817751274680631468`10., 0.58101409060754916069413411605637520552`10.}, \ {0.10552001495081394438994750706155363302`10., 0.22242517263409444008047462276936715858`10., \ -0.03123196218993484001438174680202227369`10.}}, \ {{0.14379330009296495407333793536963639781`10., 0.02310394547537703360817751274680631468`10., 0.58101409060754916069413411605637520552`10.}, \ {-0.01645930097046247042591460285620996729`10., 0.43252280089173278376790676702512428164`10., 0.41271457151521584449938018224202096462`10.}, \ {0.10552001495081394438994750706155363302`10., 0.22242517263409444008047462276936715858`10., \ -0.03123196218993484001438174680202227369`10.}}, \ {{0.14379330009296495407333793536963639781`10., 0.02310394547537703360817751274680631468`10., 0.58101409060754916069413411605637520552`10.}, \ {0.22606705517260500259979494330764282495`10., \ -0.03684675096394777332742265230081102345`10., \ -0.54603854328090140057838652865029871464`10.}, \ {0.40125467931090727187015656454456311419`10., \ -0.01487274791839898910715736766805434734`10., 0.00166485845898677538167401721222930712`10.}}, \ {{0.22606705517260500259979494330764282495`10., \ -0.03684675096394777332742265230081102345`10., \ -0.54603854328090140057838652865029871464`10.}, \ {0.67343203811032026351313106715679168701`10., \ -0.00722531137087333019675128298331401311`10., \ -0.50724543215112882776907099469099193811`10.}, \ {0.40125467931090727187015656454456311419`10., \ -0.01487274791839898910715736766805434734`10., 0.00166485845898677538167401721222930712`10.}}, \ {{0.67343203811032026351313106715679168701`10., \ -0.00722531137087333019675128298331401311`10., \ -0.50724543215112882776907099469099193811`10.}, \ {0.62068324671781538448556148068746551871`10., \ -0.04109172049086395883676914309035055339`10., 0.43668220311461170002331755313207395375`10.}, \ {0.40125467931090727187015656454456311419`10., \ -0.01487274791839898910715736766805434734`10., 0.00166485845898677538167401721222930712`10.}}, \ {{0.62068324671781538448556148068746551871`10., \ -0.04109172049086395883676914309035055339`10., 0.43668220311461170002331755313207395375`10.}, \ {0.14379330009296495407333793536963639781`10., 0.02310394547537703360817751274680631468`10., 0.58101409060754916069413411605637520552`10.}, \ {0.40125467931090727187015656454456311419`10., \ -0.01487274791839898910715736766805434734`10., 0.00166485845898677538167401721222930712`10.}}, \ {{0.62068324671781538448556148068746551871`10., \ -0.04109172049086395883676914309035055339`10., 0.43668220311461170002331755313207395375`10.}, \ {0.67343203811032026351313106715679168701`10., \ -0.00722531137087333019675128298331401311`10., \ -0.50724543215112882776907099469099193811`10.}, \ {0.79187734517734790351151397235961512986`10., 0.20456872448860752990734564624709197414`10., 0.00360399339447874917143676987045118303`10.}}, \ {{0.67343203811032026351313106715679168701`10., \ -0.00722531137087333019675128298331401311`10., \ -0.50724543215112882776907099469099193811`10.}, \ {0.90339887001981922232118904503295198083`10., 0.39780535114134973895261282450519502163`10., \ -0.49767982164323409932649155962280929089`10.}, \ {0.79187734517734790351151397235961512986`10., 0.20456872448860752990734564624709197414`10., 0.00360399339447874917143676987045118303`10.}}, \ {{0.90339887001981922232118904503295198083`10., 0.39780535114134973895261282450519502163`10., \ -0.49767982164323409932649155962280929089`10.}, \ {0.96061304173482298107700216860393993556`10., 0.45331546030854047435454390324593987316`10., 0.49359205573796699484390160250768531114`10.}, \ {0.79187734517734790351151397235961512986`10., 0.20456872448860752990734564624709197414`10., 0.00360399339447874917143676987045118303`10.}}, \ {{0.96061304173482298107700216860393993556`10., 0.45331546030854047435454390324593987316`10., 0.49359205573796699484390160250768531114`10.}, \ {0.62068324671781538448556148068746551871`10., \ -0.04109172049086395883676914309035055339`10., 0.43668220311461170002331755313207395375`10.}, \ {0.79187734517734790351151397235961512986`10., 0.20456872448860752990734564624709197414`10., 0.00360399339447874917143676987045118303`10.}}}; Now I convert the triangulated faces into a `Polyhedron` poly = Polyhedron[triangulatedpoly] this successfully converts the faces into a polyhedron, which passes the `RegionQ` and `ConstantRegionQ` test {ConstantRegionQ[poly], RegionQ[poly]} (* {True,True} ) However, `RegionDistance` or `SignedRegionDistance` cannot be used on poly to check the distance of a point from a polyhedron. `RegionMember` cannot be used as well. All these evaluations do not return a function. With these functions not working many useful computations cannot be performed with Polyhedrons. Hope this issue gets resolved in the upcoming version. This issue was also reported on Mathematica StackExchange: https://mathematica.stackexchange.com/questions/221491/regiondistance-and-signedregiondistance-do-not-work-with-polyhedron-objects Attachments:* problem with polyhed.nb

Consider this simple example (tested in Mathematica 12.0 and 12.1):

triangulatedfaces = {{{0.96061304173482298107700216860393993556`10., 
    0.45331546030854047435454390324593987316`10., 
    0.49359205573796699484390160250768531114`10.}, \
{0.73084004010743375268077670625643804669`10., 
    0.74870596934463617966315496232709847391`10., 
    0.42952723572831885689993214327841997147`10.}, \
{0.43334606124448857077024372405987991524`10., 
    0.41689319196522271064517626870821878672`10., 
    0.45817105631011349367408683026466271084`10.}}, \
{{0.73084004010743375268077670625643804669`10., 
    0.74870596934463617966315496232709847391`10., 
    0.42952723572831885689993214327841997147`10.}, \
{0.15756394918966518114977759523753775284`10., 
    0.89301676609471791756789116334402933717`10., 
    0.4037575264860177037817834388988558203`10.}, \
{0.43334606124448857077024372405987991524`10., 
    0.41689319196522271064517626870821878672`10., 
    0.45817105631011349367408683026466271084`10.}}, \
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Now I convert the triangulated faces into a Polyhedron

poly = Polyhedron[triangulatedpoly]

this successfully converts the faces into a polyhedron, which passes the RegionQ and ConstantRegionQ test

{ConstantRegionQ[poly], RegionQ[poly]}
(* {True,True} *)

However, RegionDistance or SignedRegionDistance cannot be used on poly to check the distance of a point from a polyhedron. RegionMember cannot be used as well. All these evaluations do not return a function. With these functions not working many useful computations cannot be performed with Polyhedrons.

Hope this issue gets resolved in the upcoming version.

This issue was also reported on Mathematica StackExchange: https://mathematica.stackexchange.com/questions/221491/regiondistance-and-signedregiondistance-do-not-work-with-polyhedron-objects

POSTED BY: Ali Hashmi

2 Replies

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Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 4 years ago

With `Polygon` instead of `Polyhedron` we get a distance: In[119]:= RegionDistance[Polygon[triangulatedfaces], {1, 1, 1}] Out[119]= 0.676006498 For points outside the polyhedron it may suffice. Unfortunately, `RegionMember` also fails for this polyhedron: RegionMember[Polyhedron[triangulatedfaces], {1/2, 1/2, 0}]

POSTED BY: Gianluca Gorni

Ali Hashmi

Ali Hashmi, University of Helsinki

Posted 4 years ago

Yeah. I hope these functionalities can be extended for Polyhedron. Because currently I am quite limited in the computation that I can perform on them.

POSTED BY: Ali Hashmi

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