Hi Pista! This comes just in time to vet my results, got for better or worse after a Bo > Spherical Trig > Wolfram search.
At first glance I see a slight difference in our formulae, but won't ask about it yet (esp. lest it prove cosmetic). Comparing further.... You've gone to a lot of trouble here. Thank you! Pete Istvan Kadar wrote: > Hi Pete, > > A NUMERICAL EXAMPLE > > NB. A B > known NB. \ / > edge-angles NB. \ / > a=:57 01 45.2 NB. \ c / > b=:87 42 41.1 NB. \ / > c=:55 37 19.6 NB. \ / > NB. D > unknown NB. a | b > face-angles NB. | > C=: ? NB. | > A=: ? NB. | > B=: ? NB. | > NB. C > > a + b + c << 360 > (57 01 45.2+87 42 41.1+55 37 19.6=200 21 45.9<<360) > > A formula for the solution > > cos_C =: ((cos c)-~(cos a)*cos b)%(-sin a)*sin b > C =: acos cos_C > > ]sin_a=:1&o.rfd((%60)p.~a) > 0.838948 > 9j7":sin_a > 0.8389482 > ]cos_a=:2&o.rfd((%60)p.~a) > 0.544211 > 9j7":cos_a > 0.5442112 > > ]sin_b=:1&o.rfd((%60)p.~b) > 0.999202 > 9j7":sin_b > 0.9992024 > ]cos_b=:2&o.rfd((%60)p.~b) > 0.0399327 > 9j7":cos_b > 0.0399327 > > ]cos_c=:2&o.rfd((%60)p.~c) > 0.564649 > 9j7":cos_c > 0.5646485 > > ]cos_C =: ((cos_c)-~cos_a*cos_b)%-sin_a*sin_b > 0.647656 > 9j7":cos_C =: ((cos_c)-~cos_a*cos_b)%-sin_a*sin_b > 0.6476563 > _2&o.0.6476563 > 0.866292 > dfr=:rfd^:_1 > 9j7":_2&o.0.6476563 > 0.8662919 radian > dfr 0.8662919 > 49.6349 > > C=:49.6349 degree (49° 38' 05.5" ) > > Best regards > Pista > > 2009/8/22 PMA <[email protected]> > >> Bo, Thank you for these leads! >> >> I felt the algebra would be just plain, >> but hadn't the grasp to specify it. >> Will pursue.... >> >> Best regards, >> Pete >> >> >> Bo Jacoby wrote: >>> Isn't it just plain linear algebra? You have a 3-corner and knows >>> the 3 cosines of angles between 3 vectors. Compute the cosines >>> of angles between pairwise normals to the vectors. >>> >>> Venlig hilsen, Bo. >>> >>> >>> --- Den fre 21/8/09 skrev Sherlock, Ric <[email protected]>: >>> >>>> Fra: Sherlock, Ric <[email protected]> >>>> Emne: Re: [Jprogramming] Szilassi's toroidal heptahedron: interfacial >> angles? Last try. >>>> Til: "Programming forum" <[email protected]> >>>> Dato: fredag 21. august 2009 03.07 >>>> Hi Peter, >>>> You could try providing some sample data and show what you >>>> expect the result to be. >>>> That might elicit a better response. >>>> >>>>> From: PMA >>>>> >>>>> Here is a final crack at posing my question -- this is >>>> as whittled as >>>>> I can whittle: >>>>> >>>>> Given a 3-D vertex of 3 faces with all edge-to-edge >>>> angles known, >>>>> how does one calculate its face-to-face angles (all, >>>> one per edge)? >>>>> If there come to mind other sites especially >>>> interested in this sort >>>>> of query, I'd appreciate hearing. >>>>> >>>> ---------------------------------------------------------------------- >>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>> >>> >>> Trænger du til at se det store billede? Kelkoo giver dig gode >> tilbud på LCD TV! Se her http://dk.yahoo.com/r/pat/lcd >>> ---------------------------------------------------------------------- >>> For information about J forums see http://www.jsoftware.com/forums.htm >>> >>> >> >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
