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.
> >>>
> >> ----------------------------------------------------------------------
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> >>
> >
> >
> > 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
> > ----------------------------------------------------------------------
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> >
> >
>
>
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