Re: Silly question
- From: "Jaco van Niekerk" <sparky@xxxxxxxxxx>
- Date: Mon, 29 Aug 2005 11:15:43 +0200
Sorry, my mistake...
It works!
"Jaco van Niekerk" <sparky@xxxxxxxxxx> wrote in message
news:deuj25$8g4$1@xxxxxxxxxxxxxxxxxxxxx
> I'm still getting awkward values:
>
> Allow me to rephrase:
>
> v=
> arcsin(Pz / C) for Px^2 + Py^2 >= A^2.
> +pi - arcsin(Pz/C) if Pz >= 0
> -pi - arcsin(Pz/C) if Pz < 0
>
> u=
> +arccos(Px / (A + Bcos(v))) for Py >= 0
> -arccos(Px / (A + Bcos(v))) for Py >= 0
>
> Did I understand correctly?
>
>
> "Robert Israel" <israel@xxxxxxxxxxx> wrote in message
> news:deu91c$ejc$1@xxxxxxxxxxxxxxxxxxxxxxxxx
>> In article <deu6pj$bqg$1@xxxxxxxxxxxxxxxxxx>,
>> Jaco van Niekerk <sparky@xxxxxxxxxx> wrote:
>>>Hello
>>>
>>>I have a torus, say F(u,v) = X(u,v)i + Y(u,v)j + Z(u,v)k
>>>
>>>with
>>> X(u,v) = Acos(u) + Bcos(u)cos(v)
>>> Y(u,v) = Asin(u) + Bsin(u)cos(v)
>>> Z(u,v) = Csin(v)
>>>
>>> A, B and C are constants
>>
>> ... with, I presume, A > B > 0 and C > 0. Yes, this is a torus
>> for, say, -pi <= u <= pi and -pi <= v <= pi.
>>
>>>Now, for the silly part. I have a point P that definitely lies on the
>>>surface. Now I need to find a pair (u,v) for the point P. Now this seems
>>>trivial, but on my graphics display (I'm writing a program) it does not
>>>work! This is what I've done:
>>>
>>>Pz = Csin(v)
>>>sin(v) = Pz/C
>>>v = arcsin(Pz/C)
>>
>> That gives you a v in [-pi/2, pi/2];
>> OK if cos(v) >= 0, which is true if Px^2 + Py^2 >= A^2.
>> Otherwise v = pi - arcsin(Pz/C) (if Pz >= 0), or -pi - arcsin(Pz/C)
>> (if Pz < 0)
>>
>>>Px = Acos(u) + Bcos(u)cos(v)
>>>Px = cos(u)[A + Bcos(v) ]
>>>since I have v, I can calculate u
>>>cos(u) = Px / (A + Bcos(v))
>>>u = arccos(Px / (A + Bcos(v)))
>>
>> OK if Py >= 0. Otherwise -that.
>>
>>>Yet, my u, v pair is not what it should be. What am I doing wrong?
>>
>> Looking in the wrong intervals.
>>
>> Robert Israel israel@xxxxxxxxxxx
>> Department of Mathematics http://www.math.ubc.ca/~israel
>> University of British Columbia Vancouver, BC, Canada
>>
>
>
.
- References:
- Silly question
- From: Jaco van Niekerk
- Re: Silly question
- From: Robert Israel
- Re: Silly question
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