Dear Murray,
I found the following relation (considering C a unit circle): d * sin((phi+theta)/2) = sin((phi-theta)/2) More general, if C has a radius r, the relation becomes: d * sin((phi+theta)/2) = r * sin((phi-theta)/2) from which it´s very simple to obtain the value of one variable, knowing the other two. If you wanna know how it came, just send me an e-mail and I will try to write down the solution... yours faithfully, ##################################### # MSc. Edson Ricardo de A. Silva # # Computer Graphics Group (CRAB) # # Federal University of Ceara (UFC) # ##################################### ---------- Forwarded message ---------- Date: Thu, 13 Jun 2002 20:11:17 +0000 From: Paulo Santa Rita <[EMAIL PROTECTED]> Reply-To: [EMAIL PROTECTED] To: [EMAIL PROTECTED] Subject: [obm-l] Geometry Problem >Hi. Firstly, this is not homework, I actually want this for a bit of >software I am writing. >Secondly, while I know it would be better if I worked it out myself, I'd >rather get the solution than not, even at the price of missing the >opportunity to brush up my geometry skills. > >I am attempting to lay out points on the Poincare projection of the >hyperbolic plane. I have done up a diagram at >http://www.users.bigpond.com/pmurray/Math1.gif > >I have a unit circle C, with a centre at O. >I have a radius of that circle r. >I have another circle D, that intersects C at right angles at a point P and >that intersects the radius R at point Q. > >Angle POr we shall call theta. >Angle Dr we shall call phi. (that is, the angle between r and the tangent >to >D at Q). >Distance OQ we shall call d. > >1 - given phi and d, what is theta? >2 - given phi and theta, what is d? > >That's all I think I need, although if you feel like working out phi from >theta and d, feel free. > >Please reply to me at [EMAIL PROTECTED] > >.. _________________________________________________________________ Chegou o novo MSN Explorer. Instale já. É gratuito: http://explorer.msn.com.br ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~nicolau/olimp/obm-l.html O administrador desta lista é <[EMAIL PROTECTED]> ========================================================================= ========================================================================= Instruções para entrar na lista, sair da lista e usar a lista em http://www.mat.puc-rio.br/~nicolau/olimp/obm-l.html O administrador desta lista é <[EMAIL PROTECTED]> =========================================================================
