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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

1402.0. "Finding points in Algebriac space." by SUBWAY::BERG () Mon Mar 25 1991 14:02

   I am trying to do some Xwindow graphics in which I am plotting semi-
   circular points in space (by "semi" I mean that the points are all 
   dispersed around a central point, but that for each point the diameter
   is variable). Thus each seperate point is a different diameter from 
   the center which allows continually growing data to be represented 
   as a spiral over time.

   The question is how to represent this graphically. I know one angle
   (it's always 1 degree), and the measurements for all three sides. By
   alternately defining one the the points of the angle to be a random
   point I can even define all three angles and and all three measure-
   ments. The question is, how do I calculate the x,y coordinates of 
   this point. All the math books that I have show how to calculate this
   for points on a smooth curve, but none for this kind of situation.

   I know that this can be done because I can use a ruler and protractor
   on a sheet of paper to calculate it (always my ultimate proof). What
   equation can I use for it? 

   P.S. For those of you visual types with DDIF viewing capabilities, 
   the next reply is a graphical representation of the question.
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1402.1Supposed graphical aidSUBWAY::BERGMon Mar 25 1991 14:084
    Sorry, I was assuming latest version of NOTES. My mistake. I cann't
    include DDIF pictures in this notes files. Sorry ... :-(

1402.2Maybe this works (?)SUBWAY::BERGMon Mar 25 1991 14:1119
1402.3Maybe this worksVMSDEV::HALLYBThe Smart Money was on GoliathMon Mar 25 1991 17:1220
1402.4Close, but no radiusSUBWAY::BERGFri Mar 29 1991 13:0919
Re: -1

    I think that a point missed here is that we are not dealing with a true
    circle, but instead randomly spaced points located about a central point.
    I have no radius because d1 and d2 are NOT equal.

    The problem that I have is that all of the textbooks that I have looked 
    at make similiar assumptions, that all angle calculations are based upon 
    circles. What I need is a calculation to figure out x, y coordinates 
    based upon triangles or other shapes that are not fixed.

    Again, there must be a way to do this because it is simple to calculate
    on a piece of paper. The number is always there, all that I need is a
    way to calculate it.

P.S. Sorry for the delay in responding to my own problem but working in PSS,
     I am frequently called away to work on other various projects and I don't
     always have access to systems.
1402.5supporting the answer in .3CSSE::NEILSENWally Neilsen-SteinhardtFri Mar 29 1991 15:5621
.4>    I think that a point missed here is that we are not dealing with a true
>    circle, but instead randomly spaced points located about a central point.
>    I have no radius because d1 and d2 are NOT equal.

Unless I am missing something, .3 gives you the answer you want.  It does not
matter whether the points are on a circle or not.

It might make things clearer if you added a subscript to r and a, like this

    
    	xi = ri cos ai
    	yi = ri sin ai

This works for any randomly chosen point, specified by any ri and ai.  It does
not matter whether there is a circle there or not.

I gather you have a simple case in that 

	ai = i * a1

which can make the math simpler.
1402.6have you tried Cornu spiral?CALS::GELINEAUThu Oct 03 1991 12:486
    try looking at the Cornu (sp?) spiral graph; it's found in most
    undergrad optics (physics) texts - i didn't look at your graphics so
    i'm not sure if it will help but your original note made me think of
    the spiral immediately.
    
    Angela