POV-Ray : Newsgroups : povray.general : Closest points on two circles : Re: Closest points on two circles Server Time
4 Aug 2024 22:17:54 EDT (-0400)
  Re: Closest points on two circles  
From: ABX
Date: 25 Mar 2003 10:05:04
Message: <1dr08v84tdvdfssmiiu40ikec3sqqa542j@4ax.com>
On Wed, 26 Mar 2003 01:32:53 +1100, Edward Coffey <eco### [at] alphalinkcomau>
wrote:
> Yes, but as I stated in my original post, the mathematics of this is 
> quite complex

I would go for approximation. If it has to be calculated once you probably can
use approximation as Tom Melly suggested. Otherwise I think there is possible
fast approximation using functions. Consider your circles as toruses with minor
radius = 0. Then construct two functions which represent your circles
  #declare torus1=function(x,y,z){...}
  #declare torus2=function(x,y,z){...}
using transformations and shapes available in IsoCSG library. Then define space:
  #declare space=function(x,y,z){torus1(x,y,z)*torus2(x,y,z)};
I imagine the edge with nearest distance has probably lowest possible values
larger than 0. IIRC there are some analyze methods for finding that path but I
can't recall exact names.

ABX


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