Path: utzoo!utgpu!water!watmath!clyde!att-cb!osu-cis!tut.cis.ohio-state.edu!mailrus!umix!uunet!mcvax!cernvax!cui!marco
From: marco@cui.UUCP (Marco BALDASSARRE)
Newsgroups: comp.graphics
Subject: Re: Mapping algorithm question
Keywords: 2d mapping
Message-ID: <115@cui.UUCP>
Date: 15 Apr 88 13:47:44 GMT
Organization: University of Geneva/Switzerland
Lines: 49
Posted: Fri Apr 15 13:47:44 1988

From article <844@agora.uucp> , by rick@agora.uucp ( Rick Coates ) :
>A new question:  I am interested in mapping one 2d area into another.
>The first area may be rectangular, the second a collection of vectors
>with four points defined as corresponding to the original rectangle's.

>This is a 'rubber sheet' analogy, where you draw a picture on a stretchable
>sheet, then deform it.

Have you ever thought of using a 3D modelling of bi-dimensional deformations ?
Your bi-dimensional deformations - rubber sheet analogy -  musst look like 
this ( locally ! ) :


                #1                      #2


		*	*		*		
					      *
			    ------->
						*
		*	*		  *


This is a special case of the model I had worked on some time ago(where we talk 
about squatched/stretched edges - *not* determined by four points but by edge-
functions ).

What about 2D mapping thru bi-linear interpolation of delta_x(x,y) & 
delta_y(x,y) : ( - the general model is 2D mapping using interpolation of
delta_x(x,y) & delta_y(x,y) by ruled/lofted surfaces ...)


          delta_x                         delta_y

		^				^
		|  ^ y 				|  ^ y
		| /     #1			| /     #1
		|/				|/
		.------> x			.------> x 


Where delta_x(x,y) is determined by the difference between x1 & x2 , 
and   delta_y(x,y) is determined by the difference between y1 & y2 ,
( x1,x2,y1,y2 known at the 4 discrete locations only ). :-)
____________________________________________________________________________
      Marco A. Baldassarre          
    Computer Sciences Center       
      University of Geneva            
  ICBM:46o13'38"[N]/6o7'30"[E]