Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Path: utzoo!mnetor!seismo!think!nike!lll-crg!lll-lcc!pyramid!voder!apple!turk
From: turk@apple.UUCP (Ken "Turk" Turkowski)
Newsgroups: net.graphics
Subject: Re: Possible way of anti-aliasing.
Message-ID: <214@apple.UUCP>
Date: Wed, 15-Oct-86 02:46:45 EDT
Article-I.D.: apple.214
Posted: Wed Oct 15 02:46:45 1986
Date-Received: Wed, 15-Oct-86 20:22:48 EDT
References: <280@joevax.UUCP> <265@hoqam.UUCP> <7706@sun.uucp> <109@pixar.UUCP> <1234@turtlevax.UUCP> <1229@megaron.UUCP> <551@bambi.UUCP>
Reply-To: turk@apple.UUCP (Ken "Turk" Turkowski)
Distribution: net
Organization: Apple Computer Inc., Cupertino, USA
Lines: 34
Keywords: Fourier, texture mapping, sample-rate conversion, convolution, DSP
Summary: Frequency response of texture mapping via mip-maps

In article <551@bambi.UUCP> steve@bambi.UUCP (Steve Miller) writes:
>A good reference here is "Pyramidal Parametrics," by Lance Williams,
>Siggraph Proceedings, 1983.  Basically, Lance interpolates between pairs
>of pre-filtered images of spheres, where the images include highlights.
>
>Anyone planning to implement this approach should also read "Summed-Area
>Tables for Texture Mapping," by Franklin Crow, Siggraph Proceedings 1984.

It seems as though one could use arbitrary kernels in the pyramidal
parametrics (mip-maps), but you are constrained to box filters for
summed-area tables.  Am I correct?

If the sequence images were filtered with ideal low-pass filters, then
the linearity of the Fourier transform implies that the frequency
response of the interpolated image would be:

 |H(w)| ^
	|-------------------+	-   -	-   -	+	<--  Height of second
	|		    |				     step determined
	|		    |	-   -	-   -	+	<--  by interpolation
	|		    |				     parameter blending
	|		    +-------------------+	<--  between adjacent
	|					|	     mip-maps.
	|		    +	-   -	-   -	|	<--
	|					|
	|---------------------------------------+---------------> w

Of course, we don't have ideal low-pass filters, but the diagram illustrates
the effect in the frequency domain, of interpolation between adjacent mip-maps.
-- 
Ken Turkowski @ Apple Computer, Inc., Cupertino, CA
UUCP: {sun,nsc}!apple!turk
CSNET: turk@Apple.CSNET
ARPA: turk%Apple@csnet-relay.ARPA