Article View: net.graphics
Article #1519Re: Possible way of anti-aliasing.
From: turk Ken Turk Turkowski
Date: Fri, 17 Oct 1986 21:02
Date: Fri, 17 Oct 1986 21:02
34 lines
2432 bytes
2432 bytes
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
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<309@ndmce.uucp>Path:
arc1-ca.pugleaf.net!utzoo!watmath!clyde!cuae2!ltuxa!we53!sw013b!dj3b1!killer!ndmce!pollux!infotel!ut-ngp!ut-sally!seismo!think!nike!lll-crg!lll-lcc!pyramid!voder!apple!turkReferences:
<280@joevax.UUCP> <265@hoqam.UUCP> <7706@sun.uucp> <109@pixar.UUCP> <1234@turtlevax.UUCP> <1229@megaron.UUCP> <551@bambi.UUCP>Show Full Headers
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Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: arc1-ca.pugleaf.net!utzoo!watmath!clyde!cuae2!ltuxa!we53!sw013b!dj3b1!killer!ndmce!pollux!infotel!ut-ngp!ut-sally!seismo!think!nike!lll-crg!lll-lcc!pyramid!voder!apple!turk From: turk@apple.UUCP@ndmce.uucp (Ken "Turk" Turkowski) Newsgroups: net.graphics Subject: Re: Possible way of anti-aliasing. Message-ID: <309@ndmce.uucp> Date: Fri, 17-Oct-86 17:02:00 EDT Article-I.D.: ndmce.309 Posted: Fri Oct 17 17:02:00 1986 Date-Received: Tue, 21-Oct-86 05:20:18 EDT References: <280@joevax.UUCP> <265@hoqam.UUCP> <7706@sun.uucp> <109@pixar.UUCP> <1234@turtlevax.UUCP> <1229@megaron.UUCP> <551@bambi.UUCP> Sender: news@ndmce.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