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From: ken@turtlevax.UUCP (Ken Turkowski)
Newsgroups: net.graphics
Subject: Re: Re: Texture mapping
Message-ID: <832@turtlevax.UUCP>
Date: Mon, 15-Jul-85 18:27:46 EDT
Article-I.D.: turtleva.832
Posted: Mon Jul 15 18:27:46 1985
Date-Received: Thu, 18-Jul-85 06:22:47 EDT
References: <809@turtlevax.UUCP> <6700018@datacube.UUCP>
Reply-To: ken@turtlevax.UUCP (Ken Turkowski)
Organization: CADLINC, Inc. @ Menlo Park, CA
Lines: 25

In article <6700018@datacube.UUCP> shep@datacube.UUCP writes:
>  Backward mapping has the problem of usually selecting only one point
>in source space. Thus making it useless for many mappings.

That's right.  The NEIGHBORHOOD covered by the convolution kernel in
the target space as well as the TARGET POINT must be transformed by the
inverse mapping.

For linear transformations (i.e. mapping to a polygon) this is
trivial.  For "nice" nonlinear transformations (differentiable to
several orders) the neighborhood mapping can be linearized on a
per-target-pixel basis.

If the mapping is really warped, like a twisting transformation, the
rectangular neighborhood in the target could map into a weird shape
like a bow-tie or its inverse, where sided-ness changes like a Moebius
strip.  It is possible to map an image onto things like saddles, but
such cases must be dealt with on an individual basis:  it is hard to
get a general algorithm to work fast on the easy cases, yet do the
right thing for the hard ones.
-- 

Ken Turkowski @ CADLINC, Menlo Park, CA
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