Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site turtlevax.UUCP Path: utzoo!watmath!clyde!burl!ulysses!ucbvax!decvax!decwrl!turtlevax!ken 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 UUCP: {amd,decwrl,hplabs,nsc,seismo,spar}!turtlevax!ken ARPA: turtlevax!ken@DECWRL.ARPA