Conformal Image Warping

Cover Conformal Image Warping
Conformal Image Warping
Carl Frederick
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The texture value at 7. = f^Uw) is retrieved and used as the value at w. Effectively, we find all the points in the z-plane which map to our piece of the w-plane by f(z). We still get aliasing by this method but it can be handled easily by one of the standard methods for pre-filtering [18] [3]. See figure 1 for examples of familiar elementary functions in complex variables. Figure 2 gives an example of a mapping generated by composition from fractional linear maps and elementary functions. 3. N...umerical conformal mapping The above example described a method for texture mapping elementary analytic mappings. In the present section, we describe a method for constructing numerical con- formal mappings from one finite region to another which is applicable to the case where only the shapes of the two regions to be mapped (and a point and orientation correspon- dence) are known. In this approach, one of the regions of interest is triangulated (e. G. Using a Voronoi method [6]). The second region may then be triangulated by mapping the nodes of the initial triangulation to the the second region, and then using the initial connectivity matrixt to triangulate the second region.

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