An Alternative for Wang Tiles: Colored Edges versus Colored Corners

Abstract

In this article we revisit the concept of Wang tiles and introduce corner tiles, square tiles with colored corners. During past years, Wang tiles have become a valuable tool in computer graphics. Important applications of Wang tiles include texture synthesis, tile-based texture mapping, and generating Poisson disk distributions. Through their colored edges, Wang tiles enforce continuity with their direct neighbors. However, Wang tiles do not directly constrain their diagonal neighbors. This leads to continuity problems near tile corners, a problem commonly known as the corner problem. Corner tiles, on the other hand, do impose restrictions on their diagonal neighbors, and thus are not subject to the corner problem. In this article we show that previous applications of Wang tiles can also be done using corner tiles, but that corner tiles have distinct advantages for each of these applications. Compared to Wang tiles, corner tiles are easier to tile, textures synthesized with corner tiles contain more samples from the original texture, corner tiles reduce the required texture memory by a factor of two for tile-based texture mapping, and Poisson disk distributions generated with corner tiles have better spectral properties. Corner tiles result in cleaner, simpler, and more efficient applications.

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