Figure 1: Examples of woven objects constructed with ribbons: Venus consists of five distinct cycles. The bunny has eight cycles, the rocker arm has only two cycles, and the genus-three object has 16 cycles. The first three models are created by the Quadcover method [Kalberer et al. 2007], courtesy of Wenping Wang and Li Yupei. The genus-three object is created using TopMod3D [Akleman et al. 2008]. AbstractIn this paper, we show how to create plain-weaving over an arbitrary surface. To create a plain-weaving on a surface, we need to create cycles that cross other cycles (or themselves) by alternatingly going over and under. We use the fact that it is possible to create such cycles, starting from any given manifold-mesh surface by simply twisting every edge of the manifold mesh. We have developed a new method that converts plain-weaving cycles to 3D thread structures. Using this method, it is possible to cover a surface without large gaps between threads by controlling the sizes of the gaps. We have developed a system that converts any manifold mesh to a plain-woven object, by interactively controlling the shapes of the threads with a set of parameters. We have demonstrated that by using this system, we can create a wide variety of plain-weaving patterns, some of which may not have been seen before.

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Figure 1: Examples of woven objects constructed with ribbons: Venus consists of five distinct cycles. The bunny has eight cycles, the rocker arm has only two cycles, and the genus-three object has 16 cycles. The first three models are created by the Quadcover method [Kalberer et al. 2007], courtesy of Wenping Wang and Li Yupei. The genus-three object is created using TopMod3D [Akleman et al. 2008]. AbstractIn this paper, we show how to create plain-weaving over an arbitrary surface. To create a plain-weaving on a surface, we need to create cycles that cross other cycles (or themselves) by alternatingly going over and under. We use the fact that it is possible to create such cycles, starting from any given manifold-mesh surface by simply twisting every edge of the manifold mesh. We have developed a new method that converts plain-weaving cycles to 3D thread structures. Using this method, it is possible to cover a surface without large gaps between threads by controlling the sizes of the gaps. We have developed a system that converts any manifold mesh to a plain-woven object, by interactively controlling the shapes of the threads with a set of parameters. We have demonstrated that by using this system, we can create a wide variety of plain-weaving patterns, some of which may not have been seen before.

We show that for every surface of positive genus, there exist many quadrilateral manifold meshes that can be texturemapped with locally translated copies of a single square-texture pattern. This implies, for instance, that every positivegenus surface can be covered seamlessly with any of the 17 plane symmetric wallpaper patterns. We identify sufficient conditions for meshes to be classified as "quad-pattern-coverable", and we present several methods to construct such meshes. Moreover, we identify some mesh operations that preserve the quad-pattern-coverability property. For instance, since vertex insertion remeshing, which is the remeshing operation behind Catmull-Clark subdivision, preserves quad-pattern-coverability, it is possible to cover any surface of positive genus with iteratively finer versions of the same texture.Keywords: Modeling