基于圆堆砌的纹理生成方法

人造的装饰性纹理在人们的生活中得到了广泛地应用。传统的基于实例的纹理生成方法首先会在 目标区域放置一些很小的图元，然后通过迭代的方式让这些图元增长，最后填充整个目标区域。在迭代的过程中 相邻的图元之间会发生交叉与覆盖，因此需要对图元做变形、裁剪或其他处理，然而这种处理方式往往会花费大 量的时间。基于过程化的方法通过设计很多结构复杂的规则，在二维平面生成具有丰富层次的纹理，但这种方法 比较难拓展到三维空间。本文提出了一种基于圆堆砌的纹理生成方法，可以生成二维或三维的纹理。圆堆砌问题 属于 NP-hard 问题，本文将该问题转换成一个最优化问题，从而能够快速近似求解，求解出圆堆砌后就可以在圆 上定义规则来对圆形进行填充或替换以生成纹理。由于采用的是设计规则的方式生成纹理，该方法可以避免图元 之间发生的交叉覆盖的问题。

Circle packing based texture generation

Artificial decorative textures are in wide use in our lives. The traditional case-based texture generation methods would first place some small primitives on the target area, then iteratively grow these primitives, and finally fill the entire target area. In the iteration process, there would be intersections and overlays between adjacent primitives, entailing the deforming, clipping, and other processing of primitives, which was usually time-consuming. Procedure-based methods can generate textures with rich layers in the two-dimensional plane by designing various rules with complex structures. However, such methods would be difficult to extend to the 3D space. This paper provided a texture generation method based on circle packing, thereby generating 2D or 3D textures. As an NP-hard problem, the circle packing problem could be converted into a nonlinear optimization problem, so that it could be quickly and approximately solved. With the problem solved, different rules could be defined to fill or replace the circle to generate textures. Since the texture is generated by rules, the proposed method could avoid intersections and overlays between primitives.