基于球谐函数的单花形生成及应用

Generation and application of single patterns based on spherical harmonic function

利用计算机技术生成花形图案能为设计师提供新的素材与创作灵感,有效地解决传统设计存在的低效、版权等问题。现有的花形图案生成方法或平铺整个图像空间而难以提取单花形素材,或虽能生成单花形但其变化形式难以人为控制,从而为花形的二次设计带来一定困难。为此,本文提出一种基于球谐函数的单花形图案生成方法并在理论上构造了对称花形图案的生成条件。首先根据一种显式表达的球谐函数生成离散曲面,然后基于等高线分割法对曲面进行分割并着色,最后运用垂直投影法生成二维图形作为花形图案。同时,结合铺砌规则将该方法生成的花形进行二次设计并应用于纺织品图案设计及产品设计中。计算机仿真实验表明,该方法能生成各种富于变化的单花形图案且变化形式容易控制,并验证了所生成图案在纺织品产品设计应用中的可行性。

Textile pattern design is an important component of textile production.Patterns with artistic beauty can inject added value into textiles and improve market competitiveness.The traditional way of designing patterns mainly relies on manuals,which requires designers to explore creative inspiration in a short period of time and thus is time consuming and laborious.Therefore,it is sometimes difficult to meet the personalized demands in the current"fast-paced"society.The problem can be partially solved by using digital art graphics which are based on mathematical models,e.g.,fractal graphics,dynamical systems graphics,quasi-regular patterns,etc.With the help of computer technology,a large number of digital art graphics with natural beauty and rich changes can be generated very efficiently.Such graphics can be used as textile pattern materials for secondary design.Thus,it can significantly improve the design efficiency,and provide new creative inspiration for traditional textile pattern design.However,most existing methods usually generate patterns tiling the whole image space,which is difficult to extract single patterns as designing material.Some methods can generate single patterns but are hard to control its variations.To this end,we propose a single pattern generation method based on spherical harmonic functions and construct conditions for generating patterns with symmetric property.First,the mesh surface is sampled and discretized from a specific closed-form spherical harmonic function with several parameters.Then,the surface is segmented into several closed domains and colored separately by contour segmentation.And the 2 D pattern can be obtained by vertical projection.To control the pattern style,different types of symmetry conditions for parameters are constructed.Compared with those methods tiling the whole image space,patterns generated by our method have single independent structures and can be directly used as the basic materials for design and save the efforts of element extraction.Besides,our method is much easier to control the variation of the pattern by adjusting parameters with symmetric conditions.Finally,we apply the generated graphics combined with the tiling structure to design textile patterns and simulate products as silk scarf,pillow and carpet.In the future,mo re control techniques and vectorization techniques will be further studied for the pattern generatio n,so as to provide a more convenient means for designers to carry out secondary design.