The mandala thangka, as a religious art in Tibetan Buddhism, is an invaluable cultural and artistic heritage. However, drawing a mandala pattern of thangka style is both time- and effort-consuming and requires mastery due to intricate details. Retaining and digitizing this heritage is an unresolved research challenge to date. In this paper, we propose a parametric approach to model and generate mandala thangka patterns to address this issue. Specifically, we construct parameterized models of three stylistic elements used in the interior mandalas of Nyingma school in Tibetan Buddhism according to their geometric features, namely the star, crescent, and lotus flower motifs. Varieties of interior mandala patterns are successfully generated using these parameterized motifs based on the hierarchical structures observed from hand-drawn mandalas. Moreover, we design a user interaction tool which can flexibly generate stylized mandala patterns with arbitrary shapes and colors. The experimental results show that our approach can efficiently generate beautifully-layered colorful traditional mandala patterns used in Buddhism and stylized mandala patterns used in modern art design, which significantly reduce the time and effort in manual production and, more importantly, contributes to the digitization of this great heritage.

曼陀罗唐卡是藏传佛教的一种宗教艺术，是一种宝贵的文化和艺术遗产。但是，绘制唐卡样式的曼荼罗图案既费时又费力，并且由于复杂的细节而需要精通。保留和数字化这一遗产是迄今为止尚未解决的研究挑战。在本文中，我们提出了一种参数化方法来建模和生成曼荼罗唐卡模式以解决此问题。具体来说，我们根据藏族佛教在宁玛派内曼荼罗中使用的三种风格元素的几何特征（即星形，新月形和莲花图案）构建了参数化模型。基于从手绘曼荼罗观察到的层次结构，使用这些参数化的主题可以成功生成各种内部曼荼罗图案。此外，我们设计了一个用户交互工具，可以灵活地生成具有任意形状和颜色的风格化曼荼罗图案。实验结果表明，我们的方法可以有效地生成佛教使用的层次分明的彩色传统曼荼罗图案和现代艺术设计中使用的程式化曼荼罗图案，这大大减少了手工制作的时间和精力，更重要的是，它有助于数字化曼陀罗的数字化。这个伟大的遗产。