圆组填充算法驱动的平面马赛克模拟

为了生成不规则嵌片排列紧凑的马赛克图案,提出一种基于圆组排列的平面马赛克模拟方法.首先借助嵌片多边形的直骨架得到一组逼近嵌片轮廓的圆;然后以圆半径的平方为权值,在平面上生成关于圆组的Power图,使每组圆各自对应一个Power区域;最后采用松弛法,将圆组在其对应Power区域内尽可能增长到最大.通过不断迭代生成Power图和放大圆组,最后得到嵌片紧凑排列的结果.实验结果表明,该方法得到的马赛克图案有较高的覆盖率,能适应不同嵌片,具有较强的鲁棒性和灵活性.国家自然科学基金(61472332);;福建省自然科学基金(2018J01104);;中央高校基本科研业务费专项基金(20720150002

Learning Gradient Fields for Scalable and Generalizable Irregular Packing

The packing problem, also known as cutting or nesting, has diverse applications in logistics, manufacturing, layout design, and atlas generation. It involves arranging irregularly shaped pieces to minimize waste while avoiding overlap. Recent advances in machine learning, particularly reinforcement learning, have shown promise in addressing the packing problem. In this work, we delve deeper into a novel machine learning-based approach that formulates the packing problem as conditional generative modeling. To tackle the challenges of irregular packing, including object validity constraints and collision avoidance, our method employs the score-based diffusion model to learn a series of gradient fields. These gradient fields encode the correlations between constraint satisfaction and the spatial relationships of polygons, learned from teacher examples. During the testing phase, packing solutions are generated using a coarse-to-fine refinement mechanism guided by the learned gradient fields. To enhance packing feasibility and optimality, we introduce two key architectural designs: multi-scale feature extraction and coarse-to-fine relation extraction. We conduct experiments on two typical industrial packing domains, considering translations only. Empirically, our approach demonstrates spatial utilization rates comparable to, or even surpassing, those achieved by the teacher algorithm responsible for training data generation. Additionally, it exhibits some level of generalization to shape variations. We are hopeful that this method could pave the way for new possibilities in solving the packing problem

Surface Mosaic Synthesis with Irregular Tiles

Mosaics are widely used for surface decoration to produce appealing visual effects. We present a method for synthesizing digital surface mosaics with irregularly shaped tiles, which are a type of tiles often used for mosaics design. Our method employs both continuous optimization and combinatorial optimization to improve tile arrangement. In the continuous optimization step, we iteratively partition the base surface into approximate Voronoi regions of the tiles and optimize the positions and orientations of the tiles to achieve a tight fit. Combination optimization performs tile permutation and replacement to further increase surface coverage and diversify tile selection. The alternative applications of these two optimization steps lead to rich combination of tiles and high surface coverage. We demonstrate the effectiveness of our solution with extensive experiments and comparisons