The rich and evocative patterns of natural tessellations endow them with an unmistakable artistic appeal and structural properties which are echoed across design, production, and manufacturing. Unfortunately, interactive control of such patterns‐as modeled by Voronoi diagrams, is limited to the simple two dimensional case and does not extend well tofreeform surfaces. We present an approach for direct modeling and editing of such cellular structures on surface meshes. The overall modeling experience is driven by a set of editing primitives which are efficiently implemented on graphics hardware. We feature a novel application for 3D printing on modern support‐free additive manufacturing platforms. Our method decomposes the input surface into a cellular skeletal structure which hosts a set of overlay shells. In this way, material saving can be channeled to the shells while structural stability is channeled to the skeleton. To accommodate the available printer build volume, the cellular structure can be further split into moderately sized parts. Together with shells, they can be conveniently packed to save on production time. The assembly of the printed parts is streamlined by a part numbering scheme which respects the geometric layout of the input model.

中文翻译：

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表面上细胞结构的交互式建模与增材制造的应用

自然镶嵌的丰富而令人回味的图案赋予它们明确无误的艺术魅力和结构特性，这些特性在设计、生产和制造中都得到了呼应。不幸的是，这种模式的交互控制——如 Voronoi 图建模的那样，仅限于简单的二维情况，不能很好地扩展到自由曲面。我们提出了一种在表面网格上直接建模和编辑此类细胞结构的方法。整体建模体验由一组在图形硬件上有效实现的编辑基元驱动。我们在现代无支持增材制造平台上展示了​​ 3D 打印的新应用。我们的方法将输入表面分解为细胞骨架结构，该结构包含一组覆盖壳。这样，节省材料可以引导到外壳，而结构稳定性则引导到骨架。为了适应可用的打印机构建体积，蜂窝结构可以进一步拆分为中等大小的部分。与外壳一起，它们可以方便地包装以节省生产时间。打印零件的装配通过零件编号方案简化，该方案尊重输入模型的几何布局。