Surface-based geometric modeling has many advantages in terms of visualization and traditional subtractive manufacturing using computer-numerical-control cutting-machine tools. However, it is not an ideal solution for additive manufacturing because to digitally print a surface-represented geometric object using a certain additive manufacturing technology, the object has to be converted into a solid representation. However, converting a known surface-based geometric representation into a printable representation is essentially a redesign process, and this is especially the case, when its interior material structure needs to be considered. To specify a 3D geometric object that is ready to be digitally manufactured, its representation has to be in a certain volumetric form. In this research, we show how some of the difficulties experienced in additive manufacturing can be easily solved by using implicitly represented geometric objects. Like surface-based geometric representation is subtractive manufacturing-friendly, implicitly described geometric objects are additive manufacturing-friendly: implicit shapes are 3D printing ready. The implicit geometric representation allows to combine a geometric shape, material colors, an interior material structure, and other required attributes in one single description as a set of implicit functions, and no conversion is needed. In addition, as implicit objects are typically specified procedurally, very little data is used in their specifications, which makes them particularly useful for design and visualization with modern cloud-based mobile devices, which usually do not have very big storage spaces. Finally, implicit modeling is a design procedure that is parallel computing-friendly, as the design of a complex geometric object can be divided into a set of simple shape-designing tasks, owing to the availability of shape-preserving implicit blending operations.

中文翻译：

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使用隐函数进行面向增材制造的几何建模


基于表面的几何建模在可视化和使用计算机数控切削机床的传统减材制造方面具有许多优势。然而，它并不是增材制造的理想解决方案，因为要使用某种增材制造技术数字打印表面表示的几何对象，必须将对象转换为实体表示。然而，将已知的基于表面的几何表示转换为可打印表示本质上是一个重新设计过程，当需要考虑其内部材料结构时尤其如此。要指定可进行数字化制造的 3D 几何对象，其表示必须采用某种体积形式。在这项研究中，我们展示了如何通过使用隐式表示的几何对象轻松解决增材制造中遇到的一些困难。就像基于表面的几何表示有利于减材制造一样，隐式描述的几何对象也有利于增材制造：隐式形状可以进行 3D 打印。隐式几何表示允许将几何形状、材料颜色、内部材料结构和其他所需属性组合在一个描述中作为一组隐式函数，并且不需要转换。此外，由于隐式对象通常是按程序指定的，因此在其规范中使用的数据非常少，这使得它们对于现代基于云的移动设备的设计和可视化特别有用，而这些设备通常没有很大的存储空间。 最后，隐式建模是一种并行计算友好的设计过程，因为由于形状保持隐式混合操作的可用性，复杂几何对象的设计可以分为一组简单的形状设计任务。