Polyhedral Partitioning of Space for Digital Modelling of Topology and Geometry

物体的拓扑和几何描述是科学技术的基本要求。充分满足这一需求的数字解决方案的科学基础是一个世界性的研究课题。已知的问题涉及两个基本的科学问题：数字模型的准确性和复杂性。经验表明，由于数字设备的存储和处理特性，将大型和复杂的原始数据数字映射到足够逼真的计算机模型时，不可避免地会出现错误。因此，必须构建模型并执行映射，以便可以观察和控制误差。所采用的方法不仅必须是正确和足够准确的，而且还必须是有效和稳健的。为了解决这一基本科学问题，提出了对具有胞状结构的多面体对象进行空间划分，其内外边界由具有直边的平面组成，拓扑计算机模型可以用于研究随时间变化的邻域。这样的社区在许多技术领域都很重要，例如在疏散控制方面。存在通过具有多边形结构的对象的数字映射来创建二维模型的先进方法。对于具有多面体结构的物体的三维模型，尚不存在类似的数字测绘方法。现有的三维概念在技术上并不容易应用，因为在技术中同时使用抽象和直观的方法。初步研究表明，通过更多的研究，可能会实现显著的改善。提出了一种新的多面体对象的数字模型结构，该结构基于节点、边、面和单元的传统特征的扩展，只需要两种结构关系来映射原始对象：定向平面多边形和对象边缘的面二面体圈。这大大降低了模型的复杂性。该项目的工作计划描述了一个接口模型和一个核心模型，前者旨在简化建造和使用，后者的数据结构和方法经过优化，可有效和可靠地处理空间分区的拓扑和几何形状。界面和核心模型之间的映射是自动的，因此用户不需要熟悉核心模型。将开发、实施、测试、记录、验证和验证新方法的理论、数据结构和方法。工作方案和数据处理是有计划的，以便联合项目可以在柏林和莫斯科同时进行。所得结果在工程实践中具有广泛的适用性。国际合作，特别是在学术发展和建立信息模型领域的合作，可望产生巨大的附加值。

Topological and geometrical description of objects is a fundamental requirement in science and technology. Scientific foundations for digital solutions, which satisfy this demand adequately, are a world-wide topic of research. The known problems relate to two basic scientific issues: the accuracy and the complexity of the digital models.Experience shows that digital mapping of large and complex originals to sufficiently realistic computer models is associated with unavoidable errors due to the storage and processing characteristics of digital devices. It is therefore essential to structure the models and to perform the mapping such that the errors can be observed and controlled. The methods employed must not only be correct and sufficiently accurate, they must also be efficient and robust. It is proposed to address this basic scientific problem by space partitioning for polyhedral objects with cell structure, whose outer and inner boundaries are composed of flat surfaces with straight edges.Topological computer models can be used to study neighborhood that varies with time. Such neighborhood is of importance in many areas of technology, for example in evacuation control. Advanced methods exist which create two-dimensional models by digital mapping of objects with polygonal structure. Comparable methods of digital mapping do not yet exist for three-dimensional models of objects with polyhedral structure. The available three-dimensional concepts are not readily applied in technology, where the abstract and the intuitive approach are used simultaneously. Preliminary research has revealed that significant improvements can probably be achieved through additional research. It is proposed to investigate a novel digital model structure for polyhedral objects, which is based on extensions of conventional characteristics of nodes, edges, faces and cells, and which requires only two structural relations to map the originals: oriented plane polygons and dihedral cycles of faces at the edges of the object. This reduces the complexity of the models significantly. The work program for the project describes an interface model, which is designed for simple construction and use, and a core model, whose data structure and methods are optimized for efficient and reliable handling of the topology and the geometry of the space partitioning. The mapping between interface and core model is automatic such that the user need not be familiar with the core model. The theory, data structure and methods for the novel approach will be developed, implemented, tested, documented, verified and validated. The work program and data handling are planned such that the joint project can readily be performed simultaneously at Berlin and at Moscow. The results are widely applicable in engineering practice. Significant added value is expected to result from the international cooperation, particularly in the areas of academic development and of building information modelling.