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全球性的研究课题。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，将大型和复杂的原件数字映射到足够逼真的计算机模型与不可避免的错误有关。因此，必须构建模型并进行映射，以便可以观察和控制误差。所采用的方法不仅必须正确和足够准确，还必须有效和稳健。对于具有胞状结构的多面体物体，其内外边界由具有直边的平面组成，可以通过空间划分来解决这一基本科学问题，拓扑计算机模型可以用来研究随时间变化的邻域。这样的邻域在许多技术领域中是重要的，例如在疏散控制中。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高级方法。对于具有多面体结构的物体的三维模型，还不存在类似的数字映射方法。现有的三维概念并不容易应用于技术，其中抽象和直观的方法同时使用。初步研究表明，通过进一步研究，可能会取得重大进展。提出了一种新的多面体对象的数字模型结构，它是基于传统的节点，边，面和细胞的特征的扩展，它只需要两个结构关系来映射原件：有向平面多边形和二面角圈的面在边缘的对象。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，该模型设计用于简单的构造和使用，以及一个核心模型，其数据结构和方法经过优化，以有效和可靠地处理空间分区的拓扑结构和几何形状。接口和核心模型之间的映射是自动的，使得用户不需要熟悉核心模型。新方法的理论，数据结构和方法将被开发，实施，测试，记录，验证和验证。工作计划和数据处理的规划应确保联合项目能够在柏林和莫斯科同时进行。研究结果具有广泛的工程应用价值。预计国际合作将带来巨大的附加值，特别是在学术发展和建筑信息建模领域。

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.