On The Lower Bound Of Edge Guards Of Polyhedral Terrains

Guarding polyhedral terrains is a relatively new problem in computational geometry. It is known as NP-hard problem. In 1997, P. Bose, T. Shermer, G. Toussaint and B. Zhu stated the bounds on the number of guards and proposed some algorithms for placing vertex and edge guards. In this contribution, we point to the inconsistency in the proof of the lower bound of the number of edge guards. We show that following the approach of Bose et al. for an n-vertex polyhedral terrain only a weaker lower bound of ?(2n?4)/7? can be achieved. Hence deriving the proof for the lower bound equal to ?(4n?4)/13? originally stated by Bose et al. remains an open issue.     

Recent Trends,Applications, and Perspectives in 3D Shape Similarity Assessment

The recent introduction of 3D shape analysis frameworks able to quantify the deformation of a shape into another in terms of the variation of real functions yields a new interpretation of the 3D shape similarity assessment and opens new perspectives. Indeed, while the classical approaches to similarity mainly quantify it as a numerical score, map‐based methods also define (dense) shape correspondences. After presenting in detail the theoretical foundations underlying these approaches, we classify them by looking at their most salient features, including the kind of structure and invariance properties they capture, as well as the distances and the output modalities according to which the similarity between shapes is assessed and returned. We also review the usage of these methods in a number of 3D shape application domains, ranging from matching and retrieval to annotation and segmentation. Finally, the most promising directions for future research developments are discussed.     

回归传统：当代数字化建筑几何建构策略研究

当复杂形式的建筑设计日益普遍,几何学对于建筑师理解复杂建筑形体的操作实质变得前所未有的重要,并以此催发几何学与建筑学关联性的重新审视。本文从梳理两者关系的演变历程出发,分析了当代数字化建筑实践的4种几何建构策略——几何生形、几何转化、协同模拟和几何重构,并结合具体案例研究,指出面向建筑本体需求的数字化几何思维是建筑学传统的回归,可以为数字化建筑设计提供更为合理的认识和参考。     

Self‐similarity for accurate compression of point sampled surfaces

Most surfaces, be it from a fine‐art artifact or a mechanical object, are characterized by a strong self‐similarity. This property finds its source in the natural structures of objects but also in the fabrication processes: regularity of the sculpting technique, or machine tool. In this paper, we propose to exploit the self‐similarity of the underlying shapes for compressing point cloud surfaces which can contain millions of points at a very high precision. Our approach locally resamples the point cloud in order to highlight the self‐similarity of the shape, while remaining consistent with the original shape and the scanner precision. It then uses this self‐similarity to create an ad hoc dictionary on which the local neighborhoods will be sparsely represented, thus allowing for a light‐weight representation of the total surface. We demonstrate the validity of our approach on several point clouds from fine‐arts and mechanical objects, as well as a urban scene. In addition, we show that our approach also achieves a filtering of noise whose magnitude is smaller than the scanner precision.     

Real‐Time Modelling of Fibrous Muscle

Relatively recently it has become apparent that providing human kind with a better healthcare requires personalized, predictive and integrative medicine, for which the building of virtual physiological human (VPH) framework accessible via virtual patient avatar is necessary. Real‐time modelling and visual exploration of such a complex avatar is a challenging task. In this paper, we propose a real‐time method for automatic modelling of an arbitrarily large number of muscle fibres in the volume of a muscle represented by its surface mesh. The method is based on an iterative morphing of predefined fibres template into the muscle volume exploiting harmonic scalar field computed on the surface of muscle. Experiments with muscles of thighs and pelvis show that the method produces realistic shapes of fibres. Our sequential VTK‐based C++ implementation is capable of producing 64 fine fibres within a muscle of 10K triangles in less than 170 ms on commodity hardware making the method suitable for VPH purposes as well as for interactive educational medical software.     

Feature‐Preserving Surface Completion Using Four Points

We present a user‐guided, semi‐automatic approach to completing large holes in a mesh. The reconstruction of the missing features in such holes is usually ambiguous. Thus, unsupervised methods may produce unsatisfactory results. To overcome this problem, we let the user indicate constraints by providing merely four points per important feature curve on the mesh. Our algorithm regards this input as an indication of an important broken feature curve. Our completion is formulated as a global energy minimization problem, with user‐defined spatial‐coherence constraints, allows for completion that adheres to the existing features. We demonstrate the method on example problems that are not handled satisfactorily by fully automatic methods.     

Shape Decomposition using Modal Analysis

We introduce a novel algorithm that decomposes a deformable shape into meaningful parts requiring only a single input pose. Using modal analysis, we are able to identify parts of the shape that tend to move rigidly. We define a deformation energy on the shape, enabling modal analysis to find the typical deformations of the shape. We then find a decomposition of the shape such that the typical deformations can be well approximated with deformation fields that are rigid in each part of the decomposition. We optimize for the best decomposition, which captures how the shape deforms. A hierarchical refinement scheme makes it possible to compute more detailed decompositions for some parts of the shape.
Although our algorithm does not require user intervention, it is possible to control the process by directly changing the deformation energy, or interactively refining the decomposition as necessary. Due to the construction of the energy function and the properties of modal analysis, the computed decompositions are robust to changes in pose as well as meshing, noise, and even imperfections such as small holes in the surface.     

Upgrading Computational Design

Shajay Bhooshan heads up the computation and design ZHACODE group at Zaha Hadid Architects (ZHA) and is a course master at the Architectural Association Design Research Laboratory (AADRL). Here he argues that Parametricism 2.0 has a vital role to play in the progressing of computational design. Assimilating the exploratory developments of the last 15 years, he asserts how the next phase of Parametricism will enable a further consolidation and evolution of digital practices.     

基于空间行为的数字几何空间建造 上海卜石艺术馆改造设计

文章通过介绍卜石艺术馆的改造,探讨了空间行为塑形在建筑设计方法上的应用。指出建筑师在对人的行为过程进行推演和模拟时,形成了几何折叠的空间界面,这种反向生形手法,是一个自下而上的过程,也是在数字性能化设计中所用到的设计逻辑,这种逻辑同时又作为建造方式的指导,给予建筑师实现多维空间创造的可能。     

结构面对岩体爆破块度分布影响的分形探讨

在前人研究成果的基础上，应用分形几何理论探讨了结构面对岩体爆破块度分布影响的分形规律，得出了几点有益的结论．