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Digital Reproduction of Ancient Mosaics
Published in Filippo Stanco, Sebastiano Battiato, Giovanni Gallo, Digital Imaging for Cultural Heritage Preservation, 2017
Filippo Stanco, Sebastiano Battiato, Giovanni Gallo
A very interesting technique can be found in [27]; the authors present a new and efficient method to interactively create visually pleasing and impressive ancient mosaics. The algorithm is based again on the Lloyds method for CVT (Centroidal Voronoi Tessellation) computation and can be viewed as a smart extension and/or optimization of the technique proposed by Hausner [30]. They use a placement algorithm in an interactive fashion enabling the user to arrange tiles of various shapes and sizes. The user can easily control the distribution process by adding some other data such as contour lines and directional information. Tiles can be sized or shaped in order to better approximate the master image features. Additionally, this technique is less time consuming than using heuristic-controlled automatic methods. An interactive tool is preferred because “the proper arrangement of individual tiles is a highly artistic process” [27]. These authors claim that heuristic methods produce unwanted artifacts such as misaligned tiles. In more details this algorithm can be summarized as follows:
Modelling blast movement and muckpile formation with the position-based dynamics method
Published in International Journal of Mining, Reclamation and Environment, 2021
Centroidal Voronoi Tessellation (CVT) was adopted to discretise the whole rock mass volume into small irregular-shaped blocks. CVT is a Voronoi tessellation whose generating points are the centroids (centres of mass) of the corresponding Voronoi regions [26]. Because CVT could eliminate those strange and sharp corner blocks, it means CVT is relatively ideal for the whole rock mass volume discretisation. In this study, Voronoi generators (seed points) are arranged in a hierarchical and random way to generate the polyhedral Voronoi regions. The steps of the whole rock mass volume discretisation are as follows: (1) Determining the total numbers of generators and the hierarchies of discretisation; (2) Determining the numbers of generators and iterations in each hierarchy; (3) Inputting the whole rock mass volume geometrical model and calculating the centroid, taking the centroid as the mean value of random generators; (4) Calculating the variance and covariance matrix of random generators, and to generate n sample generators; (5) Generating Voronoi diagrams in any shapes and setting the colours; (6) 3D-Llody algorithm is adopted to optimise the Voronoi diagrams; (7) Starting the next hierarchy discretisation; (8) Finally, outputting the information, including block vertices, centroids coordinate and relationships between the vertices. Figure 1 depicts the whole rock mass volume discretisation.
Plants and architecture: the role of biology and biomimetics in materials development for buildings
Published in Intelligent Buildings International, 2019
R. T. Durai Prabhakaran, Morwenna J. Spear, Simon Curling, Peter Wootton-Beard, Philip Jones, Iain Donnison, Graham A. Ormondroyd
Architects have also looked to cell packing and the efficiency of hexahedral or polyhedral forms to create domed and free-form building envelopes. The plant may typically have palisade cells in the epidermis of its leaf, creating a strong cohesive unit through which stiffness and flexibility are balanced to retain leaf shape despite wind or mechanical forces. Architects, seeking to create free-form exterior surfaces of buildings of stiff yet efficient lightweight design, may mimic this in the use of cell-based structures. Some attribute the bioinspiration to the honeycomb of bees, or to the mineralised skeleton of radiolaria (Pottmann et al. 2015), and the technique has been abstracted into computer optimised design processes, which may in future make it difficult to attribute a specific bioinspiration source. A high profile example is the Heydar Aliyev Cultural Centre in Baku (built 2007), by Zaha Hadid Architects with Werner Sobek (Zaha Hadid 2012). The complex abstract form can be modelled using a weighted centroidal Voronoi tessellation (Pottmann et al. 2015). The space frame allowed the building skin to be free form, while the substructure incorporated flexible connections between the rigid grid of the structure and the space frame and its sheathing (Winterstetter et al. 2015; Januszkiewicz 2016). The skeletal space frame is entirely enclosed by the building cladding, the finished structure therefore simply expresses the weightlessness, undulations and fluidity of the form.
CVT-based 3D image segmentation and quality improvement of tetrahedral/hexahedral meshes using anisotropic Giaquinta-Hildebrandt operator
Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2018
Kangkang Hu, Yongjie Jessica Zhang, Guoliang Xu
Note that the HEWCVT energy function uses the edge-weighted distance to all generators for each voxel. It means that all the generators partially influence the harmonic average for each voxel. By taking into account the physical information and using the harmonic form of energy function, HEWCVT is robust to the initialisation and can eliminate the noise in the 3D image during the segmentation. To calculate the updated centroids , we minimise the HEWCVT energy function with respect to the generators (). If the generators of the Voronoi regions of F equal to their corresponding centroids, i.e. for , then we call the Voronoi tessellation a centroidal Voronoi tessellation of F. The detailed implementation of HEWCVT-3D is explained as follows: