Novel frameworks for surface mosaic synthesis and irregular object packing

This work presents novel methods to address two problems. One is synthesizing digital mosaic art over surfaces with irregular tiles. And the other is packing irregular objects in both 2- and 3-dimension. Mosaics are widely used for surface decoration to produce appealing visual effects. A method is presented for synthesizing digital surface mosaics with irregularly shaped tiles, which are a type of tiles often used for mosaics design. The method employs both continuous optimization and combinatorial optimization to improve tile arrangement. In the continuous optimization step, the base surface is iteratively partitioned into approximate Voronoi regions of the tiles. Then the positions and orientations of the tiles are optimized to achieve a tight fit. Combination optimization performs tile permutation and replacement to further increase surface coverage and diversify tile selection. The alternating applications of these two optimization steps lead to rich combination of tiles and high surface coverage. Extensive experiments and comparisons are conducted to demonstrate the effectiveness of the solution. Packing is one classical but hard problem. Apart from the interest to the academic communities, it has been broadly adopted in a diverse range of industrial situations in the past, such as the textile industry and logistics. During the recent years, the 3D printing technique goes into the spotlight. Subsequently, the packing problem attracts more people's attention as one of the magnifiers of 3D printers' power. However, from the technical perspective, more challenges follow the involvement of a third dimension. In this work, two frameworks are designed and investigated, targeting the packing problem. One is built atop the continuous optimization in the surface mosaicking methodology, supplemented by global optimization techniques. And the other is modeled as a system endowed with potential energy, through minimizing which a packing arrangement is achieved. Both exhibit great potential in producing compact packing results and are easily extensible from two to three dimension.published_or_final_versionComputer ScienceDoctoralDoctor of Philosoph