■Tsutomu Kinoshita, Katsutsugu Matsuyama, Kouichi Konno:An Estimation of Earthenware’s Surface Shape Using Quadric Surfaces, The Journal of the Art and Science, Vol.13, No.1, pp.21-33, (2014).

(PDF:http://www.art-science.org/journal/v13n1/v13n1pp21/artsci-v13n1pp21.pdf)


Abstract:
In most cases, earthenware is broken when it is excavated from ruins. This situation requires restoration for assembling the earthenware's pieces. The point clouds measured by a three-dimensional device are useful to restore the earthenware. Some methods to find adjacent pieces of earthenware using a computer have been proposed. These methods aim to restore broken earthenware by connecting adjacent pieces with using digital data. If, however, earthenware with large missing portions is restored, it is impossible to estimate the adjacent piece using local adjacency. Due to this, it is necessary to estimate the whole shape of earthenware. It is also possible to continue sequential local estimation for estimating whole shape of earthenware, but the distortion occurs in many cases. In this paper, we propose a method to estimate the whole shape of earthenware with quadric surfaces. Since most earthenware is produced to be as close as rotational shapes, quadric surfaces are suitable to represent rotational shapes. In our method, the uneven pattern on the surface is removed in the first step according to the Taubin's smoothing method. Next, the point cloud from which uneven patterns are removed is divided into several groups. After that, each point cloud is fitted to quadric surfaces represented by the algebraic equation. Finally, the sequences of points generated from quadric surfaces are interpolated and the free-form surfaces corresponding to the surface of the earthenware are generated.