Direct Reconstruction of Displaced Subdivision Surface from Unorganized Points

In this paper we propose a new mesh reconstruction algorithm that produces a displaced subdivision mesh directly from unorganized points. The displaced subdivision surface is a new mesh representation that defines a detailed mesh with a displacement map over a smooth domain surface. This mesh representation has several benefits — compact mesh size, piecewise regular connectivity — to overcome limitations of irregular mesh produced by ordinary mesh reconstruction scheme, but the original displaced subdivision surface generation algorithm needs an explicit polygonal mesh to be converted. Our approach is producing displaced subdivision surface directly from input points during the mesh reconstruction process. The main ideas of our algorithm are building initial coarse control mesh by the shrink-wrapping like projection and sampling fine surface detail from unorganized points along the each limit vertex normal without any connectivity information of given points. We employ an existing subdivision surface fitting scheme to generate a parametric domain surface, and suggest a surface detail sampling scheme that determines a valid sampling triangle which can be made with combinations of input points. We show several reconstruction examples and applications to show the validity of suggested sampling technique and benefits of the result like multiresolution modeling.