In rapid prototyping, a hollowed prototype is preferred and significantly reduces the building time and material consumption in contrast to a solid model. Most rapid prototyping obtains solid thin shell by gradually adding or solidifying materials layer by layer. This is a non-trivial problem to offset a solid which involves finding all self-intersections and filling gaps after raw offsetting. While Catmull-Clark subdivision (CCS) surfaces are widely used in solid modeling, the hollow solid/thin shell problems are not well addressed yet. In this paper, we explore earlier methods of obtaining thin shell CCS solid and present a new thin solid approach. With this new scheme, one can efficiently avoid creases and handle gaps.The new scheme is heuristic, but inner surface is parametric, so computation of the inner surface is simplified. And with offsetting Bezier crust applied, the inner surface maintains the mesh structure and continuity of the outer surface. The obtained thin shell solid is C 2 continuous everywhere, except at extraordinary points, where it is C 1 continuous.

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An elegant and efficient mesh clustering algorithm is presented. The faces of a polygonal mesh are divided into different clusters for mesh coarsening purpose by approximating the Centroidal Voronoi Tessellation of the mesh. The mesh coarsening process after clustering can be done in an isotropic or anisotropic fashion. The presented algorithm improves previous techniques in local geometric operations and parallel updates. The new algorithm is very simple but is guaranteed to converge, and generates better approximating meshes with the same computation cost. Moreover, the new algorithm is suitable for the variational shape approximation problem with L 2,1 distortion error metric and the convergence is guaranteed. Examples demonstrating efficiency of the new algorithm are also included in the paper.

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The automatic detection of engineering drawing modifications made by other designers is central to improving CAD/CAPP working efficiency levels. Engineering drawings include numerous entities, but only a few entities are modified. It is difficult for designers to identify modified entities in a complex drawing. This paper presents a novel means of detecting entities in engineering drawings created by other designers that employs semi-fragile watermark technologies. Modifications will change embedded watermarks. Consequently, detection is realized by analyzing changes. The approach was implemented, and the experimental results demonstrate that the method is reliable and can accurately detect entities that have been modified, deleted and added.