This paper presents a new combinatorial approach to surface reconstruction with sharp features. Different from other postprocessing methods, the proposed method provides a systematic way to identify and reconstruct sharp features from unorganized sample points in one integrated reconstruction process. In addition, unlike other approximation methods, the reconstructed triangulated surface is guaranteed to pass through the original sample points. In this paper, the sample points in the sharp regions are defined as characteristic vertices (c-vertices), and their associated poles (c-poles) are used as a "sculptor" to extract triangles from a Delaunay structure for the sharp features. But, for smooth surface regions, an efficient region-growing scheme is used for triangle extraction and connection. Since only the c-poles associated with the sharp regions are used to participate in the Delaunay computation with the sample points, the proposed algorithm is adaptive in the sense that, given a sampled object with less sharp features, the triangulation becomes more efficient. To validate the proposed algorithm, some detailed illustrations are given. Experimental results show that it is robust and highly efficient.

The authors present an optimal match scheme that aligns the measurement data with the design data in CAD-directed dimensional inspection. The principle of this scheme is to determine the actual measured points on the nominal surface by minimizing the sum of the squared distances of the measurement data from the surface with respect to the parameters of a rigid body transformation. Its computational efficiency and robustness against singularity are discussed. Two applications are examined. The first is determining the design coordinate system with respect to a machine coordinate system. The second is comparative analysis for precision measurement. For determining the design coordinate system, a sensitivity measure is proposed and confirmed experimentally. For error comparative analysis, a statistical model is developed to determine the minimum number of required measurement points so that the sampled points can closely represent the entire population.>

A hierarchical planning system is presented which uses heuristics for path planning in dimensional inspection using coordinate measuring machines (CMMs). The objective is to automate the planning of a collision-free inspection path. The system demonstrates that the inspection paths of geometrically complex real world parts with multiple features can automatically be generated with efficiency. This is made possible by appropriate CMM abstractions, genuine 3-D collision detection, and heuristic modifications of reasonably assumed default inspection paths. Automatic selection and modification of probe angle based on a local accessibility analysis of a given feature are also presented. The collision-free inspection path can then be simulated in a CAD environment before it is carried out by the real CMM.>