Topologically robust 3D modeling for shape approximation

This paper proposes a topologically robust and accurate shape modeling procedure that approximates a real 3D object based not on the widely used so-called ICP (iterative closed point) algorithm or the Delaunay triangulation for the noise resistive modeling and for the matrix-form meshing. A geometric model with desired meshing, not limited to a triangular one, but also quadrilateral, hexagonal or n-gonal mesh, is directly reconstructed based on a solid modeling approach. The radial distance of each scanning point from the axis of the cylindrical coordinates is measured using a laser triangulation sensor. The angular and vertical positions of the laser beam are two other coordinate values of the scanning to be simultaneously acquired. A face array listing (topology), which defines the vertex (sampling point) connectivity and the shape of the mesh, is assigned to meet the desired meshing, including that for watermarking. An example shows the procedure is immune to occasional triangulation noises. Stable meshing, and hence, an accurate shape approximation, free from the misconnection unavoidable in the ICP-based modeling, is then accomplished. This proposal allows a versatile, accurate and practical shape approximation, though limited to a one-axis rotational application at this moment.