Reconstrução de superfícies tridimensionais utilizando B-splines com peso associado à redução do número de pontos de controle

Abstract

The reconstruction of three-dimensional surfaces can be divided into two parts: obtaining the surface coordinates of the object to be reconstructed and the application of an algorithm to reconstruct the three-dimensional surface. The first one is to obtain a cloud of points representing the surface which generally consists of thousands of points distributed around the actual surface of the object. For this step the dissertation presents a study from a scanner s laser in order to create a cloud of points based on its reading features. The second stage of reconstruction consists in the application of the surface reconstruction algorithm that enable, from the cloud of points, to get the surface information by filtering out possible errors, to perform the surface reconstruction. This dissertation presents a methodology which is based on the division of the point cloud into cross sections, where in each section is applied a method for reducing the points based on definition of micro-regions and the calculation of their center of mass and then, performing a selection of the center of mass that can be considered as belonging the surface. Next parameters are obtained to allow the best fitting of a weighted cubic Bspline namely: calculation of the weights applied to each point to be adjusted, which is performed as a function of radius of a circle formed by three consecutive points; definition of the best starting points of the curve to obtain the best curve fitting; calculation of derived vector in the closing point of the curve so as to provide a continuous closing and the definition of the optimal number of control points for the best curve fitting. Once all parameters had been obtained is possible to perform the adjustment of the weighted cubic B-spline curve by applying an adjustment with interpolation and derived constraints from the beginning and end points using the least squares method. Finally, it is possible to perform interpolation of the adjusted curves to the cross sections in the longitudinal direction to obtain a smooth bi-directional surface that best represents the actual object.