Research On The Theory And Application Of Geometric Constraint Based Model Reconstruction In Reverse Engineering

As one of the most important components of advanced manufacturing technologies, reverse engineering is no longer simply for prototype duplication, but has gradually developed into a key supporting tool for product innovative design and new product development. In such a situation, the CAD models reverse engineering creates are no longer the traditional solid models, but the feature models, which are with more capability of innovative design and support the product life time cycle. Under the background of feature modeling oriented reverse engineering technologies, research work regarding the theory and application of geometric constraint based model reconstruction is presented in this thesis.Both analytic shapes (line, circular arc, plane, cylinder, sphere etc.) and freeform shapes (spline curve, 4-sided spline surface) appear frequently in industrial products, the problem of reconstructing these curves and surfaces under local geometric constraints is tackled in this thesis. The representations of curves and surfaces are discussed; the objective functions for curve and surface fitting are deduced, as well as the algebraic representations of the geometric constraints between these curves and surfaces. The stability issue of the objective functions of curves and surfaces in numerical optimization is analyzed, and the feasibility of improvement by using similarity transformation is presented, as well as detailed algorithmic steps.Symmetry is an important property of the shape of industrial products, and to deal with the symmetry constraint properly is of key importance to the reconstruction of symmetric models. Symmetry constraint is a global constraint, which cannot be represented by a few algebraic equations. As a result, the resolution of symmetry constraint is different from local geometric constraints. For the reconstruction of symmetric models composed of analytic curves and surfaces, explicit representations are adopted, distance functions between data points and symmetric models are deduced, as well as the objective functions for least squares model fitting, and methods to obtain initial values of parameters for symmetry transformations are also discussed. For the reconstruction of symmetric freeform curves and surfaces (represented in B-Spline model), a method based on the symmetry axis or symmetry plane extracted from point cloud is presented to construct symmetric knot vector, and symmetry constraint equations regarding the control points are deduced, problem of B-Spline curve or surface fitting under symmetry constraint equations is sloved by the Lagrange multiplier method.N-Sided hole filling appears occasionally in the reconstruction of complex CAD models in reverse engineering, this thesis presents a practical N-Sided hole filling method, which is based on discretization of boundary conditions and trimmed B-Spline surface model. Criteria for boundary discretization are discussed in detail, and mathematical model for N-Sided hole filling is given, as well as its solving method.Software module and its implementation regarding the resolution of constraints in RE-SOFT (a reverse engineering software) are introduced; and pseudo code of some data structures is presented. Finally, an example for the modeling of an industrial gas turbine blade is given to show the basic methods of reverse modeling in RE-SOFT with the assistance of commercial CAD software.