Research On Continuity Adjustment And To-Pology Recovery Technique For Complex Free-form Surface In Reverse Engineering

Reverse engineering centered on point cloud geometric modeling is one of the most active branches of CAD, and has also become one of the most important means of digital product design in modern manufacturing. Based on feature and constraint reverse modeling strategies, the theories and methods of continuity adjustment and topology recovery for complex freeform surface model are deeply researched in this dissertation.Aiming at the current techniques of drawing curves onto point clouds which are weak robustness while dealing with multi-layer point set surface models, and are lack of guiding by intuitive geometric features contained in point clouds, an approach based on spatial grid and directed by curvature map is proposed, which provides an essential tool for freeform surface reconstruction based on a user defined curve network. Firstly, subdivide point clouds into spatial grids and estimate curvature based on three parameters Shepard surface. Secondly, choose data point (point used to construct initial curve) according to geometric features illustrated in curvature image, then apply point projection algorithm based on spatial grids to calculate each projected vertex of chosen data point. Thirdly, interpolate each projected vertex of chosen data point to construct the initial curve. And finally, construct normal curve with the same knot sequences as the initial curve to determine project directions of curve, then apply binary division algorithm and projection algorithm based on spatial grids to project the initial curve onto point set surfaces.In order to deal with inconsistencies among the confluent region, where multiple surfaces meet, a new local consistent mending scheme for complex freeform surface model is proposed, by the combined use of global beautification technique for freeform surface model and N-Sided hole filling method, which is based on discretization of boundary conditions and trimmed B-spline surface model. Firstly, utilize the infinitesimal deformation technique of differentiable manifold to beautify the multiple surfaces approximated to point cloud subject to tight error globally, which can generate convergent G1 smooth B-spline surfaces and improve the shape of the model. Secondly, clip the local region containing N-patch corner off the original multiple surfaces, and then reconstruct the trimmed area based on discretization of boundary conditions and trimmed B-spline surface model to satisfy approximate G1 continuity with adjacent surfaces while reflecting the feature trend of the original surface.Since there has been seldom research on smoothly stitching trimmed surface patches together, this dissertation studies the problem of global continuity adjustment, damaged region repair and local shape optimization for complex trimmed surface model, and presents a uniform method for dealing with continuity adjustment of trimmed surfaces and geometric repair of local broken region. Constrained B-spline surface refitting technique and trim calculation are first utilized to achieve global G1 continuity, and then local shape optimization functional is applied to reduce fitting error and improve local quality of refitted surface patch.Considering that the local consistent mending technique destroys the topology of original CAD model and increases the number of surface patches needed for freeform surface shape modeling, a topology recovery approach dealing with complex freeform surface model after local consistent mending is proposed. The process of this mehtod includes two steps. Firstly, construct the curve network which determine the geometry and topology properties of recovery freeform surface model; secondly, apply freeform surface fitting method to create B-spline surface patches to recover the topology of trimmed ones. Corresponding to the two levels of enforcing boundary conditions on a B-spline surface, two solution schemes are presented respectively. In the first solution scheme, non-constrained B-spline surface fitting method is utilized to piecewise recover trimmed confluent surface patches and then employs global beautification technique to smoothly stitch the recovery surface patches. In the other solution scheme, constrained B-spline surface fitting technique based on discretization of boundary conditions is directly applied to recover topology of surface model after local geometry repair while achieving G1 continuity simultaneously.All the algorithms proposed in this dissertation have been embedded in RE-SOFT, a feature-based reverse modeling system. Typical industrial components are used to illustrate the validation of the proposed continuity adjustment and topology recovery method and to reveal its practical value in reverse engineering. Finally, some topics for future research are presented and discussed briefly.