دانلود رایگان مقاله تبدیل Watertigh سطوح برش شده CAD برای اسپلاین کلاف - تاچر

Abstract

The boundary representations (B-reps) that are used to represent shape in Computer-Aided Design systems create unavoidable gaps at the face boundaries of a model. Although these inconsistencies can be kept below the scale that is important for visualisation and manufacture, they cause problems for many downstream tasks, making it difficult to use CAD models directly for simulation or advanced geometric analysis, for example. Motivated by this need for watertight models, we address the problem of converting B-rep models to a collection of cubic C1 Clough–Tocher splines. These splines allow a watertight join between B-rep faces, provide a homogeneous representation of shape, and also support local adaptivity. We perform a comparative study of the most prominent Clough–Tocher constructions and include some novel variants. Our criteria include visual fairness, invariance to affine reparameterisations, polynomial precision and approximation error. The constructions are tested on both synthetic data and CAD models that have been triangulated. Our results show that no construction is optimal in every scenario, with surface quality depending heavily on the triangulation and parameterisation that are used.

6. Conclusion and future work

We have performed a comparative study of seven C1 cubic Clough–Tocher spline constructions, combined with three split point types. An iterative method aimed at improving C2 discontinuities, which can be applied to any spline variant, was also included. We compared the constructions on visual fairness, invariance to affine reparameterisations, polynomial precision and approximation error. The constructions were tested on both synthetic data and on triangulated CAD models. Our results show that no construction is optimal across all assessment criteria and that surface quality depends heavily on the triangulation and parameterisation that are used. Nevertheless, if only one construction was to be chosen, we would recommend KaG, the construction of Kashyap (1996) augmented by boundary mid-edge gradients. Avenues for future research include improving the stitching process of several Clough–Tocher splines which are separately parameterised. We achieved C0 continuity by adjusting some of the boundary control points, however, it should be possible to join several splines with at least G1 continuity across their interfaces without compromising their internal C1 continuity. Our tests showed strong boundary effects for the majority of constructions. We believe that boundary influence should be investigated in more detail and freedoms at boundary edges put to better use, ideally in conjunction with the boundary adjustment mentioned above. The triangulation and parameterisation that are used strongly influence the fairness of the resulting approximations. It would be interesting to investigate this influence in more detail. This is also linked to the use of Clough–Tocher splines in isogeometric analysis (Jaxon and Qian, 2014).