Localized construction of curved surfaces from polygon meshes: A simple and practical approach on GPU

We present a method for refining nn-sided polygons on a given piecewise linear model by using local computation, where the curved polygons generated by our method interpolate the positions and normals of vertices on the input model. Firstly, we construct a Bézier curve for each silhouette edge. Secondly, we employ a new method to obtain C1C1 continuous cross-tangent functions that are constructed on these silhouette curves. An important feature of our method is that the cross tangent functions are produced solely by their corresponding facet parameters. Gregory patches can therefore be locally constructed on every polygon while preserving G1G1 continuity between neighboring patches. To provide a flexible shape control, several local schemes are provided to modify the cross-tangent functions so that the sharp features can be retained on the resultant models. Because of the localized construction, our method can be easily accelerated by graphics hardware and fully run on the Graphics Processing Unit (GPU).

Research highlights
► A localized construction method to generate smooth parametric surface patches interpolating (instead of approximating) the vertices and the normal vectors of an input coarse mesh.
► The amount of information needs to be sent is less than other relevant approaches in literature.
► A method works on n-sided polygons.
► A highly parallel algorithm that suits the production of curved polygons on graphics hardware.