Nonlinear interpolation between slices
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Illustrative visualization: interrogating triangulated surfaces
Computing - Geometric Modelling, Dagstuhl 2008
G1 continuity triangular patches interpolation based on PN triangles
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
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In order to achieve the impression of a smooth surface while rendering a polygon mesh, normal vector vectors may be provided in the vertices of the mesh that are the average of the surface normals of the adjacent polygons. Interpolation of these normal vectors while rendering of the polygons in the mesh, and using the interpolated normal vectors in the shading computations, yields a smoothly varying intensity distribution. There is an inherent mismatch, however, between the smoothness of the shading thus achieved and the non-smoothness of the geometry which is particularly visible at silhouettes, showing as straight edges and non-smooth edge junctions at the silhouette vertices. In this paper, a remedy for these artifacts is suggested. The remedy consists of subdividing each input polygon into a mesh of polygons prior to rendering. The shape of this resulting polygon mesh is controlled by the normal vectors that are provided in the vertices of the original polygon, unlike other subdivision schemes that make use of adjacent polygons. With our method, polygons equipped with vertex normal vectors can therefore be processed without further knowledge of neighbor polygons. This makes the method well-suited in the context of graphics libraries, such as OpenGl, that treat polygons typically on a per-polygon basis. So the proposed computation of the mesh which replaces the original polygon can be viewed as a filter which may operate as a process in front of a traditional polygon rendering pipeline.