General Principles
Introduction
Polylines Nets
Curved Polygons Nets
Guides and Geometric Interfacing
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Curved Polygons Nets
Curved Polygons Nets are an extension of Polylines Net and therefore an extension of classical Meshes.
Curved Polygons Nets
A Curved Polygons Net is a Mesh whose vertices are connected with Curved Edges. A Curved Edge is a smooth mathmatical model which can be approximated with a Polyline. Therefore, we can generate a Polyline Net from a Curved Polygons Net by tessellating its curves.
Fig. 1 A Curved Polygons Net is converted first into a Polylines Net by converting its curves into a Polylines; than a Polylines Net Filling algorithm is applied to generate a triangles mesh.
Since the Edges are Curved, so are the faces and that's where the Curved Polygons come from.
Curved Polygons Nets and Levels of Detail
The important aspect of Curved Polygons Nets is that there is not only one way to convert a Curved Polygons Net into a Polylines Net. That is: we can tessellate the curves in the net with a different number of lines to shift between performances and quality. Such amount of vertices may even be completely heterogeneous, that is: the polylines surrounding a Curved Polygons (after converting the model to a Polylines Net) don't need to have the same amount of lines, since the algorithms we use for filling are designed to interpolate polylines with different sizes. From a practical point of view, this is an extremely powerful feature, since it allows an ad hoc customization of the process and therefore an ad hoc optimization of the final mesh.
Fig. 2 A Curved Polygons Net model made with Curved Poly. You can clearly see that the Curved Edges can be tessellated with a different, heterogeneous, amount of segments, affecting the amount of triangles in the final mesh. This image is part of a Curved Poly Demo about Levels of Detail.
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