A Shape-Preserving Data Embedding Algorithm for NURBS Curves and Surfaces

Existing data embedding algorithms for polygonal meshes and their attributes can’t be applied to the majority of (geometric) computer aided design (CAD) applications, for two major reasons. First, these CAD systems employ parametric curves and surfaces, not polygonal meshes, as their main shape-defining primitives. Second, most CAD applications do not tolerate modifications of model topology and/or geometry that are introduced by existing data embedding algorithms. This paper proposes a new data embedding algorithm for non-uniform rational B-spline (NURBS) curves and surfaces, which employs rational linear reparameterization for embedding messages. The algorithm exactly preserves the shape, — that is, the geometry and topology — of its embedding targets. Furthermore, it preserves the data size of the model. We consider these two properties, preservation of shape and preservation of data size, can be significant with regard to the use of data embedding in CAD applications. In addition to the shapeand data size-preserving data embedding algorithm for NURBS curves and surfaces, this paper outlines additional methods for embedding data in various types of parametric curves and surfaces.