A shape-preserving data embedding algorithm for NURBS curves and surfaces

Existing data embedding algorithms for polygonal meshes and their attributes cannot 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. We propose 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 how 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 shape- and data size-preserving data embedding algorithm for NURBS curves and surfaces, we outline additional methods for embedding data in various types of parametric curves and surfaces.