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

Three-dimensional (3D) (geometric) Computer Aided Design (CAD) has become increasingly popular in manufacturing industries. It is used to design, for example, automobile exterior, chassis, or engine blocks. A majority of these systems represent shapes by using parametric curves and surfaces, such as Bezier and NURBS (Non-uniform Rational B-Spline) curves and surfaces, as their main tools to define shapes.
Despite their popularity, to the author’s knowledge, no data embedding algorithm designed specifically for CAD systems has been studied in the past. While algorithms did exist that embedded data into 3D polygonal meshes, most CAD systems employed curves and surfaces as their main shape-defining primitive. Even if polygonal meshes are used in a CAD, alterations of geometry and topology introduced by these data embedding algorithms could not be tolerated.
This paper proposes a new data embedding algorithm for NURBS curves and surfaces, which employed rational linear reparameterization for encoding messages. The most significant feature of the algorithms is exact preservation of geometric shape of its targets, that are, NURBS curves and NURBS tensor product surfaces. Furthermore, the algorithm preserves data size of the model.
The paper also suggests additional methods to embed data in parametric curves and surfaces, classified by shape- and size-preservation properties of the methods.