Modifying the shape of rational B-splines. part 1: curves
Computer-Aided Design
The NURBS book
Watermaking three-dimensional polygonal models
MULTIMEDIA '97 Proceedings of the fifth ACM international conference on Multimedia
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Robust Watermarking and Affine Registration of 3D Meshes
IH '02 Revised Papers from the 5th International Workshop on Information Hiding
A Shape-Preserving Data Embedding Algorithm for NURBS Curves and Surfaces
CGI '99 Proceedings of the International Conference on Computer Graphics
Wavelet-based blind watermarking of 3D models
Proceedings of the 2004 workshop on Multimedia and security
Computer Graphics and Geometric Modelling: Mathematics
Computer Graphics and Geometric Modelling: Mathematics
Watermarking algorithms for 3D NURBS graphic data
EURASIP Journal on Applied Signal Processing
Computer Graphics in C#: Principles and Practices
Computer Graphics in C#: Principles and Practices
Disappearing Cryptography: Information Hiding: Steganography & Watermarking
Disappearing Cryptography: Information Hiding: Steganography & Watermarking
Blind watermarking of NURBS curves and surfaces
Computer-Aided Design
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We present an algorithm for embedding robust reversible watermarks into CAD models that are represented by a collection of NURBS (Non Uniform Rational B-Spline) surface patches. Changes to the geometry of the surface representation are introduced by moving one control point per surface patch. This approach provides robustness against converting the model into the mesh representation. The information needed to restore the original control point location is added to the knot vectors of the patch, thus enabling recovery of the original model from the watermarked NURBS representation. We exploit the properties of the NURBS representation for preserving the continuity between adjacent patches. Continuity is the major criterion of designers for assessing the quality of surface models.