Standard Free-Form Deformations (FFD) built upon tensor-product B-Splines have been proved useful to model the warp between two views of a deformable surface. In this paper, we show that the standard FFD is the affine projection of a threedimensional tensor-product B-Spline surface. We construct a new tensor-product warp relying on Non-Uniform Cubic B-Spline: the NURBS-Warp. We show that this n...

3D models today are used in many areas, e.g. computer-aided geometric design, animation, and computer games. The areas have different demands; computer-aided geometric design must have exact models, cartoons must look good and games must have real-time feedback. Computer-aided design software commonly uses trimmed NURBS as primitives, which have some support in low level graphic visualization l...

Surface reconstruction from sets of cross-sectional data is important in a variety of applications. The problem of generating a ship hull surface from non-regular cross-sectional curves is addressed. Generating non-uniform rational B-splines (NURBS) surfaces that represent cross-sectional curves is a challenge, since the number of control points is growing due to the non-avoidable process of ha...

N -sided hole filling plays an important role in vertex blending. To deal with the case that the corner is surrounded by rational surfaces (i.e. NURBS surfaces), an algorithm to fill n-sided holes with ε-G1 continuous NURBS patches that interpolate the given boundary curves and approximate the given cross-boundary derivatives is presented based on Piegl’s method. The NURBS surfaces joining alon...

Two watermarking algorithms for 3D nonuniform rational B-spline (NURBS) graphic data are proposed: one is appropriate for the steganography, and the other for watermarking. Instead of directly embedding data into the parameters of NURBS, the proposed algorithms embed data into the 2D virtual images extracted by parameter sampling of 3D model. As a result, the proposed steganography algorithm ca...

infancy, there should be much more researches and discussions in various elds, including surface representation. We believe and it is strongly required that the NURBS be supported in 3-D visual communication and compression. Then, the contribution in this paper might come true in the real world. References 11 M. Soucy and D. Laurendeau, A general surface approach to the integration of a set of ...

Owning to the high-speed feed rate and ultra spindle speed have been used in modern machine tools, the tool-path generation plays a key role in the successful application of a High-Speed Machining (HSM) system. Because of its importance in both high-speed machining and tool-path generation, approximating a contour by NURBS format is a potential function in CAD/CAM/CNC systems. It is much more c...

This paper presents a method for the direct manipulations of B-spline and non-uniform rational B-splines (NURBS) curves using geometric constraints. A deformable model is developed to define the deformation energy functional of B-spline and NURBS curves. The finite element method is used to minimize the deformation energy functional and solve for the deformed shape of curves subjected to constr...

Triangular B-splines are a new tool for modeling a broad class of objects deened over arbitrary, non-rectangular domains. They provide an elegant and uniied representation scheme for all piecewise continuous polynomial surfaces over planar triangulations. To enhance the power of this model, we propose triangular NURBS, the rational generalization of triangular B-splines, with weights as additio...