Data processing: generic control systems or specific application – Specific application – apparatus or process – Product assembly or manufacturing
Reexamination Certificate
1998-04-10
2001-03-06
Grant, William (Department: 2786)
Data processing: generic control systems or specific application
Specific application, apparatus or process
Product assembly or manufacturing
C700S187000, C345S419000
Reexamination Certificate
active
06198979
ABSTRACT:
FIELD OF THE INVENTION
The current invention is generally related to a method of and a system for generating free-form surfaces, and more particularly related to a method of and a system for generating free-form surfaces with NURBS boundary Gregory patches.
BACKGROUND OF THE INVENTION
To design complex free-form surfaces using a computer aided design (CAD) system, designers generally define a curve mesh that consists of characteristic lines such as boundary curves and cross sections from which the mesh is interpolated. One of commonly used curves is Bezier curves each of which is defined by a predetermined number of points in space. For example, four points including two control points define a cubic Bezier curve in three dimensional space. A plurality of curves may be joined to form a more complex curve. To facilitate the definition of a complex curve, the Non Uniform Rational B-spline (NURBS) curve is a powerful tool since a NURBS curve can represent multiple composite curves including complicated Bezier curves.
To take advantage of a NURB curve, Japanese Patent Publication Hei 7-282117 discloses a method of joining curve meshes including NURBS curves in a first order geometric (G
1
)continuous manner. Roughly speaking, G
1
continuity means that the directions (but not necessarily the magnitudes) of the two tangent vectors are equal at a joint of the adjacent surfaces. Prior attempts have been also made to use a NURB curve as a common boundary between free-form surfaces. An irregular curve mesh bounded by NURBS curves can be smoothly interpolated by using a general boundary Gregory patch which has been disclosed in U.S. Pat. No. 5,619,625. However, the general boundary Gregory patch cannot join adjacent NURBS surfaces with G
1
continuity. Chiyokura et al. proposed a Gregory patch (Chiyokura and Kimura, Design of Solids with Free-form Surfaces, Computer Graphics, Proc.SIGGRAPH 83, Vol. 17, No. 3, pp289-298, 1983) and a rational boundary Gregory patch (Chiyokura et al. G
1
Surface Interpolation over Irregular Meshes with Rational Curves, NURBS for Curve and Surface Design, Farin, G. Ed., pp. 15-34, SIAM, Philadelphia, 1991) as a curve surface to be joined in a G
1
continuous manner. Both the Gregory patch and the rational boundary Gregory patch have a cross boundary derivative which has independent parameters u, v for each direction, and this characteristics enables the insertion of an irregular curve mesh in a G
1
continuous manner. Furthermore, Liu et al. proposed a method of using a high degree Bezier curve to smoothly insert a curve mesh (Liu and Sun, G
1
Interpolation of mesh curves, Computer Aided Design, Vol. 26, No. 4, pp. 259-267, 1994).
The above described methods enable smooth connections after the curve mesh is modified but require that the curve in the curve mesh is rational Bezier curve. However, when filet offsetting or boolean operations are performed, it is difficult to express certain mesh curves by rational Bezier curves. A NURBS curve can express those mesh lines, and a curve mesh contains the NURBS curve. Since it is impossible to use a NURBS curve as a boundary for a Gregory patch and a Bezier curve surface, it is practically impossible to interpolate an irregular curve mesh containing NURBS curves.
Konno et al. have proposed the use of a NURBS boundary Gregory patch for inserting an irregular curve mesh containing NURBS curves (Konno and Chiyokura, Interpolation Method of Free Surface Using NURBS boundary Gregory Patch, Proceeding of Information Processing Academy, Vol. 35, No. 10, pp.2203-2213, 1994), (Konno and Chiyokura, An Approach of Designing and Controlling Free-Form Surfaces by Using NURBS Boundary Gregory Patches, Computer Aided Geometri Design, Vol. 13, No. 9, pp. 825-849, 1996). Although the NURBS boundary Gregory patch enables a free-surface to have G
1
continuity with an adjacent surface regardless of the limitations of a curve mesh, since the above described method divides the NURBS curves into rational Bezier curves, these separate curves in the formed surface generally have Co continuity. In other words, the formed free-surface has mathematically broken areas and remains to be improved to have C
1
continuity.
SUMMARY OF THE INVENTION
In order to solve the above and other problems, according to a first aspect of the current invention, a method of generating free-form surfaces with NURBS boundary Gregory patches, includes the steps of: a) selecting a common NURBS boundary curve between two free-form surfaces; b) joining the two free-form surfaces in G
1
continuity; and c) maintaining C
1
continuity in each of the joined free-form surfaces.
According to a second aspect of the current invention, a method of generating free-form surfaces with NURBS boundary Gregory patches, includes the steps of: a) storing information on control points and corresponding weights for a common NURBS boundary curve; b) storing information on control points and corresponding weights of a curve connected to a terminal of the common NURBS boundary curve; c) determining conditions for a G
1
continuity at the terminal based upon the information stored in said steps a) and b); d) forming along the common NURBS boundary free-form surfaces that are G
1
continuous with each other; and e)making each of the surfaces formed in said step d) C
1
continuous based upon information stored in said steps a) and b) as well as the conditions determined in said step c).
According to a third aspect of the current invention, a recording medium containing a computer program for generating free-form surfaces with NURBS boundary Gregory patches, the computer program, includes the steps of: a) selecting a common NURBS boundary curve between two free-form surfaces; b) joining the two free-form surfaces in G
1
continuity; and c) maintaining C
1
continuity in each of the joined free-form surfaces.
According to a fourth aspect of the current invention, A recording medium containing a computer program for generating free-form surfaces with NURBS boundary Gregory patches, includes the steps of: a) storing information on control points and corresponding weights for a common NURBS boundary curve; b) storing information on control points and corresponding weights of a curve connected to a terminal of the common NURBS boundary curve; c) determining conditions for a G
1
continuity at the terminal based upon the information stored in said steps a) and b); d) forming along the common NURBS boundary free-form surfaces that are G
1
continuous with each other; and e) making each of the surfaces formed in said step d) C
1
continuous based upon information stored in said steps a) and b) as well as the conditions determined in said step c).
These and various other advantages and features of novelty which characterize the invention are pointed out with particularity in the claims annexed hereto and forming a part hereof. However, for a better understanding of the invention, its advantages, and the objects obtained by its use, reference should be made to the drawings which form a further part hereof, and to the accompanying descriptive matter, in which there is illustrated and described a preferred embodiment of the invention.
REFERENCES:
patent: 5119309 (1992-06-01), Cavendish et al.
patent: 5459821 (1995-10-01), Kuriyama et al.
patent: 5481659 (1996-01-01), Nosaka et al.
patent: 5619625 (1997-04-01), Konno et al.
patent: 5883631 (1999-03-01), Konno et al.
patent: 3-80373 (1991-04-01), None
patent: 7-282117 (1995-10-01), None
Kouichi Konno and Hiroaki Chiyokura, An Approach of Designing Free-Form Surfaces by Using Nurbs Boundary Gregory Patches, Oct. 1994, Computer Aided Geometric Design, vol. 35, No. 10, pp. 2203-2213.
Chiyokura and Kimura, “Design of Solids with Free-Form Surfaces, Computer Graphics”, Proc. SIGGRAPH 83, vol. 17, No. 3, pp. 289-298, 1983.
Chiyokura et al., “G1 Surface Interpolation Over Irregular Meshes with Rational Curves, Nurbs for Curve and Surface Design”, Farin, G. Ed., pp. 15-34, SIAM, Philadelphia, 1991.
Liu and Sun, “G1 Interpolation of Mesh Curves, Computer Aide
Grant William
Knoble & Yoshida LLC
Ricoh & Company, Ltd.
Rodriguez Paul
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