Global error bounds and amelioration of sweep surfaces

With the prescription of a (piecewise) polynomial or rational cross section and axis curves, contemporary sweep or generalized cylinder constructors are incapable of creating an exact or even an approximation with a bounded error of the actual sweep surface that is represented in the same functional space, in general. An approach is presented to bound the maximal error of the sweep approximation. This bound is automatically exploited to adaptively refine and improve the sweep approximation to match a prescribed tolerance. Finally, methods are considered to eliminate the self-intersecting regions in the sweep surface resulting from an axis curve with large curvature.

[1]  Gershon Elber,et al.  Error bounded variable distance offset operator for free form curves and surfaces , 1991, Int. J. Comput. Geom. Appl..

[2]  Sabine Coquillart,et al.  A Control-Point-Based Sweeping Technique , 1987, IEEE Computer Graphics and Applications.

[3]  Fopke Klok.  Two moving coordinate frames for sweeping along a 3D trajectory , 1986, Comput. Aided Geom. Des..

[4]  Pekka Siltanen,et al.  Normal orientation methods for 3D offset curves, sweep surfaces and skinning , 1992, Comput. Graph. Forum.

[5]  Nicholas M. Patrikalakis,et al.  Topological and differential-equation methods for surface intersections , 1992, Comput. Aided Des..

[6]  I. J. Schoenberg,et al.  On Variation Diminishing Spline Approximation Methods , 1988 .

[7]  G. Farin.  NURB curves and surfaces: from projective geometry to practical use , 1995 .

[8]  John K. Johnstone,et al.  A rational model of the surface swept by a curve * , 1995, Comput. Graph. Forum.

[9]  Willem F. Bronsvoort,et al.  A method for converting the surface of a generalized cylinder into a B-spline surface , 1992, Comput. Graph..

[10]  Tom Lyche,et al.  Mathematical methods in computer aided geometric design , 1989 .

[11]  Manfredo P. do Carmo,et al.  Differential geometry of curves and surfaces , 1976 .

[12]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[13]  Soon-Bum Lim,et al.  Approximate General Sweep Boundary of a 2D Curved Object, , 1993, CVGIP Graph. Model. Image Process..