Appeal No. 2006-2963
Application No. 10/309,969
interval based upon the identified points thus modeling the section of the curve. Such a
technique enables modeling each respective curve section such that changes in the
data only affect the curve locally. As a result, a point in one section can be altered
without affecting the modeled curve in subsequent sections.
Representative claim 1 is reproduced as follows:
1. A method of modeling at least one section on a curve f, wherein
modeling a section comprises:
providing a pair of positions(fi, fi+1)of the section of the curve, wherein the
pair of positions includes associated directions (di, di+1) and associated
curvatures (ki, ki+1);
identifying points b0, b1, b2, b3, and b4 based upon the pair of positions(fi,
fi+1) and associated directions(di, di+1)and curvatures(ki, ki+1); and
determining a quartic interpolant p(t) over an interval (i < t < i+1)based
upon points b0, b1, b2, b3, and b4 to thereby model the section of the curve,
wherein the Interpolant p(t) has a position, direction and curvature equal to fi, di
and ki, respectively, at t = i, and wherein the interpolant p(t) has a position,
direction and curvature equal to fi+1, di+1and ki+1, respectively, at t= i + 1.
The examiner relies on the following references:
Peters, Jörg,(“Peters”), Local Generalized Hermite Interpolation by Quartic C2 Space
Curves, ACM Trans. On Graphics, Vol. 8, No. 3, p. 235-42,(1989)(“Peters”).
de Boor, Carl, et al.(“de Boor”), High Accuracy Geometric Hermite Interpolation, Comp.
Aided Geometric Des. 4, 269-78,(1987).
The following rejections are on appeal before us:
1. Claims 1, 8-11, 18-21, and 28-30 stand rejected under 35 U.S.C. § 102(b) as
being anticipated by Peters.
2
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