B-spline curve approximation. zhu ping. 08.02.20. 1. Application 2. Some works 3. Discussion. Outline. Arctile:. The NURBS Book. Les Pigel&Wayne Tiller, 2nd 1996 Knot Placement for B-Spline Curve Approximation. Anshuman Razdan, Technical Report 1999
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1. Start with the minimum or a small number of knots
2. Start with the maximum or many knots
2. Relate to initial knots
1. Given a parametric curve.
2. Evaluated at arbitrary discrete values within the parameter range.
1. Closely approximate with a C2 cubic B-spline curve.
1. Pick appropriate points on the given curve
3. Select end conditions
4. Solve the tri-diagonal linear systems of equations
How to obtain sampling points
1. Estimate the number of sampling points;
2. Find samping points on the given curve
Approximated by a finite number of circular arc segments
1. arc length
(1) curvature extrema
if , insert a auxiliary knot in the middle of the
Computer-Aided Design 2005
Su BQ,Liu DY:<<Computational geometry—curve and surface modeling>>
1. smoothing of discrete curvature
2. divide the initial parameter-curvature set into several subsets
3. iteratively bisect each segment untill satisfy the heuristic rule
4. check the adjacent intervals that joint at a feature point
Hyungjun Park, since 2001,a faculty member of Industrial Engineering at Chosun University,
geometric modeling, CAD/CAM/CG application
Joo-Haeng Lee, a senior researcher in ETRI
CAD&CG, robotics application
1. compare with KTP and NKTP:when |m-n| is small, it is sensitive to parameter values.
stability, robustness to noise and error-boundedness
2. dominant point selection
3. knot placement(adaptive using the parameter values of the selected dominant points)
4. least-squares minimization
are the parameter values of points
1. Selection of seed points from
2. Choice of a new dominant point
Based on the adaptive refinement paradigm
fewer dominant points at flat regions and more at
local curvature maximum(LCM) points, inflection points
251 input points
10 initial dominant points
The segment is to be refined.
13 dominant points
2. optimal selection of dominant points as genetic
3. B-spline surface and spatial curve