Name
Abstract | ||
|---|---|---|
Curve fitting with splines is a fundamental problem in computer-aided design and engineering. However, how to choose the number of knots and how to place the knots in spline fitting remain a difficult issue. This paper presents a framework for computing knots (including the number and positions) in curve fitting based on a sparse optimization model. The framework consists of two steps: first, from a dense initial knot vector, a set of active knots is selected at which certain order derivative of the spline is discontinuous by solving a sparse optimization problem; second, we further remove redundant knots and adjust the positions of active knots to obtain the final knot vector. Our experiments show that the approximation spline curve obtained by our approach has less number of knots compared to existing methods. Particularly, when the data points are sampled dense enough from a spline, our algorithm can recover the ground truth knot vector and reproduce the spline. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1016/j.cad.2014.08.022 | Computer-Aided Design |
Keywords | Field | DocType |
Spline fitting,Knot calculation,Sparse optimization | Spline (mathematics),Mathematical optimization,Curve fitting,Smoothing spline,Flat spline,Perfect spline,Knot (unit),Optimization problem,Convex optimization,Mathematics | Journal |
Volume | Issue | ISSN |
58 | C | 0010-4485 |
Citations | PageRank | References |
13 | 0.66 | 9 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hongmei Kang | 1 | 21 | 3.01 |
| Falai Chen | 2 | 403 | 32.47 |
| Yusheng Li | 3 | 31 | 8.30 |
| jiansong deng | 4 | 458 | 38.59 |
| Zhouwang Yang | 5 | 361 | 24.64 |