Computer Science – Numerical Analysis
Scientific paper
2010-06-01
Computer Science
Numerical Analysis
14 pages, 19 figures, prepare for LMS
Scientific paper
We study variational problems for curves approximated by B-spline curves. We show that, one can obtain discrete Euler-Lagrange equations, for the data describing the approximated curves. Our main application is to the curve completion problem in 2D and 3D. In this case, the aim is to find various aesthetically pleasing solutions as opposed to a solution of a physical problem. The Lagrangians of interest are invariant under the special Euclidean group action for which B-spline approximated curves are well suited. Smooth Lagrangians with special Euclidean symmetries involve curvature, torsion, and arc length. Expressions in these, in the original coordinates, are highly complex. We show that, by contrast, relatively simple discrete Lagrangians offer excellent results for the curve completion problem. The methods we develop for the discrete curve completion problem are general and can be used to solve other discrete variational problems for B-spline curves.
Mansfield Elizabeth
Zhao Jun
No associations
LandOfFree
Discrete Variational Calculus for B-spline Approximated Curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Discrete Variational Calculus for B-spline Approximated Curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Discrete Variational Calculus for B-spline Approximated Curves will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-513520