Michael Kallay
Abstract
The problem of finding the plane curve of minimal elastic energy with prescribed endpoints and end-directions was solved in 1983 by B. K. P. Horn. Here the solution is discussed, given a very short proof, and extended to include a constant on length.
- 1 CARLSON, B. C., AND NOT{S, A.M. Algorithms for incomplete elliptic integrals. ACM Trans. Math. Soft. 7 (1981), 398-403. Google Scholar
Digital Library
- 2 FORSYTH, A.R. Calculus of Variations. Dover, New York, 1949.Google Scholar
- 3 HORN, B. K.P. The curve of least energy. ACM Trans. Math. Soft. 9 (1983), 441-460. Google ScholarDigital Library
- 4 KALLAY, M. A method to approximate the space curve of minimal energy and prescribed length. Comput. Aided Des. (to appear). Google ScholarCross Ref
- 5 ULLMAN, S. Filling in the gaps: The shape of subjective contours and a model for their generation. Biol. Cybern. 25 (1976), 1-6.Google ScholarDigital Library
Index Terms
- Plane curves of minimal energy
Recommendations
A constructive framework for minimal energy planar curves
Given points P 1 , P 2 , , P n in the plane, we are concerned with the problem of finding a fair curve which interpolates the points. We assume that we have a method in hand, called a basic curve method, for solving the geometric Hermite interpolation ...
Geometric constraints on quadratic Bézier curves using minimal length and energy
This paper derives expressions for the arc length and the bending energy of quadratic Bézier curves. The formulas are in terms of the control point coordinates. For fixed start and end points of the Bézier curve, the locus of the middle control point is ...
Reviews
A. Chris Rolls Newbery
The paper describes an algorithm to determine, in parametric form, the equation of a minimum-energy curve for an elastic rod with given end conditions. There may also be a constraint on the length of the rod. One or two integral equations have to be solved for determination of the parameters. The equations are simple in structure and said to be easily solved. The presentation is clear, but an example would have been helpful.
Access critical reviews of Computing literature here
Become a reviewer for Computing Reviews.
Comments