Geometric distance fitting of parabolas in $\mathbb{R}^3$
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초록
We are interested in the problem of fitting a parabola to a set of data points in $\mathbb{ R}^3 $. It can be usually solved by minimizing the geometric distances from the fitted parabola to the given data points. In this paper, a parabola fitting algorithm will be proposed in such a way that the sum of the squares of the geometric distances is minimized in~$\mathbb{R}^3$. Our algorithm is mainly based on the steepest descent technique which determines an adequate number $ \lambda $ such that $h ( \lambda ) = Q ( u - \lambda \nabla Q\bigl( u \bigr) ) < Q ( u)$. Some numerical examples are given to test our algorithm.
Abstract
We are interested in the problem of fitting a parabola to a set of data points in $\mathbb{ R}^3 $. It can be usually solved by minimizing the geometric distances from the fitted parabola to the given data points. In this paper, a parabola fitting algorithm will be proposed in such a way that the sum of the squares of the geometric distances is minimized in~$\mathbb{R}^3$. Our algorithm is mainly based on the steepest descent technique which determines an adequate number $ \lambda $ such that $h ( \lambda ) = Q ( u - \lambda \nabla Q\bigl( u \bigr) ) < Q ( u)$. Some numerical examples are given to test our algorithm.
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