충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제29권2호
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  • Pages.267-281
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  • 2016
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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MULTI-DEGREE REDUCTION OF BÉZIER CURVES WITH CONSTRAINTS OF ENDPOINTS USING LAGRANGE MULTIPLIERS

  • Sunwoo, Hasik (Department of Computer Engineering Konkuk University)
  • 투고 : 2015.12.15
  • 심사 : 2016.05.09
  • 발행 : 2016.05.15
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초록

In this paper, we consider multi-degree reduction of $B{\acute{e}}zier$ curves with continuity of any (r, s) order with respect to $L_2$ norm. With help of matrix theory about generalized inverses we can use Lagrange multipliers to obtain the degree reduction matrix in a very simple form as well as the degree reduced control points. Also error analysis comparing with the least squares degree reduction without constraints is given. The advantage of our method is that the relationship between the optimal multi-degree reductions with and without constraints of continuity can be derived explicitly.

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참고문헌

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