Study of Homogeneous Parameter, Homogeneous Geometric Newton Method.
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- KIMURA Masanori
- 早稲田大学大学院
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- YAMAGUCHI Fujio
- 早稲田大学
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- WATANABE Yoshio
- ゴールドマン・サックス証券
Bibliographic Information
- Other Title
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- 同次パラメータ同次幾何的ニュートン法に関する考察
- ドウ ジ パラメータ ドウ ジ キカテキ ニュートンホウ ニ カンスル コウサツ
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Description
This paper proposes a new geometric Newton-Raphson method for dealing with a rational polynomial curve. The algorithm is robust and at the same time locally unique.<BR>Although rational polynomial curves and surfaces have become standard forms in computer-aided design, they have many problems. For example, a Newton-Raphson algorithm for dealing with a rational polynomial curve tends to be unstable. This is a fatal problem. We propose to homogenize the coordinates of a rational curve when it is applied to the Newton-Raphson algorithm. Then it becomes very robust. Furthermore the solution point becomes locally unique with respect to an initial parameter range when the parameter is also homogenized in addition to the coordinates, because with this technique we have a freedom of controlling parameter values and we can adjust the increment of the parameter appropriately.
Journal
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- Journal of the Japan Society for Precision Engineering
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Journal of the Japan Society for Precision Engineering 67 (12), 1950-1955, 2001
The Japan Society for Precision Engineering
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Details 詳細情報について
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- CRID
- 1390282679774818048
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- NII Article ID
- 110001373080
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- NII Book ID
- AN1003250X
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- ISSN
- 1882675X
- 09120289
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- NDL BIB ID
- 6078310
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- Text Lang
- ja
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- Data Source
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- JaLC
- NDL
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed