An expression of stem-form by the moments

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  • モーメントによる樹幹形の表現
  • モーメント ニヨル ジュカンケイ ノ ヒョウゲン

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Stem-form can be thought of as a system involving diameters (or radii) standing upright at each height on the stem axis, and mathematically this system of diameters is equivalent to that of a mass distribution along the axis. Therefore, stem-form can be regarded as a mass distribution along the axis. According to the moment problem, a mass distribution along an axis determines its moments and reversely so. Then stemform can be determined uniquely by its moments. The stem-form derived from moments up to the γ-th order is a polynomial of γ-th degree, which is the very formula proposed by LAGRANGE. Coefficients of the polynomial are all derived from γ moments up to the γ-th order. According to linearity, an average stemform can be deduced from the expectations of the moments of the stem. Therefore to distinguish different stem-forms, it is convenient to directly compare their moments.

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