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  • » 2024.04
内心ベクトル
内心ベクトル をmathで書いてみた。
内心の算出 三角形ABCをベクトル x , y , z とする 内心 = z + zx + zx zx + zy xy × zx zx + xy × zx zx + zy = z + zy zx + zx zy zx + zy × zx + zy zx + zy + xy = z + zy zx + zx zy zx + zy + xy = z + zy ( x z ) + zx ( y z ) zx + zy + xy = xy z + zy x + zx y zx + zy + xy "内心の算出" newline "三角形ABCをベクトル" vec{x},vec{y},vec{z} "とする" newline widevec{"内心"}=vec{z}+left({widevec{zx}}+abs{widevec{zx}}over{{abs{widevec{zx}}}+abs{widevec{zy}}}widevec{xy} right) times {{abs{widevec{zx}}}over{{abs{widevec{zx}}}+{abs{widevec{xy}}}times{abs{widevec{zx}}over{{abs{widevec{zx}}}+abs{widevec{zy}}}}}} newline {}={vec{z}}+{{abs{widevec{zy}}}widevec{zx} + {abs{widevec{zx}}}widevec{zy}}over{{abs{widevec{zx}}}+{abs{widevec{zy}}}} times {{abs{widevec{zx}}+{abs{widevec{zy}}}}over{{abs{widevec{zx}}}+{abs{widevec{zy}}}+{abs{widevec{xy}}}}} newline {}={vec{z}}+{{abs{widevec{zy}}}widevec{zx} + {abs{widevec{zx}}}widevec{zy}}over{{abs{widevec{zx}}}+{abs{widevec{zy}}}+{abs{widevec{xy}}}} newline {}={vec{z}}+{{abs{widevec{zy}}}(vec{x}-vec{z}) + {abs{widevec{zx}}}(vec{y}-vec{z})}over{{abs{widevec{zx}}}+{abs{widevec{zy}}}+{abs{widevec{xy}}}} newline {}={{abs{widevec{xy}}}{vec{z}}+{abs{widevec{zy}}}vec{x} + {abs{widevec{zx}}}vec{y}}over{{abs{widevec{zx}}}+{abs{widevec{zy}}}+{abs{widevec{xy}}}}

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【2013/01/29 20:22 】 | 論理 | 有り難いご意見(0)
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