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DihedralAngle[{p1,p2},{v,w}]

p1から p2までの線で有界で v と w の方向に伸びる2つの半平面の間の角を与える．

詳細
Details and Options Details and Options
例題  
例  
スコープ  
アプリケーション  
特性と関係  
考えられる問題  
関連項目
関連するガイド
履歴
引用書式

DihedralAngle

DihedralAngle[{p1,p2},{v,w}]

p1から p2までの線で有界で v と w の方向に伸びる2つの半平面の間の角を与える．

詳細

  • DihedralAngleは，面角あるいはねじれ角としても知られている．
  • DihedralAngle[{p1,p2},{v,w}]は，法線 p2-p1があり，半平面HalfPlane[{p1,p2},v]とHalfPlane[{p1,p2},w]で分割された，平面上の単位円Circle[p1]の円弧の長さである．

例題

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例  (1)

半平面間の角度：

Wolfram Language code: DihedralAngle[{{0, 0, 0}, {0, 1, 0}}, {{1, 0, 1}, {1, 0, 0}}]
Wolfram Language code: Graphics3D[{HalfPlane[{{0, 0, 0}, {0, 1, 0}}, {1, 0, 1}], HalfPlane[{{0, 0, 0}, {0, 1, 0}}, {1, 0, 0}]}]

スコープ  (2)

DihedralAngleを使って2つの半平面間の角度を求める：

Wolfram Language code: DihedralAngle[{{0, 0, 0}, {0, 1, 0}}, {{1, 0, 1}, {1, 0, 0}}]
Wolfram Language code: Graphics3D[{HalfPlane[{{0, 0, 0}, {0, 1, 0}}, {1, 0, 1}], HalfPlane[{{0, 0, 0}, {0, 1, 0}}, {1, 0, 0}]}]

DihedralAngleは数値引数に使うことができる：

Wolfram Language code: DihedralAngle[{{0, 1, 0}, {0, 0, 0}}, {{1, 0, 1}, {1, 0, 0}}]

記号引数：

Wolfram Language code: DihedralAngle[{{0, 1, 0}, {0, 0, 0}}, {{a, b, c}, {1, 0, 0}}]

アプリケーション  (1)

クロラールのねじれ角：

Wolfram Language code: coords = QuantityMagnitude[ChemicalData["Chloral", "AtomPositions"]];
Wolfram Language code: Show[{ChemicalData["Chloral", "MoleculePlot"], Graphics3D[Table[Style[Text[i, coords[[i]]], Bold], {i, Length[coords]}]]}]

原子鎖Cl-C-C-Oのねじれ角：

Wolfram Language code: DihedralAngle[coords[[{5, 6}]], {Subtract@@coords[[{3, 5}]], Subtract@@coords[[{4, 6}]]}]

特性と関係  (2)

二面角は法線 p2-p1と点 p1で定義される平面上の平面角である：

Wolfram Language code: p1 = {0, 0, 0};p2 = {0, 0, 1}; v = {1, 0, 0};w = {0, 1, 0};
Wolfram Language code: DihedralAngle[{p1, p2}, {v, w}]
Wolfram Language code: PlanarAngle[p1[[1 ;; 2]] -> {v, w}[[All, 1 ;; 2]]]

DihedralAngle[{p1,p2},{v,w}]はPolyhedronAngle[ℛ,{p1,p2}]に等しい．ただし，v および w は，多面体 ℛ の中の{p1,p2}の隣接面のベクルである：

Wolfram Language code: ℛ = Polyhedron[{{0, 0, 0}, {0, 1, 0}, {1, 1, 0}, {1, 0, 0}, {0, 0, 1}, {0, 1, 1}, {1, 1, 1}, {1, 0, 1}}, {{2, 3, 4, 1}, {1, 4, 8, 5}, {4, 3, 7, 8}, {3, 2, 6, 7}, {2, 1, 5, 6}, {5, 8, 7, 6}}];
Wolfram Language code: p1 = {0, 0, 0};p2 = {0, 1, 0};
Wolfram Language code: {v, w} = {{0, 0, 1}, {1, 0, 0}} - {p1, p1};
Wolfram Language code: {PolyhedronAngle[ℛ, {p1, p2}], DihedralAngle[{p1, p2}, {v, w}]}
Wolfram Language code: Graphics3D[{{Opacity[.5], Green, ℛ}, Thickness[.05], Red, Line[{{p1, p1 + v}, {p1, p1 + w}}], Blue, Line[{p1, p2}]}]

考えられる問題  (1)

DihedralAngleは，記号パラメータに対して一般的な値を与える：

Wolfram Language code: DihedralAngle[{{0, 1, 0}, {0, 0, a}}, {{1, 0, 1}, {1, 0, 0}}]
Wolfram Research (2019), DihedralAngle, Wolfram言語関数， https://reference.wolfram.com/language/ref/DihedralAngle.html.

テキスト

Wolfram Research (2019), DihedralAngle, Wolfram言語関数， https://reference.wolfram.com/language/ref/DihedralAngle.html.

CMS

Wolfram Language. 2019. "DihedralAngle." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DihedralAngle.html.

APA

Wolfram Language. (2019). DihedralAngle. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DihedralAngle.html

BibTeX

@misc{reference.wolfram_2026_dihedralangle, author="Wolfram Research", title="{DihedralAngle}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/DihedralAngle.html}", note=[Accessed: 18-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_dihedralangle, organization={Wolfram Research}, title={DihedralAngle}, year={2019}, url={https://reference.wolfram.com/language/ref/DihedralAngle.html}, note=[Accessed: 18-June-2026]}