WOLFRAM

Wolfram 语言与系统参考资料中心

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

给出由通过 p1 和下标 p2 的线界定的两个半平面之间的角度，并在方向 v 和 w 上延伸.

更多信息
Details and Options Details and Options
范例  
基本范例  
范围  
应用  
属性和关系  
可能存在的问题  
参见
相关指南
历史
按以下格式引用：

DihedralAngle

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

给出由通过 p1 和下标 p2 的线界定的两个半平面之间的角度，并在方向 v 和 w 上延伸.

更多信息

范例

打开所有单元 关闭所有单元

基本范例  (1)

半平面之间的角：

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}]}]

范围  (2)

用 DihedralAngle 求两个半平面之间的角：

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 适用于数值参数：

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

符号参数：

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

应用  (1)

氯醛中的扭转角：

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]}]]}]

原子链 Cl-C-C-O 中的扭转角：

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

属性和关系  (2)

二面角是由法线 p2-p1 和点 p1 定义的平面中的平面角：

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}] 等价于 PolyhedronAngle[ℛ,{p1,p2}]，其中 v 和 w 是多面体 ℛ 上 {p1,p2} 的相邻面上的向量：

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}]}]

可能存在的问题  (1)

对于符号参数，DihedralAngle 给出通用值：

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

文本

Wolfram Research (2019)，DihedralAngle，Wolfram 语言函数，https://reference.wolfram.com/language/ref/DihedralAngle.html.

CMS

Wolfram 语言. 2019. "DihedralAngle." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/DihedralAngle.html.

APA

Wolfram 语言. (2019). DihedralAngle. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/DihedralAngle.html 年

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: 05-September-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: 05-September-2026]}