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CrossingCount[contour,p]

给出从点 p 开始的射线穿过闭合曲线 contour 的次数.

更多信息和选项
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范例  
基本范例  
范围  
应用  
属性和关系  
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CrossingCount

CrossingCount[contour,p]

给出从点 p 开始的射线穿过闭合曲线 contour 的次数.

更多信息和选项

  • CrossingCount 亦称为交叉数.
  • CrossingCount 通常用于确定应一个点是否被包含在多边形中.
  • 如果闭合曲线 contour 是自相交的，CrossingCount[contour,p] 给出从点 p 开始的所有射线中穿过曲线最少的次数.
  • 闭合曲线 contour 通常是一组线段 Line[{{p1,p2},…,{pn-1,pn},{pn,p1}}]，且必须位于一个平面上.

范例

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基本范例  (1)

计算从某点开始的射线穿过闭合曲线轮廓的次数：

Wolfram Language code: ℛ = Line[{{1, 0}, {0, 3 / 2}, {-1, 0}, {1, 0}}];
Wolfram Language code: CrossingCount[ℛ, {0, 1}]
Wolfram Language code: Graphics[{ℛ, Red, Point[{0, 1 / 2}]}]

范围  (3)

计算从某点开始的射线穿过闭合曲线轮廓的次数：

Wolfram Language code: ℛ = Line[{{1, 0}, {0, 2}, {-1, 0}, {0, 1}, {1, 0}}];
Wolfram Language code: CrossingCount[ℛ, {0, 1 / 2}]
Wolfram Language code: Graphics[{ℛ, Red, Point[{0, 1 / 2}]}]

多边形边界：

Wolfram Language code: ℛ = Polygon[{{0.35, 0.2}, {0.9, 0.75}, {0.1, 0.55}, {0.9, 0.35}, {0.42, 0.9}}, {1, 2, 3, 4, 5}];
Wolfram Language code: CrossingCount[ℛ, {0.5, 0.7}]
Wolfram Language code: Graphics[{ℛ, Red, Point[{0.5, 0.7}]}]

具有 GeoGridPosition 的多边形：

Wolfram Language code: ℛ = Polygon[GeoGridPosition[{{{-0.9950503945490105, 1.2366760550756015}, {-0.9952074890903578, 1.2369207053693891}, {-0.9952196732768064, 1.2369073327446167}, {-0.9953160063787643, 1.236848436956935}, {-0.9954141759436825, 1.2369993898475449}, {-0. ... 197645333103}, {-0.9949098578570917, 1.2368130881428654}, {-0.9948663952535768, 1.2367477711687371}, {-0.9948714472169538, 1.2367426500757825}, {-0.9949211061652593, 1.2367089232486177}, {-0.9949439717990124, 1.236746107097628}}}, "Bonne"]];
Wolfram Language code: CrossingCount[ℛ, {-0.995, 1.237}]
Wolfram Language code: Region[ℛ, Epilog -> {Red, Point[{-0.995, 1.237}]}]

应用  (1)

根据给定多边形中点的交叉数的对点进行着色：

Wolfram Language code: ℛ = DynamicModule[«3»];
Wolfram Language code: points = RandomReal[{0, 1}, {8000, 2}];
Wolfram Language code: counts = CrossingCount[ℛ, points];
Wolfram Language code: Graphics[{AbsolutePointSize[1], Point[points, VertexColors -> {Green, Blue, Red}[[counts + 1]] ]}]

属性和关系  (1)

WindingCount 是另一个计数函数：

Wolfram Language code: contour = Line[{{0.35, 0.2}, {0.42, 0.9}, {0.9, 0.35}, {0.1, 0.55}, {0.9, 0.75}, {0.35, 0.2}}];
Wolfram Language code: {WindingCount[contour, {0.5, 0.5}], CrossingCount[contour, {0.5, 0.5}]}
Wolfram Research (2019)，CrossingCount，Wolfram 语言函数，https://reference.wolfram.com/language/ref/CrossingCount.html.

文本

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_crossingcount, author="Wolfram Research", title="{CrossingCount}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/CrossingCount.html}", note=[Accessed: 15-September-2026]}

BibLaTeX

@online{reference.wolfram_2026_crossingcount, organization={Wolfram Research}, title={CrossingCount}, year={2019}, url={https://reference.wolfram.com/language/ref/CrossingCount.html}, note=[Accessed: 15-September-2026]}