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CollinearPoints[{p1,p2,p3,…,pn}]

检验点 p1,p2,p3,…,pn 是否共线.

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范例  
基本范例  
范围  
应用  
基本应用  
几何  
属性和关系  
参见
相关指南
历史
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CollinearPoints

CollinearPoints[{p1,p2,p3,…,pn}]

检验点 p1,p2,p3,…,pn 是否共线.

更多信息

  • CollinearPoints 也被称为直线式.
  • 通常用于检验一个组点是否落在同一条直线上.
  • 若点 p3,…,pn 都在 p1 和 p2 经过的直线上，则 CollinearPoints[{p1,p2,p3,…,pn}] 给出 True.
  • 对于共线点 p1、p2 和 p3，矩阵 {p2-p1,p3-p1} 的秩小于或等于 1.

范例

打开所有单元 关闭所有单元

基本范例  (2)

点 {0,0},{1,2},{2,4} 为共线：

Wolfram Language code: pts = {{0, 0}, {1, 2}, {2, 4}};
Wolfram Language code: CollinearPoints[pts]

绘制这些点：

Wolfram Language code: Graphics[{Line[pts], Red, Point[pts]}]

求经过点 {0,1} 和 {1,2} 的直线方程式：

Wolfram Language code: CollinearPoints[{{0, 1}, {1, 2}, {x, y}}]

范围  (4)

CollinearPoints 可作用于二维点：

Wolfram Language code: CollinearPoints[{{1, 1}, {3, 4}, {5, 6}}]

三维点：

Wolfram Language code: CollinearPoints[{{1, 2, 1}, {3, 4, 1}, {5, 6, 1}, {7, 8, 1}}]

维点：

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

CollinearPoints 可作用于数字坐标：

Wolfram Language code: CollinearPoints[{{1, 1}, {3, 4}, {5, 6}}]

符号坐标：

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

在一组坐标上的 CollinearPoints：

Wolfram Language code: CollinearPoints[{{1, 2, 1}, {3, 4, 1}, {5, 6, 1}, {7, 8, 1}}]

点列表：

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

多个点：

Wolfram Language code: CollinearPoints[Point[{{0, 0, 1}, {1, 0, 1}, {1, 3, 1}, {a, b, c}}]]

CollinearPoints 可作用于较大的集合：

Wolfram Language code: pts = RandomPoint[Line[{{0, 0}, {1, 0}}], 10 ^ 6];
Wolfram Language code: CollinearPoints[pts]//AbsoluteTiming

应用  (4)

基本应用  (3)

求出两个点都在一条经过原点的直线上的条件：

Wolfram Language code: CollinearPoints[{{0, 0}, {a, b}, {c, d}}]

显式实例：

Wolfram Language code: {{a, b}, {c, d}} /.  FindInstance[% && a ≠ 0, {a, b, c, d}, Reals, 3]

求经过点 {0,1} 和 {1,2} 的直线方程式：

Wolfram Language code: CollinearPoints[{{0, 1}, {1, 2}, {x, y}}]

绘制共线点：

Wolfram Language code: pts = {{0, 0}, {1, 1}, {2, 2}};
Wolfram Language code: CollinearPoints[pts]
Wolfram Language code: Graphics[{InfiniteLine[pts[[1 ;; 2]]], Red, Point[pts]}]

几何  (1)

非共线点组成一个多边形：

Wolfram Language code: pts = {{0, 0}, {1, 3}, {2, 2}};
Wolfram Language code: CollinearPoints[pts]
Wolfram Language code: Graphics[Polygon[pts]]

共线点：

Wolfram Language code: pts = {{0, 0}, {1, 1}, {2, 2}};
Wolfram Language code: CollinearPoints[pts]
Wolfram Language code: Graphics[{EdgeForm[StandardGray], Polygon[pts]}]

属性和关系  (5)

对于共线点而言，PositivelyOrientedPoints 返回 False：

Wolfram Language code: pts = {{0, 0}, {1, 2}, {2, 4}};
Wolfram Language code: {CollinearPoints[pts], PositivelyOrientedPoints[pts]}

对于共线点而言，NegativelyOrientedPoints 返回 False：

Wolfram Language code: pts = {{0, 0}, {1, 2}, {2, 4}};
Wolfram Language code: {CollinearPoints[pts], NegativelyOrientedPoints[pts]}

共线点也共面：

Wolfram Language code: pts = RandomPoint[Line[{{0, 0, 0}, {1, 1, 1}}], 5];
Wolfram Language code: {CollinearPoints[pts], CoplanarPoints[pts]}

使用 RegionMember 可测试点是否共线：

Wolfram Language code: RegionMember[Line[{{0, 0}, {1, 1}}], {2, 2}]
Wolfram Language code: CollinearPoints[{{0, 0}, {1, 1}, {2, 2}}]

使用 InfiniteLine 可绘制图形图像：

Wolfram Language code: pts = {{0, 0}, {1, 1}, {2, 2}};
Wolfram Language code: Graphics[{InfiniteLine[pts[[1 ;; 2]]], Red, Point[pts]}]
Wolfram Research (2020)，CollinearPoints，Wolfram 语言函数，https://reference.wolfram.com/language/ref/CollinearPoints.html.

文本

Wolfram Research (2020)，CollinearPoints，Wolfram 语言函数，https://reference.wolfram.com/language/ref/CollinearPoints.html.

CMS

Wolfram 语言. 2020. "CollinearPoints." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/CollinearPoints.html.

APA

Wolfram 语言. (2020). CollinearPoints. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/CollinearPoints.html 年

BibTeX

@misc{reference.wolfram_2026_collinearpoints, author="Wolfram Research", title="{CollinearPoints}", year="2020", howpublished="\url{https://reference.wolfram.com/language/ref/CollinearPoints.html}", note=[Accessed: 09-September-2026]}

BibLaTeX

@online{reference.wolfram_2026_collinearpoints, organization={Wolfram Research}, title={CollinearPoints}, year={2020}, url={https://reference.wolfram.com/language/ref/CollinearPoints.html}, note=[Accessed: 09-September-2026]}