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CollinearPoints[{p1,p2,p3,…,pn}]

点 p1,p2,p3,…,pnが共線かどうかを調べる．

詳細
Details and Options Details and Options
例題  
例  
スコープ  
アプリケーション  
基本的なアプリケーション  
幾何  
特性と関係  
関連項目
関連するガイド
履歴
引用書式

CollinearPoints

CollinearPoints[{p1,p2,p3,…,pn}]

点 p1,p2,p3,…,pnが共線かどうかを調べる．

詳細

  • CollinearPointsは直進性としても知られている．
  • 点の集合が1本の直線上にあるかどうかを調べるためによく使われる．
  • CollinearPoints[{p1,p2,p3,…,pn}]は，点 p3,…,pnが p1と p2を通る直線上にある場合にTrueを与える．
  • 点 p1，p2，p3が共線であるとき，行列{p2-p1,p3-p1}の階数は1以下である．

例題

すべて開く すべて閉じる

例  (2)

点{0,0},{1,2},{2,4}は同一線上にある：

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

点をプロットする：

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

点{0,1}と点{1,2}を通る直線の方程式を求める：

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

スコープ  (4)

CollinearPointsは二次元の点に使うことができる：

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

三次元の点：

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

次元の点：

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は数値座標に使うことができる：

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

記号座標：

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

座標集合上のCollinearPoints：

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

点のリスト：

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

複数の点：

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

CollinearPointsは大きい集合に使うことができる：

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

アプリケーション  (4)

基本的なアプリケーション  (3)

2点が原点を通る直線上にあるための条件を求める：

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

明示的な場合：

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

点{0,1}と点{1,2}を通る直線の方程式を求める：

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

共線点を描く：

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]}]

幾何  (1)

多角形からの共線ではない点：

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

共線点：

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

特性と関係  (5)

PositivelyOrientedPointsは，共線点にはFalseを返す：

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

NegativelyOrientedPointsは，共線点にはFalseを返す：

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

共線点は共面である：

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

RegionMemberを使って点が共線かどうかを調べる：

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

InfiniteLineを使ってグラフィック画像を描画する：

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言語関数， https://reference.wolfram.com/language/ref/CollinearPoints.html.

テキスト

Wolfram Research (2020), CollinearPoints, Wolfram言語関数， https://reference.wolfram.com/language/ref/CollinearPoints.html.

CMS

Wolfram Language. 2020. "CollinearPoints." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CollinearPoints.html.

APA

Wolfram Language. (2020). CollinearPoints. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CollinearPoints.html

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: 05-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: 05-September-2026]}