WOLFRAM

Wolfram言語 ＆ システムドキュメントセンター

CanonicalizePolygon[poly]

共通座標および内側と外側の境界で表す多角形 poly の正準表現を与える．

CanonicalizePolygon[poly,"filter"]

指定されたフィルタをかけた poly の正準表現を与える．

詳細
Details and Options Details and Options
例題  
例  
スコープ  
基本的な用法  
指定  
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

CanonicalizePolygon

CanonicalizePolygon[poly]

共通座標および内側と外側の境界で表す多角形 poly の正準表現を与える．

CanonicalizePolygon[poly,"filter"]

指定されたフィルタをかけた poly の正準表現を与える．

詳細

  • CanonicalizePolygonは，さまざまな表現や説明から多角形の単純な標準表現を得るのに使われる．
  • CanonicalizePolygonは，多角形を最適化された標準形Polygon[{p1,p2,…},{outer1,outer2inner2,…}]に変換する．
  • 点 piは交差しない線分の端点で，Sort順にソートされる．
  • 外側境界 outerkは，端点で接触している可能性はあるがその他の交差はない線分{pi,pj}の閉曲線である．
  • 内側境界 innerkは，端点で接触している可能性はあるがその他の交差はない線分{pi,pj}の閉曲線である．
  • 一般的な多角形指定で，線および点を表す退化した多角形を与えることができる．"filter"指定を使うことで，これらの低次元成分を保持するかどうかが制御できる．
  • 次は，可能な"filter"指定である．
  • All線や点を含む全成分
    Full全次元成分のみ

例題

すべて開く すべて閉じる

例  (1)

Polygonの正準形を求める：

Wolfram Language code: 𝒫 = Polygon[{{1, 0}, {0, Sqrt[3]}, {-1, 0}}];
Wolfram Language code: CanonicalizePolygon[𝒫]
Wolfram Language code: Graphics[%]

スコープ  (9)

基本的な用法  (7)

CanonicalizePolygonは多角形に使うことができる：

Wolfram Language code: Polygon[{{0, 0}, {1., 0.}, {0.5, 1}}];
Wolfram Language code: CanonicalizePolygon[%]

三角形：

Wolfram Language code: CanonicalizePolygon[Triangle[]]

長方形：

Wolfram Language code: CanonicalizePolygon[Rectangle[]]

穴のある多角形：

Wolfram Language code: Polygon[{{0, 0}, {3, 0}, {3, 3}, {0, 3}, {1, 1}, {1, 2}, {2, 2}, {2, 1}}, {1, 2, 3, 4} -> {{5, 6, 7, 8}}];
Wolfram Language code: CanonicalizePolygon[%]

CanonicalizePolygonは地理実体の多角形に使うことができる：

Wolfram Language code: CanonicalizePolygon[Polygon[["france"]]]

GeoPositionを使った多角形：

Wolfram Language code: Polygon[GeoPosition[{{{40.083441, -88.235716}, {40.083607, -88.257488}, {40.082603, -88.257149}, {40.076136999999996, -88.25740499999999}, {40.076178, -88.270888}, {40.076516, -88.271558}, {40.083686, -88.271512}, {40.083659999999995, -88.267046}, ... 33323}, {40.098112, -88.228687}, {40.095216, -88.228627}, {40.095179, -88.238547}, {40.094480999999995, -88.238546}, {40.094508999999995, -88.23267}, {40.094106, -88.232556}, {40.090666999999996, -88.232477}, {40.090741, -88.235745}}}]];
Wolfram Language code: CanonicalizePolygon[%]

GeoPositionXYZを使った多角形：

Wolfram Language code: Polygon[GeoPositionXYZ[{{{150451.6968462432, -4.884430486484052*^6, 4.085078564164219*^6}, {148595.27532671497, -4.884475441490381*^6, 4.085092666620835*^6}, {148626.35829777512, -4.884546311005128*^6, 4.0850073717259285*^6}, {148618.5908634042 ... 7*^6, 4.0860187668081024*^6}, {150697.56410771207, -4.8836599487428395*^6, 4.085984535480795*^6}, {150711.88303095422, -4.883905546449982*^6, 4.0856924143435075*^6}, {150433.15479548014, -4.883908845676418*^6, 4.0856987003255524*^6}}}]];
Wolfram Language code: CanonicalizePolygon[%]

GeoPositionENUを使った多角形：

Wolfram Language code: Polygon[GeoPositionENU[{{{3378.2547059731055, -3369.2234780923936, -0.7440009205072329}, {1521.3211635380246, -3351.391253626573, -0.022340134218666208}, {1550.2571145363192, -3462.8657556618973, -0.08899812728964207}, {1528.5672303494055, -418 ... 63383291193, -0.37494203351275246}, {3654.121991908476, -2566.7472331234085, -0.5214977847472255}, {3375.420726854886, -2558.6597093173914, -0.3648706331350695}}}, GeoPosition[{40.11379115639895, -88.2753251202516, -1.0415787873318691}]]];
Wolfram Language code: CanonicalizePolygon[%]

GeoGridPositionを使った多角形：

Wolfram Language code: 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: CanonicalizePolygon[%]

自己交差のある多角形：

Wolfram Language code: Polygon[{{0.35, 0.2}, {0.9, 0.75}, {0.1, 0.55}, {0.9, 0.35}, {0.42, 0.9}}];
Wolfram Language code: CanonicalizePolygon[%]

不連続成分がある多角形：

Wolfram Language code: Polygon[{{0, 0}, {1, 0}, {0, 1}, {1, 1}, {2, 1}, {1, 2}}, {{1, 2, 3}, {4, 5, 6}}];
Wolfram Language code: CanonicalizePolygon[%]

内の多角形：

Wolfram Language code: Polygon[{{2, 3, 1, 0}, {6, 9, 1, 0}, {5, 4, 1, 0}, {8, 2, 1, 0}}, {1, 2, 3, 4}];
Wolfram Language code: CanonicalizePolygon[%]

指定  (2)

多角形の全成分を求める：

Wolfram Language code: 𝒫 = Polygon[{{{1, 0}, {0, Sqrt[3]}, {-1, 0}}, {{2, 2}, {3, 3}}}]
Wolfram Language code: CanonicalizePolygon[𝒫, All]

多角形の全次元成分を求める：

Wolfram Language code: 𝒫 = Polygon[{{{1, 0}, {0, Sqrt[3]}, {-1, 0}}, {{2, 2}, {3, 3}}}]
Wolfram Language code: CanonicalizePolygon[𝒫, Full]

アプリケーション  (2)

座標を共有する複合グラフィックスを設定する：

Wolfram Language code: 𝒞𝒫 = CanonicalizePolygon[Polygon[{{{0, 0, 0}, {2, 0, 0}, {1, 1, 2}}, {{2, 0, 0}, {2, 2, 0}, {1, 1, 2}}, {{2, 2, 0}, {0, 2, 0}, {1, 1, 2}}, {{0, 2, 0}, {0, 0, 0}, {1, 1, 2}}}]]
Wolfram Language code: Graphics3D[{GraphicsComplex[𝒞𝒫[[1]], Polygon[𝒞𝒫[[2]]]]}]

与えられた線分の自己交差点を求める：

Wolfram Language code: seg = {{-0.6, -0.8}, {0.9, 0.3}, {-0.9, 0.3}, {0.6, -0.8}, {0., 1.}, {-0.6, -0.8}};
Wolfram Language code: coords = CanonicalizePolygon[Polygon[seg]][[1]];
Wolfram Language code: intersection = Complement[coords, seg];
Wolfram Language code: Graphics[{Line[seg], PointSize[Medium], Red, Point[intersection], Blue, Point[seg]}]

特性と関係  (4)

CanonicalizePolygonを使ってPolygonCoordinatesを得る：

Wolfram Language code: 𝒫 = Polygon[{{1, 0}, {0, Sqrt[3]}, {-1, 0}}];
Wolfram Language code: First[CanonicalizePolygon[𝒫]]
Wolfram Language code: PolygonCoordinates[𝒫]

単純多角形の CanonicalizePolygonは多角形座標の数を保存している：

Wolfram Language code: 𝒫 = Polygon[{{1, 0, 0}, {0, 1, 0}, {0, 0, 1}}];
Wolfram Language code: SimplePolygonQ[𝒫]
Wolfram Language code: Length[First[#]]& /@ {𝒫, CanonicalizePolygon[𝒫]}

OuterPolygonは外側多角形の正準表現を与える：

Wolfram Language code: OuterPolygon[Polygon[{{0.35, 0.2}, {0.9, 0.75}, {0.1, 0.55}, {0.9, 0.35}, {0.42, 0.9}}]]

InnerPolygonは内側多角形の正準表現を与える：

Wolfram Language code: InnerPolygon[Polygon[{{0.35, 0.2}, {0.9, 0.75}, {0.1, 0.55}, {0.9, 0.35}, {0.42, 0.9}}]]

考えられる問題  (1)

CanonicalizePolygonは幾何領域にのみ使うことができる：

Wolfram Language code: 𝒫 = Polygon[{{0, 0, 0}, {1, 1, 0}, {0, 1, 0}, {0, 0, 1}}];
Wolfram Language code: {CanonicalizePolygon[𝒫], RegionQ[𝒫]}
Wolfram Research (2019), CanonicalizePolygon, Wolfram言語関数， https://reference.wolfram.com/language/ref/CanonicalizePolygon.html.

テキスト

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_canonicalizepolygon, author="Wolfram Research", title="{CanonicalizePolygon}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/CanonicalizePolygon.html}", note=[Accessed: 10-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_canonicalizepolygon, organization={Wolfram Research}, title={CanonicalizePolygon}, year={2019}, url={https://reference.wolfram.com/language/ref/CanonicalizePolygon.html}, note=[Accessed: 10-August-2026]}