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FindShortestCurve[reg,s,t]

領域 reg 上の2点 s と t 間の最短曲線を求める．

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例題  
例  
スコープ  
特殊領域  
数式定義領域  
メッシュ領域  
派生領域  
地理領域  
アプリケーション  
特性と関係  
考えられる問題  
関連項目
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FindShortestCurve

FindShortestCurve[reg,s,t]

領域 reg 上の2点 s と t 間の最短曲線を求める．

詳細とオプション

例題

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例  (3)

円上の2点間の最短曲線を求める：

Wolfram Language code: FindShortestCurve[Circle[], {1, 0}, {0, 1}]
Wolfram Language code: HighlightRegion[Circle[], %]

メッシュ領域上の2点間の最短経路を求める：

Wolfram Language code: path = FindShortestCurve[Sphere[], {0, 0, 1}, {0, 1, 0}];
Wolfram Language code: HighlightRegion[Sphere[], path]

最短経路の距離を計算する：

Wolfram Language code: ArcLength[path]

メッシュ上の2点間の最短曲線を求める：

Wolfram Language code: FindShortestCurve[[image], {0.11, 0.11}, {0.89, 0.555}]

メッシュ上の曲線をハイライトする：

Wolfram Language code: HighlightRegion[[image], %]

スコープ  (14)

特殊領域  (5)

線：

Wolfram Language code: FindShortestCurve[[image], {1, 0}, {3, 0}]
Wolfram Language code: HighlightRegion[[image], %]

円：

Wolfram Language code: FindShortestCurve[Circle[], {1, 0}, {0, 1}]
Wolfram Language code: HighlightRegion[Circle[], %]

球：

Wolfram Language code: FindShortestCurve[Sphere[], {0, 0, 1}, {0, 1, 0}];
Wolfram Language code: HighlightRegion[Sphere[], %]

トーラス：

Wolfram Language code: {s, t} = RandomPoint[Torus[], 2];
Wolfram Language code: FindShortestCurve[Torus[], s, t];
Wolfram Language code: HighlightRegion[Torus[], %]

アニュラス：

Wolfram Language code: FindShortestCurve[Annulus[], {1, 0}, {-0.8, 0.4}];
Wolfram Language code: HighlightRegion[Annulus[], %]

数式定義領域  (2)

ImplicitRegion：

Wolfram Language code: g = ImplicitRegion[x^2 + y^2 ≤ 1, {x, y}];
Wolfram Language code: FindShortestCurve[g, {1, 0}, {1 / 10, 4 / 5}];
Wolfram Language code: HighlightRegion[g, %]

ParametricRegion：

Wolfram Language code: g = ParametricRegion[{{s, (1 + t) s ^ 2 - t}, -1 <= s <= 1 && 0 <= t <= 1}, {s, t}];
Wolfram Language code: FindShortestCurve[g, {-2 / 5, 1 / 10}, {2 / 5, 1 / 20}];
Wolfram Language code: HighlightRegion[g, %]

メッシュ領域  (2)

1D BoundaryMeshRegion上の最短距離を求める：

Wolfram Language code: ℛ = BoundaryMeshRegion[{{0}, {1}}, Point[{{1}, {2}}]]
Wolfram Language code: FindShortestCurve[ℛ, {0}, {1}]

2D：

Wolfram Language code: ℛ = BoundaryMeshRegion[{{0, 0}, {3, 0}, {3, 3}, {0, 3}, {1, 1}, {2, 1}, {2, 2}, {1, 2}}, Line[{1, 2, 3, 4, 1}], Line[{5, 6, 7, 8, 5}]];
Wolfram Language code: FindShortestCurve[ℛ, {3, 3}, {1.5, 1}]
Wolfram Language code: HighlightRegion[ℛ, %]

3D：

Wolfram Language code: ℛ = ConvexHullMesh[RandomReal[1, {20, 3}]];
Wolfram Language code: {s, t} = RandomPoint[ℛ, 2];
Wolfram Language code: FindShortestCurve[ℛ, s, t]

1D MeshRegion上の最短距離を求める：

Wolfram Language code: ℛ = MeshRegion[{{0}, {1}, {2}, {3}}, {Line[{1, 2}], Line[{3, 4}]}]
Wolfram Language code: FindShortestCurve[ℛ, {0}, {1}]

2D：

Wolfram Language code: FindShortestCurve[MengerMesh[2], {0.11, 0.11}, {0.89, 0.55}];
Wolfram Language code: HighlightRegion[MengerMesh[2], %]

3D：

Wolfram Language code: ℛ = [image];
Wolfram Language code: FindShortestCurve[ℛ, {-0.79, -0.9, 0.}, {0.33, 0.94, 0.5}];
Wolfram Language code: HighlightRegion[ℛ, %]

派生領域  (3)

RegionIntersection上の最短曲線を求める：

Wolfram Language code: ℛ = RegionIntersection[Disk[{0, 0}, 1], Disk[{0, 1}, 1]];
Wolfram Language code: FindShortestCurve[ℛ, {0.2, 0.4}, {-0.3, 0.5}];
Wolfram Language code: HighlightRegion[ℛ, %]

TransformedRegion上の最短曲線を求める：

Wolfram Language code: ℛ = TransformedRegion[Disk[{1, 1}, 4], {Indexed[#, 1] Indexed[#, 2], Indexed[#, 1] + Indexed[#, 2]}&];
Wolfram Language code: FindShortestCurve[ℛ, {2.8, 4.9}, {-3.3, -0.2}];
Wolfram Language code: HighlightRegion[ℛ, %]

RegionBoundary上の最短曲線を求める：

Wolfram Language code: ℛ = RegionBoundary[MengerMesh[1, 3]];
Wolfram Language code: FindShortestCurve[ℛ, {0, 0, 0}, {1, 1, 1}];
Wolfram Language code: HighlightRegion[ℛ, %]

地理領域  (2)

GeoPositionによる多角形：

Wolfram Language code: ℛ = 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: {s, t} = RandomPoint[DiscretizeRegion@ℛ, 2];
Wolfram Language code: FindShortestCurve[ℛ, s, t]

GeoGridPositionによる多角形：

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: {s, t} = First[ RandomPoint[ℛ, 2]];
Wolfram Language code: FindShortestCurve[ℛ, s, t];
Wolfram Language code: HighlightRegion[ℛ, %]

アプリケーション  (6)

球面上の2点間の最短曲線：

Wolfram Language code: HighlightRegion[Sphere[], FindShortestCurve[Sphere[], {0, 0, 1}, {0, 1, 0}]]

この経路は大円上にある：

Wolfram Language code: RegionIntersection[Sphere[], InfinitePlane[{{0, 0, 1}, {0, 1, 0}, {0, 0, 0}}]]
Wolfram Language code: Show[{%%, %}]

オーストリアのインスブルックからウィーンまでの最短ツアーを求める：

Wolfram Language code: g = DiscretizeGraphics[CountryData["Austria", {"FullPolygon", "Mercator"}]];
Wolfram Language code: cities = {Entity["City", {"Innsbruck", "Tirol", "Austria"}], Entity["City", {"Vienna", "Vienna", "Austria"}]};

都市のGeoGridPosition：

Wolfram Language code: {Innsbruck, Vienna} = First[GeoGridPosition[GeoPosition[#], "Mercator"]]& /@ cities
Wolfram Language code: path = FindShortestCurve[g, Innsbruck, Vienna];

経路を表示する：

Wolfram Language code: HighlightRegion[g, path]

GeoPathと比較する：

Wolfram Language code: GeoGraphics[{Polygon[Entity["Country", "Austria"]], Red, GeoPath[cities, "Geodesic"]}]

地球上の航空機の飛行経路としての2都市間の最短距離を求める：

Wolfram Language code: a = 6378; b = 6357; earth = RegionBoundary@Ellipsoid[{0, 0, 0}, {a, a, b}];

直交地心座標系でシアトルとパリを表す：

Wolfram Language code: cities = {Entity["City", {"Seattle", "Washington", "UnitedStates"}], Entity["City", {"Paris", "IleDeFrance", "France"}]};
Wolfram Language code: pos = First@GeoPositionXYZ[cities]

シアトルとパリの位置を楕円体に写像する：

Wolfram Language code: {seattle, paris} = RegionNearest[earth, #]& /@ pos

経路を示す：

Wolfram Language code: path = FindShortestCurve[earth, seattle, paris];
Wolfram Language code: Graphics3D[{Texture[GeoGraphics[GeoBackground -> "Satellite", ImageSize -> Large, GeoProjection -> "Equirectangular"], "Spherical"], Black, Ellipsoid[{0, 0, 0}, {a, a, b}], Red, Dashed, Thickness[0.005], path}, Boxed -> False, ViewPoint -> Front]

輪ゴム上の2点間の経路を求める：

Wolfram Language code: g = DiscretizeGraphics[ParametricPlot3D[{Sin[t - (π/2)], 1.5Cos[(t/2) + (π/4)], Sin[t - π]}, {t, 0, 4 π}, PlotStyle -> Orange, Axes -> -None, Boxed -> False] /. Line[pts_, rest___] :> Tube[pts, 0.1, rest]];
Wolfram Language code: {s, t} = RandomPoint[g, 2];
Wolfram Language code: FindShortestCurve[g, s, t];

経路を表示する：

Wolfram Language code: HighlightRegion[g, %]

人体上の2点間の経路を求める：

Wolfram Language code: body = \!\(\*Graphics3DBox[«8»]\);
Wolfram Language code: {s, t} = RandomPoint[body, 2];
Wolfram Language code: FindShortestCurve[body, s, t];

経路を表示する：

Wolfram Language code: HighlightRegion[body, %]

移動ロボットが，障害物を回避しながらある地点から別の地点に移動するための効率的な経路を決定する：

Wolfram Language code: {robot, furniture} = { [image], \!\(\*Graphics3DBox[«6»]\)};

この例では，ロボットの作業スペースに障害物，具体的には家具が含まれる：

Wolfram Language code: Show[robot, furniture, Boxed -> True]

ワークスペースを2D環境として単純化する：

Wolfram Language code: workspace = [image];
Wolfram Language code: {a, b} = {Most[RegionCentroid[robot]], {20, 18}};
Wolfram Language code: path = FindShortestCurve[workspace, a, b];

経路を示す：

Wolfram Language code: HighlightRegion[workspace, path]

特性と関係  (1)

ShortestCurveDistanceはFindShortestCurveの弧の長さである：

Wolfram Language code: c = Circle[];
Wolfram Language code: {s, t} = {{-1, 0}, {0, 1}};
Wolfram Language code: ArcLength[FindShortestCurve[c, s, t]] == ShortestCurveDistance[c, s, t]

考えられる問題  (1)

近似法では，小規模では目に見える数値誤差が生じる可能性がある：

Wolfram Language code: reg = Region[FindShortestCurve[Sphere[], {0., 0., 1.}, {0., 1., 0.}], ...]

曲線を領域上に示す：

Wolfram Language code: HighlightRegion[Sphere[], reg]
Wolfram Research (2025), FindShortestCurve, Wolfram言語関数， https://reference.wolfram.com/language/ref/FindShortestCurve.html.

テキスト

Wolfram Research (2025), FindShortestCurve, Wolfram言語関数， https://reference.wolfram.com/language/ref/FindShortestCurve.html.

CMS

Wolfram Language. 2025. "FindShortestCurve." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FindShortestCurve.html.

APA

Wolfram Language. (2025). FindShortestCurve. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindShortestCurve.html

BibTeX

@misc{reference.wolfram_2026_findshortestcurve, author="Wolfram Research", title="{FindShortestCurve}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/FindShortestCurve.html}", note=[Accessed: 10-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_findshortestcurve, organization={Wolfram Research}, title={FindShortestCurve}, year={2025}, url={https://reference.wolfram.com/language/ref/FindShortestCurve.html}, note=[Accessed: 10-August-2026]}