{"id":104408,"date":"2026-09-12T13:33:06","date_gmt":"2026-09-12T05:33:06","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/104408.html"},"modified":"2026-09-12T13:33:06","modified_gmt":"2026-09-12T05:33:06","slug":"%e3%80%90%e8%ae%a1%e7%ae%97%e5%87%a0%e4%bd%95%e3%80%91%e9%97%b5%e5%8f%af%e5%a4%ab%e6%96%af%e5%9f%ba%e5%b7%ae%e6%bc%94%e7%a4%ba","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/104408.html","title":{"rendered":"\u3010\u8ba1\u7b97\u51e0\u4f55\u3011\u95f5\u53ef\u592b\u65af\u57fa\u5dee\u6f14\u793a"},"content":{"rendered":"

\u672c\u6587\u6d89\u53ca\u77e5\u8bc6\u70b9<\/h2>\n

\u6570\u5b66 \u51e0\u4f55<\/p>\n

\u6f14\u793a\u5de5\u5177<\/h2>\n

\u6f14\u793a\u5de5\u5177\u57fa\u4e8eCad，\u652f\u6301Cad2013\u53ca\u66f4\u9ad8\u7248\u672c\u3002 \u4eb2\u58eb\u5e93\u7248\u672c：2026.9.4 Cliper\u5e93\u7248\u672c：2.0.0.0 \u70b9\u51fb\u4e0b\u8f7d\u4eb2\u58eb\u6570\u5b66\u6f14\u793a\u5de5\u5177\u7bb1<\/p>\n

\u76f8\u5173\u5b9a\u4e49<\/h2>\n

\u95f5\u53ef\u592b\u65af\u57fa\u548c：\u6570\u5b66\u5b9a\u4e49：<\/p>\n

A<\/p>\n

\u2295<\/p>\n

B<\/p>\n

=<\/p>\n

{<\/p>\n

a<\/p>\n

+<\/p>\n

b<\/p>\n

\u2223<\/p>\n

a<\/p>\n

\u2208<\/p>\n

A<\/p>\n

,<\/p>\n

b<\/p>\n

\u2208<\/p>\n

B<\/p>\n

}<\/p>\n

A \\\\oplus B =\\\\{a+b \\\\mid a \\\\in A,b \\\\in B \\\\}<\/p>\n

<\/span><\/span>A<\/span><\/span>\u2295<\/span><\/span><\/span><\/span>B<\/span><\/span>=<\/span><\/span><\/span><\/span>{<\/span>a<\/span><\/span>+<\/span><\/span><\/span><\/span>b<\/span><\/span>\u2223<\/span><\/span><\/span><\/span>a<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>A<\/span>,<\/span><\/span>b<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>B<\/span>}<\/span><\/span><\/span><\/span><\/span> \u76f4\u89c2\u7406\u89e3：\u5c06B\u7684\u526f\u672c\u653e\u7f6e\u5230A\u7684\u6bcf\u4e2a\u70b9\u4e0a，\u53d6\u5e76\u96c6\u3002 \u5f62\u6001\u5b66（\u81a8\u80c0\u8150\u8680\u3001\u5f00\u95ed\u64cd\u4f5c)\u548c\u96c6\u5408\u8bba\u7684\u95f5\u53ef\u592b\u65af\u57fa\u5dee\u548c\u8ba1\u7b97\u51e0\u4f55（\u673a\u5668\u4eba\u5b66)\u7684\u95f5\u53ef\u592b\u65af\u57fa\u5dee\u4e0d\u540c\u3002 \u8ba1\u7b97\u51e0\u4f55\u7684\u95f5\u53ef\u592b\u65af\u57fa\u5dee：<\/p>\n

A<\/p>\n

\u2296<\/p>\n

B<\/p>\n

=<\/p>\n

{<\/p>\n

a<\/p>\n

\u2212<\/p>\n

b<\/p>\n

\u2223<\/p>\n

a<\/p>\n

\u2208<\/p>\n

A<\/p>\n

,<\/p>\n

b<\/p>\n

\u2208<\/p>\n

B<\/p>\n

}<\/p>\n

A \\\\ominus B=\\\\{a – b \\\\mid a\\\\in A,b\\\\in B\\\\}<\/p>\n

<\/span><\/span>A<\/span><\/span>\u2296<\/span><\/span><\/span><\/span>B<\/span><\/span>=<\/span><\/span><\/span><\/span>{<\/span>a<\/span><\/span>\u2212<\/span><\/span><\/span><\/span>b<\/span><\/span>\u2223<\/span><\/span><\/span><\/span>a<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>A<\/span>,<\/span><\/span>b<\/span><\/span>\u2208<\/span><\/span><\/span><\/span>B<\/span>}<\/span><\/span><\/span><\/span><\/span>\u3002<\/p>\n

\u4e3b\u8981\u7528\u9014<\/h2>\n

\u4e34\u754c\u591a\u8fb9\u5f62(NFP)\u2013\u6392\u6837\u7b97\u6cd5\u7684\u6838\u5fc3<\/h3>\n

<\/p>\n

N<\/p>\n

F<\/p>\n

P<\/p>\n

(<\/p>\n

P<\/p>\n

,<\/p>\n

Q<\/p>\n

)<\/p>\n

=<\/p>\n

P<\/p>\n

\u2295<\/p>\n

(<\/p>\n

\u2212<\/p>\n

Q<\/p>\n

)<\/p>\n

NFP(P,Q)=P\\\\oplus (-Q)<\/p>\n

<\/span><\/span>N<\/span>F<\/span>P<\/span>(<\/span>P<\/span>,<\/span><\/span>Q<\/span>)<\/span><\/span>=<\/span><\/span><\/span><\/span>P<\/span><\/span>\u2295<\/span><\/span><\/span><\/span>(<\/span>\u2212<\/span>Q<\/span>)<\/span><\/span><\/span><\/span><\/span>\u3002\u5b83\u8868\u793a\u96f6\u4ef6P\u7ed5\u7740Q\u6ed1\u52a8\u65f6，\u53c2\u8003\u70b9\u7684\u8f68\u8ff9\u3002<\/p>\n

\u78b0\u649e\u68c0\u6d4b（\u914d\u7f6e\u7a7a\u95f4\u969c\u788d)<\/h3>\n

<\/p>\n

A<\/p>\n

\u2295<\/p>\n

(<\/p>\n

\u2212<\/p>\n

B<\/p>\n

)<\/p>\n

A \\\\oplus (-B)<\/p>\n

<\/span><\/span>A<\/span><\/span>\u2295<\/span><\/span><\/span><\/span>(<\/span>\u2212<\/span>B<\/span>)<\/span><\/span><\/span><\/span><\/span>\u5b9a\u4e49\u4e86\u914d\u7f6e\u7a7a\u95f4\u7684\u969c\u788d\u7269\u533a\u57df\u3002<\/p>\n

\u591a\u8fb9\u5f62\u504f\u79fb<\/h3>\n

\u5bf9\u591a\u8fb9\u5f62\u81a8\u80c0(\u5411\u5916\u504f\u79fb)\u672c\u8d28\u6c42<\/p>\n

P<\/p>\n

\u2296<\/p>\n

\u5706\u76d8\u3002<\/p>\n

P \\\\ominus \u5706\u76d8\u3002<\/p>\n

<\/span><\/span>P<\/span><\/span>\u2296<\/span><\/span><\/span><\/span>\u5706\u76d8\u3002<\/span><\/span><\/span><\/span><\/span><\/p>\n

\u64cd\u4f5c\u8bf4\u660e<\/h2>\n

\u4e00，\u9009\u62e9\u95f5\u53ef\u592b\u65af\u57fa\u5dee\u7684\u88ab\u51cf\u6570(\u6a21\u677f\u56fe\u50cf)\u3002 \u4e8c，\u9009\u62e9\u95f5\u53ef\u592b\u65af\u57fa\u7684\u51cf\u6570\u3002 \u6ce8\u610f：\u53ea\u80fd\u9009\u62e9\u591a\u4e49\u7ebf，\u65e0\u8bba\u591a\u4e49\u7ebf\u662f\u5426\u95ed\u5408\u90fd\u5f53\u95ed\u5408\u5904\u7406\u3002 \u4e09，\u8ba1\u7b97\u51fa\u95f5\u53ef\u592b\u65af\u57fa\u5dee\u3002 \u56db，\u5c06\u95f5\u53ef\u592b\u65af\u57fa\u5dee\u7684\u7ed3\u679c\u8f6c\u6210\u95ed\u5408\u591a\u4e49\u7ebf，\u9006\u65f6\u9488\u7ea2\u8272，\u987a\u65f6\u9488\u9ec4\u8272\u3002<\/p>\n

\u4ee3\u7801<\/h2>\n

using<\/span> System<\/span>;<\/span>
\nusing<\/span> System.<\/span>Collections.<\/span>Generic<\/span>;<\/span>
\nusing<\/span> Autodesk.<\/span>AutoCAD.<\/span>ApplicationServices<\/span>;<\/span>
\nusing<\/span> Autodesk.<\/span>AutoCAD.<\/span>DatabaseServices<\/span>;<\/span>
\nusing<\/span> Autodesk.<\/span>AutoCAD.<\/span>EditorInput<\/span>;<\/span>
\nusing<\/span> Autodesk.<\/span>AutoCAD.<\/span>Geometry<\/span>;<\/span>
\nusing<\/span> Autodesk.<\/span>AutoCAD.<\/span>Runtime<\/span>;<\/span>
\nusing<\/span> Clipper2Lib<\/span>;<\/span>
\nusing<\/span> QinShiZACad<\/span>;<\/span>
\nusing<\/span> QinShiMath<\/span>;<\/span>
\nusing<\/span> QinShiBase<\/span>;<\/span><\/p>\n

[<\/span>CommandMethod<\/span>(<\/span>"MinkowskiDiff"<\/span>)<\/span><\/span><\/span>]<\/span>
\n public<\/span> void<\/span><\/span> MinkowskiDiff<\/span>(<\/span>)<\/span>
\n {<\/span>
\n Minkowski<\/span>(<\/span>"\u95f5\u53ef\u592b\u65af\u57fa\u5dee"<\/span>,<\/span> (<\/span>p1,<\/span> p2)<\/span> =><\/span> Clipper.<\/span>MinkowskiDiff<\/span>(<\/span>p1,<\/span> p2,<\/span>true<\/span>)<\/span>)<\/span>;<\/span>
\n }<\/span>
\n [<\/span>CommandMethod<\/span>(<\/span>"MinkowskiSum"<\/span>)<\/span><\/span><\/span>]<\/span>
\n public<\/span> void<\/span><\/span> MinkowskiSum<\/span>(<\/span>)<\/span>
\n {<\/span>
\n Minkowski<\/span>(<\/span>"\u95f5\u53ef\u592b\u65af\u57fa\u548c"<\/span>,<\/span> (<\/span>p1,<\/span> p2)<\/span> =><\/span> Clipper.<\/span>MinkowskiSum<\/span>(<\/span>p1,<\/span> p2,<\/span> true<\/span>)<\/span>)<\/span>;<\/span>
\n }<\/span>
\n void<\/span><\/span> Minkowski<\/span>(<\/span>string<\/span><\/span> strName,<\/span> MinkowskiFun<\/span> fun)<\/span>
\n {<\/span>
\n QinShiZACad.<\/span>CSelAEntity<\/span> sel1 =<\/span> new<\/span> CSelAEntity<\/span>(<\/span>$"\u8bf7\u9009\u62e9\u4e00\u4e2a\u591a\u4e49\u7ebf\u505a\u4e3a<\/span>{<\/span>strName<\/span>}<\/span><\/span>\u7684\u88ab\u51cf\u6570(\u6a21\u677f\u56fe\u50cf)\\\\n"<\/span><\/span>)<\/span>;<\/span>
\n var<\/span><\/span> pr1 =<\/span> sel1.<\/span>Sel<\/span>(<\/span>)<\/span>;<\/span>
\n if<\/span> (<\/span>pr1.<\/span>Status !=<\/span> PromptStatus.<\/span>OK)<\/span>
\n {<\/span>
\n return<\/span>;<\/span>
\n }<\/span>
\n QinShiZACad.<\/span>CSelAEntity<\/span> sel2 =<\/span> new<\/span> CSelAEntity<\/span>(<\/span>$"\u8bf7\u9009\u62e9\u4e00\u4e2a\u591a\u4e49\u7ebf\u505a\u4e3a<\/span>{<\/span>strName<\/span>}<\/span><\/span>\u7684\u51cf\u6570\\\\n"<\/span><\/span>)<\/span>;<\/span>
\n var<\/span><\/span> pr2 =<\/span> sel2.<\/span>Sel<\/span>(<\/span>)<\/span>;<\/span>
\n if<\/span> (<\/span>pr2.<\/span>Status !=<\/span> PromptStatus.<\/span>OK)<\/span>
\n {<\/span>
\n return<\/span>;<\/span>
\n }<\/span><\/p>\n

Polyline<\/span> pl1,<\/span> pl2;<\/span>
\n using<\/span> (<\/span>var<\/span><\/span> tr =<\/span> CadBase.<\/span>GetDefaultDatabase<\/span>(<\/span>)<\/span>.<\/span>TransactionManager.<\/span>StartTransaction<\/span>(<\/span>)<\/span>)<\/span>
\n {<\/span>
\n pl1 =<\/span> tr.<\/span>GetObject<\/span>(<\/span>pr1.<\/span>ObjectId,<\/span> OpenMode.<\/span>ForRead)<\/span> as<\/span> Polyline<\/span>;<\/span>
\n pl2 =<\/span> tr.<\/span>GetObject<\/span>(<\/span>pr2.<\/span>ObjectId,<\/span> OpenMode.<\/span>ForRead)<\/span> as<\/span> Polyline<\/span>;<\/span>
\n }<\/span>
\n if<\/span> (<\/span>null<\/span> ==<\/span> pl1)<\/span> {<\/span> return<\/span>;<\/span> }<\/span>
\n if<\/span> (<\/span>null<\/span> ==<\/span> pl2)<\/span> {<\/span> return<\/span>;<\/span> }<\/span>
\n PathD<\/span> path1 =<\/span> PolylineToPath<\/span>(<\/span>pl1)<\/span>;<\/span>
\n PathD<\/span> path2 =<\/span> PolylineToPath<\/span>(<\/span>pl2)<\/span>;<\/span>
\n PathsD<\/span> path3 =<\/span> fun<\/span>(<\/span>path1,<\/span> path2)<\/span>;<\/span><\/p>\n

PathD<\/span> PolylineToPath<\/span>(<\/span>Polyline<\/span> pl)<\/span>
\n {<\/span>
\n PathD<\/span> path =<\/span> new<\/span> PathD<\/span>(<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span><\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> pl.<\/span>NumberOfVertices;<\/span> i++<\/span>)<\/span>
\n {<\/span>
\n var<\/span><\/span> pt =<\/span> pl.<\/span>GetPoint2dAt<\/span>(<\/span>i)<\/span>;<\/span>
\n path.<\/span>Add<\/span>(<\/span>new<\/span> PointD<\/span>(<\/span>pt.<\/span>X,<\/span> pt.<\/span>Y)<\/span>)<\/span>;<\/span>
\n }<\/span>
\n return<\/span> path;<\/span>
\n }<\/span>
\n var<\/span><\/span> pls =<\/span> path3.<\/span>ToPolylines<\/span>(<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span><\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> Math.<\/span>Min<\/span>(<\/span>7<\/span>,<\/span> pls.<\/span>Count)<\/span>;<\/span> i++<\/span>)<\/span>
\n {<\/span>
\n double<\/span><\/span> area =<\/span> Clipper.<\/span>Area<\/span>(<\/span>path3[<\/span>i]<\/span>)<\/span>;<\/span>
\n int<\/span><\/span> iColor =<\/span> 0<\/span>;<\/span>
\n if<\/span> (<\/span>Math.<\/span>Abs<\/span>(<\/span>area)<\/span> <<\/span> 1e-9<\/span>)<\/span>
\n {<\/span>\/\/\u9000\u5316\u60c5\u51b5<\/span>
\n iColor =<\/span> 0<\/span>;<\/span>
\n }<\/span>
\n else<\/span> if<\/span> (<\/span>area ><\/span> 0<\/span>)<\/span>
\n {<\/span>
\n iColor =<\/span> 1<\/span>;<\/span>
\n }<\/span>
\n else<\/span>
\n {<\/span>
\n iColor =<\/span> 2<\/span>;<\/span>
\n }<\/span>
\n pls[<\/span>i]<\/span>.<\/span>ColorIndex =<\/span> iColor;<\/span>\/\/\u5916\u8fb9\u754c\u7ea2\u8272，\u5b54\u6d1e\u9ec4\u8272<\/span>
\n }<\/span>
\n CadBase.<\/span>AddEnitys<\/span>(<\/span>pls.<\/span>ToArray<\/span>(<\/span>)<\/span>,<\/span> "0"<\/span>,<\/span> CadBase.<\/span>GetDefaultDatabase<\/span>(<\/span>)<\/span>)<\/span>;<\/span>
\n }<\/span>
\n delegate<\/span> PathsD<\/span> MinkowskiFun<\/span>(<\/span>PathD<\/span> path1,<\/span> PathD<\/span> path2)<\/span>;<\/span><\/p>\n

public<\/span> static<\/span> class<\/span> PolylineExtensions2<\/span>
\n {<\/span>
\n \/\/\/ <summary><\/span>
\n \/\/\/ PathD \u8f6c\u56de Polyline（\u4e0d\u5173\u8054\u6570\u636e\u5e93）<\/span>
\n \/\/\/ <\/summary><\/span>
\n public<\/span> static<\/span> Polyline<\/span> ToPolyline<\/span>(<\/span>this<\/span> PathD<\/span> path,<\/span> double<\/span><\/span> tolerance =<\/span> 1e-4<\/span>)<\/span>
\n {<\/span>
\n Polyline<\/span> pl =<\/span> new<\/span> Polyline<\/span>(<\/span>)<\/span>;<\/span>
\n for<\/span> (<\/span>int<\/span><\/span> i =<\/span> 0<\/span>;<\/span> i <<\/span> path.<\/span>Count;<\/span> i++<\/span>)<\/span>
\n {<\/span>
\n PointD<\/span> pt =<\/span> path[<\/span>i]<\/span>;<\/span>
\n pl.<\/span>AddVertexAt<\/span>(<\/span>i,<\/span> new<\/span> Point2d<\/span>(<\/span>pt.<\/span>x,<\/span> pt.<\/span>y)<\/span>,<\/span> 0<\/span>,<\/span> 0<\/span>,<\/span> 0<\/span>)<\/span>;<\/span>
\n }<\/span>
\n \/\/ \u5982\u679c PathD \u9996\u5c3e\u70b9\u8db3\u591f\u63a5\u8fd1（\u5dee\u503c\u5c0f\u4e8e\u5bb9\u5dee），\u5219\u8ba4\u4e3a\u5b83\u662f\u95ed\u5408\u7684<\/span>
\n if<\/span> (<\/span>path.<\/span>Count ><\/span> 1<\/span>)<\/span>
\n {<\/span>
\n PointD<\/span> first =<\/span> path[<\/span>0<\/span>]<\/span>;<\/span>
\n PointD<\/span> last =<\/span> path[<\/span>path.<\/span>Count –<\/span> 1<\/span>]<\/span>;<\/span>
\n \/\/if (Math.Abs(first.x – last.x) < tolerance &&<\/span>
\n \/\/ Math.Abs(first.y – last.y) < tolerance)<\/span>
\n \/\/{<\/span>
\n \/\/ pl.Closed = true;<\/span>
\n \/\/}<\/span>
\n \/\/ \u53ea\u6709\u81f3\u5c113\u4e2a\u70b9\u4e14\u9762\u79ef\u975e\u96f6\u7684\u8def\u5f84\u624d\u89c6\u4e3a\u6709\u6548\u95ed\u5408\u591a\u8fb9\u5f62<\/span>
\n if<\/span> (<\/span>path.<\/span>Count >=<\/span> 3<\/span> &&<\/span> Math.<\/span>Abs<\/span>(<\/span>Clipper.<\/span>Area<\/span>(<\/span>path)<\/span>)<\/span> ><\/span> 1e-6<\/span>)<\/span>
\n {<\/span>
\n pl.<\/span>Closed =<\/span> true<\/span>;<\/span>
\n }<\/span>
\n }<\/span>
\n return<\/span> pl;<\/span>
\n }<\/span><\/p>\n

\/\/\/ <summary><\/span>
\n \/\/\/ \u5c06 PathsD \u8f6c\u6362\u4e3a Polyline \u5217\u8868<\/span>
\n \/\/\/ <\/summary><\/span>
\n public<\/span> static<\/span> List<<\/span>Polyline><\/span><\/span> ToPolylines<\/span>(<\/span>this<\/span> PathsD<\/span> paths)<\/span>
\n {<\/span>
\n var<\/span><\/span> polylines =<\/span> new<\/span> List<<\/span>Polyline><\/span><\/span>(<\/span>)<\/span>;<\/span>
\n foreach<\/span> (<\/span>var<\/span><\/span> path in<\/span> paths)<\/span>
\n {<\/span>
\n \/\/ \u8c03\u7528\u5df2\u6709\u7684\u5355\u4e2a PathD \u2192 Polyline \u6269\u5c55\u65b9\u6cd5<\/span>
\n polylines.<\/span>Add<\/span>(<\/span>path.<\/span>ToPolyline<\/span>(<\/span>)<\/span>)<\/span>;<\/span>
\n }<\/span>
\n return<\/span> polylines;<\/span>
\n }<\/span>
\n }<\/span><\/p>\n

\u9519\u8bef\u89e3\u6cd5<\/h3>\n

\u76f4\u63a5\u901a\u8fc7\u524d\u4e09\u4e2a\u70b9\u7684\u5dee\u4e58\u5224\u65ad\u662f\u9006\u65f6\u9488\u6216\u987a\u5e8f\u65f6\u9488\u662f\u9519\u8bef\u7684，\u4e00：\u4e09\u70b9\u5171\u7ebf\u3002\u4e8c，\u53ef\u80fd\u662f\u51f9\u89d2\u3002\u7528clipper\u5e93\u7684\u6709\u5411\u9762\u79ef\u5224\u65ad\u66f4\u5408\u7406\u3002<\/p>\n

\u67e5\u770b\u89c6\u9891<\/h2>\n

https:\/\/edu.csdn.net\/course\/detail\/41418 \u5982\u679c\u89c6\u9891\u5ba1\u6838\u4e2d，\u53ef\u4ee5\u770b\u56fe\u3002 \u5c06\u539f\u70b9\u548c\u88ab\u51cf\u6570\u4e00\u8d77\u5e73\u79fb，\u539f\u70b9\u5728\u95f5\u53ef\u592b\u65af\u57fa\u5dee\u4e0a，\u5219\u88ab\u51cf\u6570\u548c\u51cf\u6570\u76f8\u5207\u3002<\/p>\n

\u8fb9\u957f100\u7684\u6b63\u65b9\u5f62，\u5de6\u4e0b\u89d2\u662f\u5706\u70b9，\u4f5c\u4e3a\u6a21\u677f\u56fe\u50cf(\u88ab\u51cf\u6570)<\/h3>\n

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