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绕过三个点

 

@lwx228问： JSL如何计算第四个点是否与前三个点在同一个圆上？题目是关于通过三点的圆的几何问题。 附上 JSL。

Graph with three movable points, A, B, C that draws a circle through the points具有三个可移动点 A、B、C 的图形，通过这些点绘制一个圆

该图显示了点 A、B 和 C 的三个方形黑色手柄。 把它们拖来拖去。 它显示两条蓝线，A 和 C。 它显示了它们的绿色中点和点缀的橙色垂直平分线。 它显示了平分线相交的橙色点。 它显示了圆心和半径穿过 A、B 和 C 的洋红色圆。

// https://www.geeksforgeeks.org/program-for-point-of-intersection-of-two-lines/
lineLineIntersection = Function( {Ax, Ay, Bx, By, Cx, Cy, Dx, Dy},
 {a1, b1, c1, a2, b2, c2, determinant, x, y}, // locals
 // Line AB represented as a1x + b1y = c1 
 a1 = By - Ay;
 b1 = Ax - Bx;
 c1 = a1 * (Ax) + b1 * (Ay); 
  
    // Line CD represented as a2x + b2y = c2 
 a2 = Dy - Cy;
 b2 = Cx - Dx;
 c2 = a2 * (Cx) + b2 * (Cy); 
  
 determinant = a1 * b2 - a2 * b1; 
  
 If( determinant == 0, 
    
        // The lines are parallel. This is simplified 
  // by returning a pair of FLT_MAX 
  {., .}; // return
 , // else
  x = (b2 * c1 - b1 * c2) / determinant;
  y = (a1 * c2 - a2 * c1) / determinant;
  Eval List( {x, y} );// return 
 ); 
 
); 

New Window( "Example",
 ax = 20,
 ay = 50;
 bx = 30;,
 by = 70;
 cx = 90;,
 cy = 20;
 Graph Box(
  Frame Size( 500, 500 ),
  Text( {0, 2}, "Drag the square handles" );
  Handle(
   ax,
   ay,
   ax = x;
   ay = y;
  );
  Handle(
   bx,
   by,
   bx = x;
   by = y;
  );
  Handle(
   cx,
   cy,
   cx = x;
   cy = y;
  );
  //Circle( {0, 0}, Sqrt( exx * exx + exy * exy ) );
  Text( {ax, ay}, " A" );
  Text( {bx, by}, " B" );
  Text( {cx, cy}, " C" );
  Pen Color( "blue" );
  Line( {ax, ay}, {bx, by} );// "line a"
  Line( {cx, cy}, {bx, by} );// "line c"
  slopeLineA = (ay - by) / (ax - bx);
  slopeLineC = (cy - by) / (cx - bx);
  // the slope is missing if source line is vertical
  perpSlopeA = If( Is Missing( slopeLineA ),
   0,
   -1 / slopeLineA
  );
  perpSlopeC = If( Is Missing( slopeLineC ),
   0,
   -1 / slopeLineC
  );
  midpointAx = (ax + bx) / 2;
  midpointAy = (ay + by) / 2;
  midpointCx = (cx + bx) / 2;
  midpointCy = (cy + by) / 2;
  Fill Color( "green" );
  Circle( {midpointAx, midpointAy}, .9, "FILL" );
  Circle( {midpointCx, midpointCy}, .9, "FILL" );
  // the perp slope is missing if it is vertical --
  // because source line was horizontal (rise = 0)
  Pen Color( "red" );
  Line Style( "dotted" );
  If( Is Missing( perpSlopeA ),
   pax0 = midpointAx;
   pay0 = midpointAy - 100;
   pax1 = midpointAx;
   pay1 = midpointAy + 100;
  , // else ... find two far-away points and draw line
   pax0 = midpointAx - 100;
   pay0 = midpointAy - 100 * perpSlopeA;
   pax1 = midpointAx + 100;
   pay1 = midpointAy + 100 * perpSlopeA;
  );
  Line( {pax0, pay0}, {pax1, pay1} );
  If( Is Missing( perpSlopeC ),
   pcx0 = midpointCx;
   pcy0 = midpointCy - 100;
   pcx1 = midpointCx;
   pcy1 = midpointCy + 100;
  , // else
   pcx0 = midpointCx - 100;
   pcy0 = midpointCy - 100 * perpSlopeC;
   pcx1 = midpointCx + 100;
   pcy1 = midpointCy + 100 * perpSlopeC;
  );
  Line( {pcx0, pcy0}, {pcx1, pcy1} );
  Line Style( "solid" );
  pensize(2);
  {xc, yc} = lineLineIntersection( pax0, pay0, pax1, pay1, pcx0, pcy0, pcx1, pcy1 );
  Fill Color( "orange" );
  Circle( {xc, yc}, .9, "FILL" );
  Pen Color( "magenta" );
  // choose distance to A, could use B or C too...
  Circle( {xc, yc}, Sqrt( (xc - ax) ^ 2 + (yc - ay) ^ 2 ) );
 );
);

 

通过三个点画一个圆。

Re: 绕三点

如果您来到这里，您可能正在寻找这个 JMP 14 函数 Fit Circle。

FitCircle output from the Scripting Index.脚本索引的 FitCircle 输出。