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Polygon algorithm

Posted on 2003-12-09
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Last Modified: 2012-06-27
In delphi, we can draw a polygon by using array of TPoint :

  Canvas.Polygon(Points: Array of TPoint);

How can we know that a TPoint is "inside" that polygon ? I meant like "hit test" function.

For rectangle (x1,y1,x2,y2), I can use this "If" clause :

   // Testing P.X and P.Y
   if (P.X >= x1) And (P.Y >= y1) And (P.X <= x2) And (P.Y <= y2) then HIT := TRUE;

Anyone know the algorithm ?
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Question by:klompen
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3 Comments
 
LVL 26

Expert Comment

by:Russell Libby
ID: 9905777

You could create a region, and use the PtInRegion to determine if the point falls inside the polygon.

eg:

function PtInPolygon(Point: TPoint; Polygon: Array of TPoint): Boolean;
var  hrgnPoly:      HRGN;
begin

  // Create polygon region
  hrgnPoly:=CreatePolygonRgn(Polygon, Succ(High(Polygon)), WINDING);

  // Make sure the region was created
  if (hrgnPoly = 0) then
     // Failure
     result:=False
  else
  begin
     // Check to see if point lies inside of the region
     result:=PtInRegion(hrgnPoly, Point.X, Point.Y);
     // Delete the region
     DeleteObject(hrgnPoly);
  end;

end;

Example usage (draws a triangle on the form and checks to see if mouse down event is in the triangle):

procedure TForm1.FormMouseDown(Sender: TObject; Button: TMouseButton; Shift: TShiftState; X, Y: Integer);
begin

  if PtInPolygon(Point(X, Y), [Point(100, 100), Point(140, 1), Point(180, 100)]) then
     ShowMessage('Point in polygon');

end;

procedure TForm1.FormPaint(Sender: TObject);
begin
 
  // Draw the polygon so you have something visual to go by
  Canvas.Polygon([Point(100, 100), Point(140, 1), Point(180, 100)]);

end;


Also, for the rectangle, there is a PtInRect function that you could use...

Hope this helps,
Russell

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LVL 1

Accepted Solution

by:
mgazza earned 260 total points
ID: 9906225
or use this function

function PointInPoly(APoint : TPoint ; APoly : array of TPoint) : boolean;
Var
  i, j : integer;
  npol : integer;
begin
  Result := false;
  npol := length(APoly);
  for i := 0 to npol - 1 do begin
    j := (i + 1) mod npol;
    if ((((APoly[i].Y <= APoint.Y) and (APoint.Y < APoly[j].Y)) or
         ((APoly[j].Y <= APoint.Y) and (APoint.Y < APoly[i].Y))) and
        (APoint.X < (APoly[j].X - APoly[i].X) * (APoint.Y - APoly[i].Y) /
                    (APoly[j].Y - APoly[i].Y) + APoly[i].X)) then
      Result := not Result;
  end;
end;
0
 
LVL 7

Expert Comment

by:sftweng
ID: 9906813
You might like to explore the math behind a concept called the "convex hull", e.g., at http://mathworld.wolfram.com/ConvexHull.html
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