Reply-To: "Paul Nicholls" <paul_f_nicholls@hotmail.com>
From: "Paul Nicholls" <paul_f_nicholls@hotmail.com>
Newsgroups: borland.public.delphi.graphics
Subject: For anyone who is interested - PolygonArea algorithm for you :)
Date: Thu, 21 Jun 2001 10:47:22 +1000
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This algorithm only works for concave? polygons with no holes in them - eg.
triangles, quads, etc...

const
  x = 0;
  y = 1;
  z = 2;

type
TReal = Single;
TVector = array[0..3] of TReal;

function Vector(ax,ay,az: TReal): TVector;
begin
  Result[x] := ax;
  Result[y] := ay;
  Result[z] := az;
end;

function Subtract(v1,v2: TVector): TVector;
begin
  Result := Vector([v1[x]-v2[x],v1[y]-v2[y],v1[z]-v2[z]]);
end;

function Magnitude(v: TVector): TReal;
begin
  Result := Sqrt(Sqr(v[x])+Sqr(v[y])+Sqr(v[z]));
end;

function Cross(u,v: TVector): TVector;
begin
  Result[X] := u[y] * v[z]-u[z] * v[y];
  Result[Y] := u[z] * v[x]-u[x] * v[z];
  Result[Z] := u[x] * v[y]-u[y] * v[x];
end;

function PolygonArea(Polygon: array of TVector): TReal;
var
  i,N: Integer;
  u,v: TVector;
begin
  Result := 0;
  N := High(Polygon)+1;
  for i := 0 to N - 3 do
  begin
    u := VectorSubtract(Polygon[i+1],Polygon[i]);
    v := VectorSubtract(Polygon[i+2],Polygon[i]);
    Result := Result + Magnitude(Cross(u,v));
  end;
  Result := Result/2;
end;

--
Paul Nicholls (Delphi 5)
"The plastic veneer of civilized man is easily melted in the heat of the
moment" - Paul Nicholls

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