[Simba 1.4] RandomPointTriangle

// original work at this pastebin - with description:
// https://pastebin.com/7N2iuDsF

type
  TTriangle = record A,B,C: TPoint; end;

function TTriangle.Contains(P: TPoint): Boolean; constref;
var
  c1, c2, c3: Int32;
begin
  c1 := Sign(srl.CrossProduct(A, B, P));
  c2 := srl.CrossProduct(B, C, P);
  c3 := srl.CrossProduct(C, A, P);
  Result := (c1 * c2 >= 0) and (c1 * c3 >= 0) and (Sign(c2) * c3 >= 0);
end;

function TTriangle.NearestEdge(P: TPoint): TPoint; constref;
var
  Best, Dist: Single;
  X: TPoint;
begin
  Best := srl.DistToLineEx(P, Self.A,  Self.B, Result);
  if (dist := srl.DistToLineEx(P, Self.B, Self.C, X)) < Best then begin Result := X; Best := Dist; end;
  if (dist := srl.DistToLineEx(P, Self.C, Self.A, X)) < Best then Result := X;
end;


function TTriangle.RandomWeightedPoint(Target: TPoint; weight: Single=10.0; bias: Single=1): TPoint; constref;
var
  r1, r2, r3, u, v, w, t, sum: Single;
  stdev,xr,yr: Single;
const
  eps := 0.0000001;
begin
  if bias > 0 then
  begin
    xr := abs(Self.A.x - Target.x) + abs(Self.B.x - Target.x) + abs(Self.C.x - Target.x);
    yr := abs(Self.A.y - Target.y) + abs(Self.B.y - Target.y) + abs(Self.C.y - Target.y);

    Target.X += Round(srl.GaussRand(0, xr/3 * bias) / weight);
    Target.Y += Round(srl.GaussRand(0, yr/3 * bias) / weight);
  end;

  if not Self.Contains(Target)  then
    Target := Self.NearestEdge(Target);

  r1 := Random();
  r2 := Random();
  if r1 + r2 > 1 then
  begin
    r1 := 1 - r1;
    r2 := 1 - r2;
  end;

  r3 := Random();
  sum := 1 + weight * r3 + eps;
  u := r1 / sum;
  v := r2 / sum;
  w := (1 - r1 - r2) / sum;
  t := (weight * r3) / sum;

  with Self do
  begin
    Result.X := Round(u * A.X + v * B.X + w * C.X + t * Target.X);
    Result.Y := Round(u * A.Y + v * B.Y + w * C.Y + t * Target.Y);
  end;
end;


function ArcToTriangle(start, stop: TPoint; radians: single): TTriangle;
begin
  Result.A := start;
  Result.B := stop.Rotate(-radians / 2, start);
  Result.C := stop.Rotate(+radians / 2, start);
end;