[Simba 2.0] Random weighted point

WarPie90

Jan 2nd, 2025 (edited)

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program new;
(*
Todo: Add force param perhaps?
Generates a random point within the (convex)polygon/quad/triangle, drawn towards a Target point.
Parameters:
* Target: The point towards which the distribution is drawn.
* weight: Controls the strength of attraction towards the Target (higher values = stronger attraction).
- weight = 0 gives a uniform distribution.
* bias: Introduces a Gaussian spread around the Target (higher values = wider spread).
- bias = 0 gives a purely weighted distribution towards the Target.
Should expose weight and bias to the user if used as mouse distribution method. weight of 10 might be a little high.
*)
function PolygonNearestEdge(Polygon: TPointArray; P: TPoint): TPoint;
var
dist, best: single;
I: Integer;
q: TPoint;
begin
Best := $FFFFFF;
Result := Polygon[0];
for I := 0 to High(Polygon) do
begin
dist := DistToLine(p, Polygon[i], Polygon[(i+1) mod Length(Polygon)], q);
if (dist < best) then
begin
Best := dist;
Result := q;
end;
end;
end;
function TTriangle.RandomWeightedPoint(Target: TPoint; weight: Single=10.0; bias: Single=1): TPoint;
var
r1, r2, r3, u, v, w, t, sum: Single;
stdev,xr,yr: Single;
const
eps := 0.0000001;
begin
if (bias > 0) and (weight <> 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(GaussRand(0, xr/3 * bias) / weight);
Target.Y += Round(GaussRand(0, yr/3 * bias) / weight);
end;
if not (Target in Self) 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;
// do a polygon type or.. just rename to PolygonR...
function TPointArray.RandomWeightedPoint(Target: TPoint; weight: Single=10.0; bias: Single=1): TPoint;
var
i: Integer;
tri: TTriangleArray;
xr,yr,b,sum, r, stdev, area: Single;
begin
area := PolygonArea(Self);
if bias > 0 then
begin
for i := 0 to High(Self) do xr += abs(Self[i].x - Target.x);
xr /= Length(self);
for i := 0 to High(Self) do yr += abs(Self[i].y - Target.y);
yr /= Length(self);
Target.X += Round(GaussRand(0, xr * bias) / weight);
Target.Y += Round(GaussRand(0, yr * bias) / weight);
end;
if not PointInPolygon(Target, Self) then
Target := PolygonNearestEdge(Self,Target);
for i := 0 to High(Self) do
tri += TTriangle.Create(Target, Self[i], Self[(i+1) mod Length(Self)]);
r := Random() * area;
sum := 0;
for i := 0 to High(tri) do
begin
sum += tri[i].Area;
if r < sum then
Exit(tri[i].RandomWeightedPoint(Target, weight, 0));
end;
end;
function TQuad.RandomWeightedPoint(Target: TPoint; weight: Single=10.0; bias: Single=1): TPoint;
begin
Result := Self.Corners.RandomWeightedPoint(Target, weight, bias);
end;
function TCircle.RandomWeightedPoint(Target: TPoint; weight: Single = 10.0; bias: Single = 1): TPoint;
var
angle, dist, r1, r2, sum, u, t: Single;
randX, randY: Single;
begin
if (bias > 1) and (weight <> 0) then
begin
Target.X += Round(GaussRand(0, Self.Radius * bias / 2) / weight);
Target.Y += Round(GaussRand(0, Self.Radius * bias / 2) / weight);
end;
if not Self.Contains(Target) then
Target := Self.PointAtDegrees(Target.AngleBetween([Self.x, Self.y]));
angle := Random() * 2 * Pi;
dist := sqrt(Random()) * Self.Radius;
randX := Self.X + cos(angle) * dist;
randY := Self.Y + sin(angle) * dist;
r1 := 1;
r2 := weight * Random();
sum := r1 + r2 + 0.0000001;
u := r1 / sum;
t := r2 / sum;
Result.X := Round(u * randX + t * Target.X);
Result.Y := Round(u * randY + t * Target.Y);
end;
var
t, p: TPoint;
Tri: TTriangle;
Image: TImage;
hsl: TColorHSL;
mat: TSingleMatrix;
weight: Single := 10.0;
pts,poly: TPointArray;
begin
Tri := [[100,200],[800,100],[700,400]];
pts := RandomTPA(7, [200,200,500,500]);
poly := pts.ConvexHull();
Writeln(poly);
Image := TImage.Create(800,800);
Image.DrawPolygon(tri.Corners);
Image.Show();
while True do
begin
SetLength(mat, 0,0);
mat.SetSize(800,800);
t := Target.MouseXY;
for 0 to 20000 do
begin
p := Tri.RandomWeightedPoint(T, weight, 0.5);
if Image.InImage(p.x-1,p.y-1) and Image.InImage(p.x+1,p.y+1) then
begin
mat[p.y+1,p.x] += 1;
mat[p.y-1,p.x] += 1;
mat[p.y,p.x+1] += 1;
mat[p.y,p.x-1] += 1;
mat[p.y,p.x] += 1;
end;
end;
WriteLn(weight);
if Target.MousePressed(EMouseButton.LEFT) then weight += 0.1;
if Target.MousePressed(EMouseButton.Right) then weight -= 0.1;
Image.FromMatrix(mat);
Image.DrawPolygon(Tri.Corners);
Image.Show(False);
end;
end.

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