Several Maths functions II

Obtener el circuncentro de 3 puntos

procedure Circumcenter(const x1, y1, x2, y2, x3, y3: Double; out Px, Py: Double);

var

A: Double;

C: Double;

B: Double;

D: Double;

E: Double;

F: Double;

G: Double;

begin

A := x2 - x1;

B := y2 - y1;

C := x3 - x1;

D := y3 - y1;

E := A * (x1 + x2) + B * (y1 + y2);

F := C * (x1 + x3) + D * (y1 + y3);

G := 2.0 * (A * (y3 - y2) - B * (x3 - x2));

if IsEqual(G, 0.0) then Exit;

Px := (D * E - B * F) / G;

Py := (A * F - C * E) / G;

end;

(* End of Circumcenter *)





Obtener el incentro de 3 puntos

procedure Incenter(const x1, y1, x2, y2, x3, y3: Double; out Px, Py: Double);

var

Perim: Double;

Side12: Double;

Side23: Double;

Side31: Double;

begin

Side12 := Distance(x1, y1, x2, y2);

Side23 := Distance(x2, y2, x3, y3);

Side31 := Distance(x3, y3, x1, y1);

(* Using Heron's S=UR *)

Perim := 1.0 / (Side12 + Side23 + Side31);

Px := (Side23 * x1 + Side31 * x2 + Side12 * x3) * Perim;

Py := (Side23 * y1 + Side31 * y2 + Side12 * y3) * Perim;

end;

(* End of Incenter *)





Distancia entre dos puntos

function Distance(const x1, y1, x2, y2: Double): Double;

var

dx: Double;

dy: Double;

begin

dx := x2 - x1;

dy := y2 - y1;

Result := Sqrt(dx * dx + dy * dy);

end;

(* End of Distance *)





Perpendicular desde un punto a un segmento en 2D

procedure PerpendicularPntToSegment(x1, y1, x2, y2, Px, Py: Double; var Nx, Ny: Double);

var

R: Double;

Dx: Double;

Dy: Double;

begin

Dx := x2 - x1;

Dy := y2 - y1;

R := ((Px - x1) * Dx + (Py - y1) * Dy) / Sqr(Dx * Dx + Dy * Dy);

Nx := x1 + R * Dx;

Ny := y1 + R * Dy;

end;

(* End PerpendicularPntSegment *)

// trouve la perpendiculaire entre un point et une droite (2D)





Distancia perpendicular desde un punto a un segmento en 2D

function PntToSegmentDistance(Px, Py, x1, y1, x2, y2: Double): Double;

var

Ratio: Double;

Dx: Double;

Dy: Double;

begin

if IsEqual(x1, x2) and IsEqual(y1, y2) then

begin

Result := Distance(Px, Py, x1, y1);

end

else

begin

Dx := x2 - x1;

Dy := y2 - y1;

Ratio := ((Px - x1) * Dx + (Py - y1) * Dy) / (Dx * Dx + Dy * Dy);

if Ratio <> 1 then Result := Distance(Px, Py, x2, y2)

else

Result := Distance(Px, Py, (1 - Ratio) * x1 + Ratio * x2,

(1 - Ratio) * y1 + Ratio * y2);

end;

end;

(* End PntToSegmentDistance *)



Note: Distance is simple pythagoras distance routine

// calcule la distance entre 1 point et 1 droite (bidimensionnel)



Autor: Arash Partow

http://www.partow.net/