Funciones Matemáticas

Determinar si un punto existe dentro de un triángulo

function PointInTriangle(const Px, Py, x1, y1, x2, y2, x3, y3: Double): Boolean;

var

Or1: Integer;

Or2: Integer;

Or3: Integer;

begin

Or1 := Orientation(x1, y1, x2, y2, Px, Py);

Or2 := Orientation(x2, y2, x3, y3, Px, Py);

Or3 := Orientation(x3, y3, x1, y1, Px, Py);



if (Or1 = Or2) and (Or2 = Or3) then

Result := True

else if Or1 = 0 then

Result := (Or2 = 0) or (Or3 = 0)

else if Or2 = 0 then

Result := (Or1 = 0) or (Or3 = 0)

else if Or3 = 0 then

Result := (Or2 = 0) or (Or1 = 0)

else

Result := False;

end;

(* End of PointInTriangle *)



function Orientation(const x1, y1, x2, y2, Px, Py: Double): Integer;

var

Orin: Double;

begin

(* Linear determinant of the 3 points *)

Orin := (x2 - x1) * (py - y1) - (px - x1) * (y2 - y1);



if Orin > 0.0 then

Result := +1 (* Orientaion is to the right-hand side *)

else if Orin < 0.0 then

Result := -1 (* Orientaion is to the left-hand side *)

else

Result := 0; (* Orientaion is neutral aka collinear *)

end;

(* End of Orientation *)





LIBROS:

Matemáticas, el fascinante mundo de los números

Matrix computations (Matematical Science)

Geometría analítica del plano y del espacio

Mecánica de fluidos

Geometría Afín y Euclidea