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Datei: GLOBAL.vdmrt Sprache: VDM

Original von: VDM^©

class GLOBAL

types

public Altitude = real;

public FOId = token;
public RadarId = token;

public
Coordinates ::
  X : real
  Y : real;

public Time = nat;

public String = seq of char;

public ObstacleType = <Natural> | <Artificial> | <Airport>  | <Military_Area>;

public FOWarning = ObstacleType | <EstimationWarning>;

public RadarWarning = <Saturated>;

public MinimumSafetyAltitude = nat | <NotAllowed>;

public Position ::
  coord    : Coordinates
  altitude : Altitude;

public History = seq of Position;

public Vector ::
  X : real
  Y : real;

functions

protected isPointInRange : Coordinates * nat1 * Coordinates -> bool
isPointInRange(center,range,point) ==
  (center.X - point.X)**2 + (center.Y - point.Y)**2 <= range**2;

protected vectorSum : Vector * Vector -> Vector
vectorSum(v1,v2) ==
  mk_Vector(v1.X + v2.X,v1.Y + v2.Y);

protected vectorDiv : Vector * int -> Vector
vectorDiv(v,n) ==
  mk_Vector(v.X/n,v.Y/n)
pre n <> 0;

protected addVectorToPoint : Vector * Position -> Coordinates
addVectorToPoint(v,p) ==
  mk_Coordinates(p.coord.X + v.X, p.coord.Y + v.Y);

protected vectorLength : Vector -> real
vectorLength(v) ==
  MATH`sqrt(v.X**2 + v.Y**2);

protected unitVector : Vector -> Vector
unitVector(v) ==
  let l = vectorLength(v)
  in
    mk_Vector(v.X/l,v.Y/l);

protected dotProduct : Vector * Vector -> real
dotProduct(v1,v2) ==
  v1.X * v2.X + v1.Y * v2.Y;

protected angleBetweenVectors : Vector * Vector -> real
angleBetweenVectors(v1,v2) ==
  let uv1 = unitVector(v1),
      uv2 = unitVector(v2),
      dvs = dotProduct(uv1,uv2),
      angle = MATH`acos(dvs)
  in
    radians2degree(angle);

protected radians2degree : real -> real
radians2degree(r) ==
  r * (180/MATH`pi);

protected atan2 : real * real -> real
atan2(y,x) ==
  2 * MATH`atan(y/(MATH`sqrt(x**2+y**2)+x))
pre not (x = 0 and y = 0);

protected signedVectorAngle : Vector * Vector -> real
signedVectorAngle(v1,v2) ==
  atan2(v2.Y,v2.X) - atan2(v1.Y,v1.X);

protected vectorAngle : Vector -> real * real
vectorAngle(v) ==
   mk_( radians2degree (MATH`acos(v.X / MATH`sqrt(v.X**2 + v.Y**2))),
        radians2degree( MATH`asin(v.Y / MATH`sqrt(v.X**2 + v.Y**2))));

protected vectorRotate : Vector * real -> Vector
vectorRotate(v,a) ==
  let x' = MATH`cos(a)*v.X - MATH`sin(a)*v.Y,
      y' = MATH`cos(a)*v.Y + MATH`sin(a)*v.X
  in
    mk_Vector(round(x'),round(y'));

protected round : real -> real
round(r) ==
  let fr  = floor(r),
      dif = abs(r - fr)
  in
    if(dif < 10**-10)
    then fr
    else r;

operations

public test : real * real * real * real ==>
              Vector * Vector * real * real * Vector * real * real
test(x1,y1,x2,y2) ==
  let v1 = mk_Vector(x1,y1),
      v2 = mk_Vector(x2,y2)
  in
    return mk_(unitVector(v1),
               unitVector(v2),
               dotProduct(unitVector(v1),unitVector(v2)),
               atan2(0.000001,0.0000000),
               vectorRotate(v2,signedVectorAngle(v1,v2)),
               radians2degree(signedVectorAngle(v1,v2)),
               angleBetweenVectors(v1,v2)
              );

end GLOBAL

¤ Dauer der Verarbeitung: 0.16 Sekunden (vorverarbeitet) ¤

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