Circle vs pie segment collision detection

[paul_nicholls]

Hi all,
I have added to The Probe a new element, a Sentry object (see figure 1). This object sweeps a beam (shaped like a pie segment) around itself (see figure 2), and I now want to add collision detection so that I know when the beam is touching the player.

Figure 1
sentry.jpg

Figure 2
circle vs pie segment collision.png

I know the beam center point, the radius, and the width (angle).

I know the player center point, the radius.

Any ideas as to how I can quickly return true if the beam is over the circle representing the player?

cheers,
Paul

[WILL]

Well for a circle, if you know the centre, just use a simple distance calculation to determine if it's inside it. If you need only a 'slice' (or beam as you mentioned) to be detected, get the two angles of the line segments from centre and determine if it's within those.

I don't have my AdvancedMath.pas unit handy or I'd throw up the function for you.

For your solution you'd need to compare distance then determine the angle of the object to your sentry object's beam emitter. Once you have all of that information, just use the angles of your beam arcs and the rest is comparison. Just be 0/360 conscious when doing your angle range checks.

[paul_nicholls]

I am already comparing the distance between the circle and the beam, I just wasn't sure how to compare a circle against the two angles...

hmm...I might try looking at dot products or similar + the line normal and see if I can test against the 2 lines and circle that way

cheers,
Paul

[Ñuño Martínez]

An idea: transform the object/player coordinates to polar (you know: <angle, distance>) relative to the origin of your beam. In pseudocode:

  IF vector_length (object.position - beam.position) < beam.radius THEN
    new_object.position := object.position - beam.position;
    polar_object := polar (new_object.position);
    IF polar_object.angle BETWEEN beam.angle1 AND beam.angle2 THEN
      object.hit ();
    END IF;
  END IF;

[User137]

With functions in my lib:

// Angle between 2 vectors, given in radians
function Angle(src,dest: single): single;
begin
  result:=src-dest;
  while result<-PI do result:=result+PI*2;
  while result>PI do result:=result-PI*2;
end;

// By pythagoras a^2+b^2=c^2 you don't need Sqrt() to determine the equality
function PointInCircle(const p,circle: TVector2f; const radius: single): boolean;
var x,y: single;
begin
  x:=circle.x-p.x; y:=circle.y-p.y;
  PointInCircle:=(x*x+y*y)<(radius*radius);
end;

And knowing the angle_delta that is half of pie's slice angle, we can count if point is between them:

if PointInCircle(beam.position, player.position, radius) then
  if abs(Angle(beam.angle, angle_from_beam_to_player)) < angle_delta then begin
    Collide;
  end;

You can also use this for the angle from beam to player:

function Angle(const px1,py1,px2,py2: single): single;
begin
  result:=arctan2(py2-py1,px2-px1);
  if result<0 then result:=result+PI*2;
end;

[paul_nicholls]

@?ëu?±o Mart??nez and User137: thanks guys, but you seem to have overlooked the fact that I want to check if a circle, not a point is between the 2 angle

cheers,
Paul