Circle vs pie segment collision detection

[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

[Dan]

indeed it would have been a lot easier if it was a point vs pie. but anyway, I just had a quick look into the problem and here's what I came up with:

TCircle = record
  public
    c: TG2Vec2;
    r: Single;
  end;

  TPie = record
  public
    c: TG2Vec2;
    r: Single;
    AngStart: Single;
    AngEnd: Single;
  end;
...
function CircleVsPieIntersect(const c: TCircle; const p: TPie): Boolean;
  var v1, v2, n1, n2, n3, a1, a2: TG2Vec2;
  var d1, d2, l: Single;
begin
  l := (c.c - p.c).Len;
  if l > c.r + p.r then
  begin
    Result := False;
    Exit;
  end;
  G2SinCos(p.AngStart, v1.y, v1.x);
  G2SinCos(p.AngEnd, v2.y, v2.x);
  n3 := -(v1 + v2);
  if (n3.Dot(c.c) > n3.Dot(p.c))
  and (l > c.r) then
  begin
    Result := False;
    Exit;
  end;
  n1 := v1.Perp; if n1.Dot(v1 - v2) < 0 then n1 := -n1;
  n2 := v2.Perp; if n2.Dot(v2 - v1) < 0 then n2 := -n2;
  d1 := n1.Dot(p.c) + c.r;
  d2 := n2.Dot(p.c) + c.r;
  if (n1.Dot(c.c) > d1)
  or (n2.Dot(c.c) > d2) then
  begin
    Result := False;
    Exit;
  end;
  a1 := p.c + v1 * p.r;
  a2 := p.c + v2 * p.r;
  if (
    (n1.Dot(c.c) > n1.Dot(p.c))
    and (v1.Dot(c.c) > v1.Dot(a1))
    and ((c.c - a1).Len > c.r)
  )
  or (
    (n2.Dot(c.c) > n2.Dot(p.c))
    and (v2.Dot(c.c) > v2.Dot(a2))
    and ((c.c - a2).Len > c.r)
  ) then
  begin
    Result := False;
    Exit;
  end;
  Result := True;
end;

this is not a best solution, just my solution
One limitation though, the algorithm will consider the pie to be the lesser part of the circle.
for example if the angle of your pie is > 180 then the algorithm will reverse the pie and use its smaller part.
so basically if you use a pie with an angle < 180, the algorithm will work.
There are a few methods from my game engine, so if you have any trouble understanding them - let me know.

[paul_nicholls]

Nice! Thanks Dan...I will modify it and see if it works for me

EDIT hmm...is TG2Vec2 a class or a record with methods?

cheers
Paul

[User137]

@?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

Well..

if PointInCircle(beam.position, player.position, radius) then

would change into

if PointInCircle(beam.position, player.position, radius+playerRadius) then

That leaves the "triangle check" remaining to be fixed. It could really be a circle vs triangle check.