Circle vs pie segment collision detection

[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

[Dan]

it's a record:

TG2Vec2 = record
  strict private
    function GetArr(const Index: Integer): Single; {$IFDEF G2_USE_INLINE} inline; {$ENDIF}
    procedure SetArr(const Index: Integer; const Value: Single); {$IFDEF G2_USE_INLINE} inline; {$ENDIF}
  public
    x, y: Single;
    property Arr[const Index: Integer]: Single read GetArr write SetArr; default;
    class operator Negative(const v: TG2Vec2): TG2Vec2;
    class operator Explicit(const v: TG2Vec2): TG2Vec2Ref;
    class operator Explicit(const v: TG2Vec2Ref): TG2Vec2;
    class operator Explicit(const v: TPoint): TG2Vec2;
    class operator Implicit(const v: TG2Vec2): TG2Vec2Ref;
    class operator Implicit(const v: TG2Vec2Ref): TG2Vec2;
    class operator Implicit(const v: TPoint): TG2Vec2;
    class operator Equal(const v1, v2: TG2Vec2): Boolean;
    class operator NotEqual(const v1, v2: TG2Vec2): Boolean;
    class operator Add(const v1, v2: TG2Vec2): TG2Vec2;
    class operator Add(const v: TG2Vec2; const s: Single): TG2Vec2;
    class operator Subtract(const v1, v2: TG2Vec2): TG2Vec2;
    class operator Subtract(const v: TG2Vec2; const s: Single): TG2Vec2;
    class operator Multiply(const v1, v2: TG2Vec2): Single;
    class operator Multiply(const v: TG2Vec2; const s: Single): TG2Vec2;
    class operator Multiply(const v: TG2Vec2; const m: TG2Mat): TG2Vec2;
    class operator Multiply(const v: TG2Vec2; const m: TG2Mat2): TG2Vec2;
    class operator Divide(const v: TG2Vec2; const s: Single): TG2Vec2;
    procedure SetValue(const _X, _Y: Single); {$IFDEF G2_USE_INLINE} inline; {$ENDIF}
    procedure Normalize; {$IFDEF G2_USE_INLINE} inline; {$ENDIF}
    function Normalized: TG2Vec2; {$IFDEF G2_USE_INLINE} inline; {$ENDIF}
    function Len: Single; {$IFDEF G2_USE_INLINE} inline; {$ENDIF}
    function LenSq: Single; {$IFDEF G2_USE_INLINE} inline; {$ENDIF}
    function Dot(const v: TG2Vec2): Single; {$IFDEF G2_USE_INLINE} inline; {$ENDIF}
    function Cross(const v: TG2Vec2): Single; {$IFDEF G2_USE_INLINE} inline; {$ENDIF}
    function Angle(const v: TG2Vec2): Single; {$IFDEF G2_USE_INLINE} inline; {$ENDIF}
    function Perp: TG2Vec2; {$IFDEF G2_USE_INLINE} inline; {$ENDIF}
    function Reflect(const n: TG2Vec2): TG2Vec2; {$IFDEF G2_USE_INLINE} inline; {$ENDIF}
    function Rotate(const Angle: Single): TG2Vec2; {$IFDEF G2_USE_INLINE} inline; {$ENDIF}
  end;

if you want I could just attach the whole math unit here.

[paul_nicholls]

Thanks

That would probably be easier

cheers,
Paul

[Dan]

ok here it is

[paul_nicholls]

ok here it is

Thanks mate, I will post back and let you know if I got it working

Thanks again for your time

EDIT: what about the file "Gen2.inc" that G2Math.pas uses?

cheers,
Paul

[Ñuño Martínez]

@?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

Details... BTW that was teh first idea I had, and I'm sure it made you think, don't you?

[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.