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FrustumCulling.pas
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FrustumCulling.pas
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unit FrustumCulling;
// © 2004 by Steve M.
interface
uses
SysUtils, OpenGL12, Geometry, VectorTypes;
type
TFrustum = class
private
Planes: array[0..5] of TVector4f;
procedure NormalizePlane(Plane: Integer);
public
function IsPointWithin(const p: TVector3f): Boolean;
function IsSphereWithin(const p: TVector3f; const r: Single): Boolean;
function IsBoxWithin(const p, dim: TVector3f): Boolean;
procedure Calculate;
end;
var
Frustum: TFrustum;
implementation
const
Right = 0;
Left = 1;
Bottom = 2;
Top = 3;
Back = 4;
Front = 5;
A = 0;
B = 1;
C = 2;
D = 3;
procedure TFrustum.NormalizePlane(Plane: Integer);
var
Magnitude: Single;
begin
Magnitude := Sqrt(Sqr(Planes[Plane][A])+Sqr(Planes[Plane][B])+Sqr(Planes[Plane][C]));
Planes[Plane][A] := Planes[Plane][A]/Magnitude;
Planes[Plane][B] := Planes[Plane][B]/Magnitude;
Planes[Plane][C] := Planes[Plane][C]/Magnitude;
Planes[Plane][D] := Planes[Plane][D]/Magnitude;
end;
procedure TFrustum.Calculate;
var
ProjM, ModM, Clip: array[0..15] of Single;
begin
glGetFloatv(GL_PROJECTION_MATRIX, @ProjM);
glGetFloatv(GL_MODELVIEW_MATRIX, @ModM);
// multiply projection and modelview matrix
Clip[ 0] := ModM[ 0]*ProjM[ 0] + ModM[ 1]*ProjM[ 4] + ModM[ 2]*ProjM[ 8] + ModM[ 3]*ProjM[12];
Clip[ 1] := ModM[ 0]*ProjM[ 1] + ModM[ 1]*ProjM[ 5] + ModM[ 2]*ProjM[ 9] + ModM[ 3]*ProjM[13];
Clip[ 2] := ModM[ 0]*ProjM[ 2] + ModM[ 1]*ProjM[ 6] + ModM[ 2]*ProjM[10] + ModM[ 3]*ProjM[14];
Clip[ 3] := ModM[ 0]*ProjM[ 3] + ModM[ 1]*ProjM[ 7] + ModM[ 2]*ProjM[11] + ModM[ 3]*ProjM[15];
Clip[ 4] := ModM[ 4]*ProjM[ 0] + ModM[ 5]*ProjM[ 4] + ModM[ 6]*ProjM[ 8] + ModM[ 7]*ProjM[12];
Clip[ 5] := ModM[ 4]*ProjM[ 1] + ModM[ 5]*ProjM[ 5] + ModM[ 6]*ProjM[ 9] + ModM[ 7]*ProjM[13];
Clip[ 6] := ModM[ 4]*ProjM[ 2] + ModM[ 5]*ProjM[ 6] + ModM[ 6]*ProjM[10] + ModM[ 7]*ProjM[14];
Clip[ 7] := ModM[ 4]*ProjM[ 3] + ModM[ 5]*ProjM[ 7] + ModM[ 6]*ProjM[11] + ModM[ 7]*ProjM[15];
Clip[ 8] := ModM[ 8]*ProjM[ 0] + ModM[ 9]*ProjM[ 4] + ModM[10]*ProjM[ 8] + ModM[11]*ProjM[12];
Clip[ 9] := ModM[ 8]*ProjM[ 1] + ModM[ 9]*ProjM[ 5] + ModM[10]*ProjM[ 9] + ModM[11]*ProjM[13];
Clip[10] := ModM[ 8]*ProjM[ 2] + ModM[ 9]*ProjM[ 6] + ModM[10]*ProjM[10] + ModM[11]*ProjM[14];
Clip[11] := ModM[ 8]*ProjM[ 3] + ModM[ 9]*ProjM[ 7] + ModM[10]*ProjM[11] + ModM[11]*ProjM[15];
Clip[12] := ModM[12]*ProjM[ 0] + ModM[13]*ProjM[ 4] + ModM[14]*ProjM[ 8] + ModM[15]*ProjM[12];
Clip[13] := ModM[12]*ProjM[ 1] + ModM[13]*ProjM[ 5] + ModM[14]*ProjM[ 9] + ModM[15]*ProjM[13];
Clip[14] := ModM[12]*ProjM[ 2] + ModM[13]*ProjM[ 6] + ModM[14]*ProjM[10] + ModM[15]*ProjM[14];
Clip[15] := ModM[12]*ProjM[ 3] + ModM[13]*ProjM[ 7] + ModM[14]*ProjM[11] + ModM[15]*ProjM[15];
//Clip:=MatrixMultiply(ModM, ProjM);
// extract frustum planes from clipping matrix
Planes[Right][A] := clip[ 3] - clip[ 0];
Planes[Right][B] := clip[ 7] - clip[ 4];
Planes[Right][C] := clip[11] - clip[ 8];
Planes[Right][D] := clip[15] - clip[12];
NormalizePlane(Right);
Planes[Left][A] := clip[ 3] + clip[ 0];
Planes[Left][B] := clip[ 7] + clip[ 4];
Planes[Left][C] := clip[11] + clip[ 8];
Planes[Left][D] := clip[15] + clip[12];
NormalizePlane(Left);
Planes[Bottom][A] := clip[ 3] + clip[ 1];
Planes[Bottom][B] := clip[ 7] + clip[ 5];
Planes[Bottom][C] := clip[11] + clip[ 9];
Planes[Bottom][D] := clip[15] + clip[13];
NormalizePlane(Bottom);
Planes[Top][A] := clip[ 3] - clip[ 1];
Planes[Top][B] := clip[ 7] - clip[ 5];
Planes[Top][C] := clip[11] - clip[ 9];
Planes[Top][D] := clip[15] - clip[13];
NormalizePlane(Top);
Planes[Back][A] := clip[ 3] - clip[ 2];
Planes[Back][B] := clip[ 7] - clip[ 6];
Planes[Back][C] := clip[11] - clip[10];
Planes[Back][D] := clip[15] - clip[14];
NormalizePlane(Back);
Planes[Front][A] := clip[ 3] + clip[ 2];
Planes[Front][B] := clip[ 7] + clip[ 6];
Planes[Front][C] := clip[11] + clip[10];
Planes[Front][D] := clip[15] + clip[14];
NormalizePlane(Front);
end;
function TFrustum.IsPointWithin(const p: TVector3f): Boolean;
var
i : Integer;
begin
Result:=true;
for i:=0 to 5 do
if (Planes[i][A]*p[A] + Planes[i][B]*p[B] + Planes[i][C]*p[C] + Planes[i][D]) <= 0 then begin
Result:=False;
exit;
end;
end;
function TFrustum.IsSphereWithin(const p: TVector3f; const r: Single): Boolean;
var
i : Integer;
begin
Result:=true;
for i:=0 to 5 do
if (Planes[i][A]*p[A] + Planes[i][B]*p[B] + Planes[i][C]*p[C] + Planes[i][D]) <= -r then begin
Result:=False;
exit;
end;
end;
function TFrustum.IsBoxWithin(const p, dim: TVector3f): Boolean;
// p: box position - NOTE: z is at bottom!
// dim: box dimensions
var
i : Integer;
begin
Result:=true;
for i:=0 to 5 do begin
if (Planes[i][A]*(p[A]-dim[A]/2) + Planes[i][B]*(p[B]-dim[B]/2) + Planes[i][C]*(p[C]) + Planes[i][D]) > 0 then continue;
if (Planes[i][A]*(p[A]-dim[A]/2) + Planes[i][B]*(p[B]+dim[B]/2) + Planes[i][C]*(p[C]) + Planes[i][D]) > 0 then continue;
if (Planes[i][A]*(p[A]-dim[A]/2) + Planes[i][B]*(p[B]+dim[B]/2) + Planes[i][C]*(p[C]+dim[C]) + Planes[i][D]) > 0 then continue;
if (Planes[i][A]*(p[A]-dim[A]/2) + Planes[i][B]*(p[B]-dim[B]/2) + Planes[i][C]*(p[C]+dim[C]) + Planes[i][D]) > 0 then continue;
if (Planes[i][A]*(p[A]+dim[A]/2) + Planes[i][B]*(p[B]-dim[B]/2) + Planes[i][C]*(p[C]) + Planes[i][D]) > 0 then continue;
if (Planes[i][A]*(p[A]+dim[A]/2) + Planes[i][B]*(p[B]+dim[B]/2) + Planes[i][C]*(p[C]) + Planes[i][D]) > 0 then continue;
if (Planes[i][A]*(p[A]+dim[A]/2) + Planes[i][B]*(p[B]+dim[B]/2) + Planes[i][C]*(p[C]+dim[C]) + Planes[i][D]) > 0 then continue;
if (Planes[i][A]*(p[A]+dim[A]/2) + Planes[i][B]*(p[B]-dim[B]/2) + Planes[i][C]*(p[C]+dim[C]) + Planes[i][D]) > 0 then continue;
Result := False;
end;
end;
initialization
Frustum:=TFrustum.Create;
finalization
Frustum.Free;
end.