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uFrustum.pas
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uFrustum.pas
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unit uFrustum;
interface
uses u3DTypes;
const
_planeLeft = 0;
_planeRight = 1;
_planeBottom = 2;
_planeTop = 3;
_planeNear = 4;
_planeFar = 5;
type
// de 6 planes van het frustum: left/right/bottom/top/near/far
TFrustumPlanes = array[_planeLeft.._planeFar] of TPlane;
PFrustum = ^TFrustum;
TFrustum = class(TObject)
private
Planes: TFrustumPlanes; // de box, opgemaakt uit de clip-planes van het frustum
public
// bereken de frustum-planes vanaf de huidige (OpenGL) camera-instellingen
procedure Calculate_glFrustumPlanes;
// bereken de frustum-planes vanaf de opgegeven camera-instellingen
procedure Calculate_glFrustumPlanes_Lookat(CameraPosition,CameraTarget,CameraUpY: TVector);
//
function Get_glFrustumPlanes : TFrustumPlanes;
function PointInside(const V: TVector) : boolean;
function AABBInside(const BoundingBox: TBoundingBox): boolean; overload; //Axis Aligned Bounding Box
function AABBInside(const Origin: TVector; const BoundingBox: TBoundingBox): boolean; overload;
function SphereInside(Sphere: TSphere): boolean;
end;
implementation
uses OpenGL, uCalc;
procedure TFrustum.Calculate_glFrustumPlanes;
var M, P, CC: TMatrix4x4;
C : array[0..15] of Single absolute CC;
C0,C1,C2,C3: Single;
Len, rLen: Single;
begin
// OpenGL matrices opvragen // | 0 4 8 12 |
glGetFloatv(GL_MODELVIEW_MATRIX, @M); // M = | 1 5 9 13 |
glGetFloatv(GL_PROJECTION_MATRIX, @P); // | 2 6 10 14 |
// | 3 7 11 15 |
// in 1 matrix combineren
CC := MultiplyMatrix(M,P);
(*
// C.column0
C[0] := M[0]*P[0] + M[1]*P[4] + M[2]*P[8] + M[3]*P[12];
C[1] := M[0]*P[1] + M[1]*P[5] + M[2]*P[9] + M[3]*P[13];
C[2] := M[0]*P[2] + M[1]*P[6] + M[2]*P[10] + M[3]*P[14];
C[3] := M[0]*P[3] + M[1]*P[7] + M[2]*P[11] + M[3]*P[15];
// C.column1
C[4] := M[4]*P[0] + M[5]*P[4] + M[6]*P[8] + M[7]*P[12];
C[5] := M[4]*P[1] + M[5]*P[5] + M[6]*P[9] + M[7]*P[13];
C[6] := M[4]*P[2] + M[5]*P[6] + M[6]*P[10] + M[7]*P[14];
C[7] := M[4]*P[3] + M[5]*P[7] + M[6]*P[11] + M[7]*P[15];
// C.column2
C[8] := M[8]*P[0] + M[9]*P[4] + M[10]*P[8] + M[11]*P[12];
C[9] := M[8]*P[1] + M[9]*P[5] + M[10]*P[9] + M[11]*P[13];
C[10] := M[8]*P[2] + M[9]*P[6] + M[10]*P[10] + M[11]*P[14];
C[11] := M[8]*P[3] + M[9]*P[7] + M[10]*P[11] + M[11]*P[15];
// C.column3
C[12] := M[12]*P[0] + M[13]*P[4] + M[14]*P[8] + M[15]*P[12];
C[13] := M[12]*P[1] + M[13]*P[5] + M[14]*P[9] + M[15]*P[13];
C[14] := M[12]*P[2] + M[13]*P[6] + M[14]*P[10] + M[15]*P[14];
C[15] := M[12]*P[3] + M[13]*P[7] + M[14]*P[11] + M[15]*P[15];
*)
// left plane
Planes[_planeLeft].Normal := Vector( C[3]+C[0], C[7]+C[4], C[11]+C[8] );
Planes[_planeLeft].d := C[15]+C[12];
// right plane
Planes[_planeRight].Normal := Vector( C[3]-C[0], C[7]-C[4], C[11]-C[8] );
Planes[_planeRight].d := C[15]-C[12];
// bottom plane
Planes[_planeBottom].Normal := Vector( C[3]+C[1], C[7]+C[5], C[11]+C[9] );
Planes[_planeBottom].d := C[15]+C[13];
// top plane
Planes[_planeTop].Normal := Vector( C[3]-C[1], C[7]-C[5], C[11]-C[9] );
Planes[_planeTop].d := C[15]-C[13];
// near plane
Planes[_planeNear].Normal := Vector( C[3]+C[2], C[7]+C[6], C[11]+C[10] );
Planes[_planeNear].d := C[15]+C[14];
// far plane
Planes[_planeFar].Normal := Vector( C[3]-C[2], C[7]-C[6], C[11]-C[10] );
Planes[_planeFar].d := C[15]-C[14];
end;
procedure TFrustum.Calculate_glFrustumPlanes_Lookat(CameraPosition, CameraTarget, CameraUpY: TVector);
begin
glMatrixMode(GL_MODELVIEW);
glPushMatrix;
glMatrixMode(GL_PROJECTION);
glPushMatrix;
glMatrixMode(GL_MODELVIEW);
glLoadIdentity;
// plaats de camera
gluLookAt(CameraPosition.X,CameraPosition.Y,CameraPosition.Z,
CameraTarget.X,CameraTarget.Y,CameraTarget.Z,
CameraUpY.X,CameraUpY.Y,CameraUpY.Z);
// bereken de planes van het frustum (tbv. frustum culling)
Calculate_glFrustumPlanes;
glMatrixMode(GL_PROJECTION);
glPopMatrix;
glMatrixMode(GL_MODELVIEW);
glPopMatrix;
end;
function TFrustum.Get_glFrustumPlanes : TFrustumPlanes;
begin
Result := Planes;
end;
function TFrustum.PointInside(const V: TVector) : boolean;
var i: integer;
begin
Result := false;
for i:=_planeLeft to _planeFar do
// als het punt achter een frustum-vlak ligt, dan zijn we al klaar..result==false
if DotProduct(Planes[i].Normal, V) + Planes[i].d < 0 then Exit;
Result := true;
end;
// gedeeltelijk inside?? dan resultaat = true
function TFrustum.AABBInside(const BoundingBox: TBoundingBox): boolean;
var bb: TBoundingBox;
V1,V2,V3,V4,V5,V6,V7,V8: TVector;
PlaneBB, Plane3: TPlane;
S, S0,S1,SDir: TVector;
i: integer;
begin
// als er 1 punt van de boundingbox vóór een frustum-vlak ligt, dan zijn we al klaar..result==true
Result := true;
V1 := BoundingBox.Min;
if PointInside(V1) then Exit;
V2 := BoundingBox.Max;
if PointInside(V2) then Exit;
V3 := Vector(V2.X,V1.Y,V1.Z);
if PointInside(V3) then Exit;
V4 := Vector(V2.X,V2.Y,V1.Z);
if PointInside(V4) then Exit;
V5 := Vector(V1.X,V2.Y,V1.Z);
if PointInside(V5) then Exit;
V6 := Vector(V1.X,V1.Y,V2.Z);
if PointInside(V6) then Exit;
V7 := Vector(V2.X,V1.Y,V2.Z);
if PointInside(V7) then Exit;
V8 := Vector(V1.X,V2.Y,V2.Z);
if PointInside(V8) then Exit;
Result := false;
// er is geen enkel hoekpunt van de box binnen het frustum,
// controleer of een vlak van de box zichtbaar is in beeld (gedeeltelijk in frustum).
//todo..
end;
function TFrustum.AABBInside(const Origin: TVector; const BoundingBox: TBoundingBox): boolean;
var bb: TBoundingBox;
V1,V2,V3,V4,V5,V6,V7,V8: TVector;
begin
bb.Min := AddVector(BoundingBox.Min, Origin); //AABB op location van entity plaatsen
bb.Max := AddVector(BoundingBox.Max, Origin);
Result := AABBInside(bb);
end;
function TFrustum.SphereInside(Sphere: TSphere): boolean;
begin
(*
Result := false;
if Box[0][0]*Sphere.Origin.X + Box[0][1]*Sphere.Origin.Y + Box[0][2]*Sphere.Origin.Z + Box[0][3] <= -Sphere.Radius then Exit;
if Box[1][0]*Sphere.Origin.X + Box[1][1]*Sphere.Origin.Y + Box[1][2]*Sphere.Origin.Z + Box[1][3] <= -Sphere.Radius then Exit;
if Box[2][0]*Sphere.Origin.X + Box[2][1]*Sphere.Origin.Y + Box[2][2]*Sphere.Origin.Z + Box[2][3] <= -Sphere.Radius then Exit;
if Box[3][0]*Sphere.Origin.X + Box[3][1]*Sphere.Origin.Y + Box[3][2]*Sphere.Origin.Z + Box[3][3] <= -Sphere.Radius then Exit;
if Box[4][0]*Sphere.Origin.X + Box[4][1]*Sphere.Origin.Y + Box[4][2]*Sphere.Origin.Z + Box[4][3] <= -Sphere.Radius then Exit;
if Box[5][0]*Sphere.Origin.X + Box[5][1]*Sphere.Origin.Y + Box[5][2]*Sphere.Origin.Z + Box[5][3] <= -Sphere.Radius then Exit;
Result := true;
*)
end;
end.