## Monday, October 6, 2008

### Collision detection using Separating Axis Theorem

Currently i am working on a graphics engine , which uses loose octree for occlusion culling as well as collision detection..

It works as i am expected. I have implemented  the SAT algoritham to test BOX-Triangle intersection test. It works well..Currently i am checking all the triangles inside the current camera node, It doesn't seems practical with detailes scene.

I need to add support for collision mesh( These mesh  are not rendered,they are just used for collision detection).Hmm.I can see the need for a level editor. Before that i am would like to respond my camera accoring to the geometry in the scene.

Following is the SAT code for triangle - Box intersection , I couldn't find any c++ code in internet ( Muller's is there , it is cryptic for me as well as it is not c++)

template
<typename T>
Interfaces3D::InterSection CBBox<T>::IsInsideBox(
const Triangle<T>& refTri ) const
{

// If three points are inside the box, definitily the triangle is inside the ABBBox.
if( IsInsideBox( refTri.m_Pt1 ) &&
IsInsideBox( refTri.m_Pt2 ) && IsInsideBox( refTri.m_Pt3 ) )
return Interfaces3D::InterSectionIn;

Math3D::vector<T> xAxis(1,0,0);
Math3D::vector<T> yAxis(0,1,0);
Math3D::vector<T> zAxis(0,0,1);

//..............................................................
// Intersection test using SAT (separating Axis test) algorithm.
//..............................................................
float fMin,fMax;
float fBoxMin,fBoxMax;
float fProjTri[3] = { 0,0,0 };
float fProjBox[2] = { 0,0 };

// First test is agnist the AABBox's cardianl axis.
fProjTri[0] = refTri.m_Pt1.x;
fProjTri[1] = refTri.m_Pt2.x;
fProjTri[2] = refTri.m_Pt3.x;

FindMinMax( fProjTri,3,fMin,fMax );

if( (fMin < m_XL && fMax < m_XL ) || (fMin > m_XR && fMax > m_XR ) )
return Interfaces3D::InterSectionOut; // the triangle is outside.

fProjTri[0] = refTri.m_Pt1.y;
fProjTri[1] = refTri.m_Pt2.y;
fProjTri[2] = refTri.m_Pt3.y;

FindMinMax( fProjTri,3,fMin,fMax );

if( (fMin < m_YB && fMax < m_YB ) || (fMin > m_YT && fMax > m_YT ) )
return Interfaces3D::InterSectionOut; // the triangle is outside.

fProjTri[0] = refTri.m_Pt1.z;
fProjTri[1] = refTri.m_Pt2.z;
fProjTri[2] = refTri.m_Pt3.z;

FindMinMax( fProjTri,3,fMin,fMax );

if( (fMin < m_ZF && fMax < m_ZF ) || (fMin > m_ZN && fMax > m_ZN ) )
return Interfaces3D::InterSectionOut; // the triangle is outside.
// Second test is agnist triangles normal.
Math3D::vector<T> vtNormal = refTri.m_Normal;

// project the triangle coordinates on this normal as well as the AABB corners.

// projecting Box's coordinates
Math3D::vector<T> vtRadius = GetTopLeftNear() - GetPosition();

float fExtent = vtNormal.Dot( vtRadius );
float fCenterBox = vtNormal.Dot( GetPosition() );
fProjBox[0] = fCenterBox + fExtent;
fProjBox[1] = fCenterBox - fExtent;

FindMinMax( fProjBox, 2,fBoxMin,fBoxMax );

// projecting triangle coordinates
fProjTri[0] = vtNormal.Dot( refTri.m_Pt1 );
fProjTri[1] = vtNormal.Dot( refTri.m_Pt2 );
fProjTri[2] = vtNormal.Dot( refTri.m_Pt3 );

FindMinMax( fProjTri, 3,fMin,fMax );
// Check for overlapping between pronected coordinates.
// if not overlapping , no intersection.
if( (fMin < fBoxMin && fMax < fBoxMin ) || (fMin > fBoxMax && fMax > fBoxMax ) )
return Interfaces3D::InterSectionOut; // the triangle is outside.

// Next possible SAT axis are the Cross product of each tri edges with
// box's cardinal axis.

Math3D::vector<T> satAxis[9];
Math3D::vector<T> vTmp = (refTri.m_Pt1 - refTri.m_Pt2);

// edge 0 and X,Y,Z axis
satAxis[0] = vTmp.Cross( xAxis).normalize() ;
satAxis[1] = vTmp.Cross( yAxis).normalize() ;
satAxis[2] = vTmp.Cross( zAxis).normalize() ;

// edge 1 and X,Y,Z axis
vTmp = (refTri.m_Pt3 - refTri.m_Pt2);
satAxis[3] = vTmp.Cross( xAxis).normalize() ;
satAxis[4] = vTmp.Cross( yAxis).normalize() ;
satAxis[5] = vTmp.Cross( zAxis).normalize() ;

// edge 2 and X,Y,Z axis
vTmp = (refTri.m_Pt1 - refTri.m_Pt3);

satAxis[6] = vTmp.Cross( xAxis).normalize() ;
satAxis[7] = vTmp.Cross( yAxis).normalize() ;
satAxis[8] = vTmp.Cross( zAxis).normalize() ;

for( int i = 0; i < 9 ; i ++ )
{

fExtent = satAxis[i].Dot( vtRadius );
fCenterBox = satAxis[i].Dot( GetPosition() );
fProjBox[0] = fCenterBox + fExtent;
fProjBox[1] = fCenterBox - fExtent;
FindMinMax( fProjBox, 2,fBoxMin,fBoxMax );
// projecting triangle coordinates
fProjTri[0] = satAxis[i].Dot( refTri.m_Pt1 );
fProjTri[1] = satAxis[i].Dot( refTri.m_Pt2 );
fProjTri[2] = satAxis[i].Dot( refTri.m_Pt3 );
FindMinMax( fProjTri, 3,fMin,fMax );
// check for overlapping on the SAT axis
if( (fMin < fBoxMin && fMax < fBoxMin ) || (fMin > fBoxMax && fMax > fBoxMax ) )
return Interfaces3D::InterSectionOut; // the triangle is outside.
}

return Interfaces3D::InterSectionIntersect;

}