//-----------------------------------------------------------------------------
// Given an inverse projection matrix, take the extremes of the space in transformed into world space and
// get a bounding sphere.
//-----------------------------------------------------------------------------
void CalculateSphereFromProjectionMatrixInverse( const VMatrix &volumeToWorld, Vector *pCenter, float *pflRadius )
{
// FIXME: Could maybe do better than the compile with all of these multiplies by 0 and 1.
// Need 3 points: the endpoint of the line through the center of the near + far planes,
// and one point on the far plane. From that, we can derive a point somewhere on the center line
// which would produce the smallest bounding sphere.
Vector vecCenterNear, vecCenterFar, vecNearEdge, vecFarEdge;
Vector3DMultiplyPositionProjective( volumeToWorld, Vector( 0.5f, 0.5f, 0.0f ), vecCenterNear );
Vector3DMultiplyPositionProjective( volumeToWorld, Vector( 0.5f, 0.5f, 1.0f ), vecCenterFar );
Vector3DMultiplyPositionProjective( volumeToWorld, Vector( 0.0f, 0.0f, 0.0f ), vecNearEdge );
Vector3DMultiplyPositionProjective( volumeToWorld, Vector( 0.0f, 0.0f, 1.0f ), vecFarEdge );
// Let the distance between the near + far center points = l
// Let the distance between the near center point + near edge point = h1
// Let the distance between the far center point + far edge point = h2
// Let the distance along the center line from the near point to the sphere center point = x
// Then let the distance between the sphere center point + near edge point ==
// the distance between the sphere center point + far edge point == r == radius of sphere
// Then h1^2 + x^2 == r^2 == (l-x)^2 + h2^2
// h1^x + x^2 = l^2 - 2 * l * x + x^2 + h2^2
// 2 * l * x = l^2 + h2^2 - h1^2
// x = (l^2 + h2^2 - h1^2) / (2 * l)
// r = sqrt( hl^1 + x^2 )
Vector vecDelta;
VectorSubtract( vecCenterFar, vecCenterNear, vecDelta );
float l = vecDelta.Length();
float h1Sqr = vecCenterNear.DistToSqr( vecNearEdge );
float h2Sqr = vecCenterFar.DistToSqr( vecFarEdge );
float x = (l*l + h2Sqr - h1Sqr) / (2.0f * l);
VectorMA( vecCenterNear, (x / l), vecDelta, *pCenter );
*pflRadius = sqrt( h1Sqr + x*x );
}
static inline void FrustumPlanesFromMatrixHelper( const VMatrix &shadowToWorld, const Vector &p1, const Vector &p2, const Vector &p3,
Vector &normal, float &dist )
{
Vector world1, world2, world3;
Vector3DMultiplyPositionProjective( shadowToWorld, p1, world1 );
Vector3DMultiplyPositionProjective( shadowToWorld, p2, world2 );
Vector3DMultiplyPositionProjective( shadowToWorld, p3, world3 );
Vector v1, v2;
VectorSubtract( world2, world1, v1 );
VectorSubtract( world3, world1, v2 );
CrossProduct( v1, v2, normal );
VectorNormalize( normal );
dist = DotProduct( normal, world1 );
}
void CCamera::ViewToWorld( const Vector2D &vView, Vector& vWorld)
{
Vector vView3D;
vView3D.x = 2.0 * vView.x / m_nViewWidth - 1;
vView3D.y = -2.0 * vView.y / m_nViewHeight + 1;
vView3D.z = 0;
Vector3DMultiplyPositionProjective( m_InvViewProjMatrix, vView3D, vWorld );
}
void CCamera::WorldToView( const Vector& vWorld, Vector2D &vView )
{
Vector vView3D;
Vector3DMultiplyPositionProjective( m_ViewProjMatrix, vWorld, vView3D );
// NOTE: The negative sign on y is because wc wants to think about screen
// coordinates in a different way than the material system
vView.x = 0.5 * (vView3D.x + 1.0) * m_nViewWidth;
vView.y = 0.5 * (-vView3D.y + 1.0) * m_nViewHeight;
}
static inline void CalculateAABBForNormalizedFrustum_Helper( float x, float y, float z, const VMatrix &volumeToWorld, Vector &mins, Vector &maxs )
{
Vector volumeSpacePos( x, y, z );
// Make sure it's been clipped
Assert( volumeSpacePos[0] >= -1e-3f );
Assert( volumeSpacePos[0] - 1.0f <= 1e-3f );
Assert( volumeSpacePos[1] >= -1e-3f );
Assert( volumeSpacePos[1] - 1.0f <= 1e-3f );
Assert( volumeSpacePos[2] >= -1e-3f );
Assert( volumeSpacePos[2] - 1.0f <= 1e-3f );
Vector worldPos;
Vector3DMultiplyPositionProjective( volumeToWorld, volumeSpacePos, worldPos );
AddPointToBounds( worldPos, mins, maxs );
}
static int vmatrix_Vector3DMultiplyPositionProjective (lua_State *L) {
Vector3DMultiplyPositionProjective(luaL_checkvmatrix(L, 1), luaL_checkvector(L, 2), luaL_checkvector(L, 3));
return 0;
}
