Box3<Real> Wml::ContOrientedBox (int iQuantity, const Vector3<Real>* akPoint)
{
Box3<Real> kBox;
GaussPointsFit(iQuantity,akPoint,kBox.Center(),kBox.Axes(),
kBox.Extents());
// Let C be the box center and let U0, U1, and U2 be the box axes. Each
// input point is of the form X = C + y0*U0 + y1*U1 + y2*U2. The
// following code computes min(y0), max(y0), min(y1), max(y1), min(y2),
// and max(y2). The box center is then adjusted to be
// C' = C + 0.5*(min(y0)+max(y0))*U0 + 0.5*(min(y1)+max(y1))*U1 +
// 0.5*(min(y2)+max(y2))*U2
Vector3<Real> kDiff = akPoint[0] - kBox.Center();
Real fY0Min = kDiff.Dot(kBox.Axis(0)), fY0Max = fY0Min;
Real fY1Min = kDiff.Dot(kBox.Axis(1)), fY1Max = fY1Min;
Real fY2Min = kDiff.Dot(kBox.Axis(2)), fY2Max = fY2Min;
for (int i = 1; i < iQuantity; i++)
{
kDiff = akPoint[i] - kBox.Center();
Real fY0 = kDiff.Dot(kBox.Axis(0));
if ( fY0 < fY0Min )
fY0Min = fY0;
else if ( fY0 > fY0Max )
fY0Max = fY0;
Real fY1 = kDiff.Dot(kBox.Axis(1));
if ( fY1 < fY1Min )
fY1Min = fY1;
else if ( fY1 > fY1Max )
fY1Max = fY1;
Real fY2 = kDiff.Dot(kBox.Axis(2));
if ( fY2 < fY2Min )
fY2Min = fY2;
else if ( fY2 > fY2Max )
fY2Max = fY2;
}
kBox.Center() += (((Real)0.5)*(fY0Min+fY0Max))*kBox.Axis(0) +
(((Real)0.5)*(fY1Min+fY1Max))*kBox.Axis(1) +
(((Real)0.5)*(fY2Min+fY2Max))*kBox.Axis(2);
kBox.Extent(0) = ((Real)0.5)*(fY0Max - fY0Min);
kBox.Extent(1) = ((Real)0.5)*(fY1Max - fY1Min);
kBox.Extent(2) = ((Real)0.5)*(fY2Max - fY2Min);
return kBox;
}
bool Wml::ContOrientedBox (int iQuantity, const Vector3<Real>* akPoint,
const bool* abValid, Box3<Real>& rkBox)
{
if ( !GaussPointsFit(iQuantity,akPoint,abValid,rkBox.Center(),
rkBox.Axes(),rkBox.Extents()) )
{
return false;
}
// Let C be the box center and let U0, U1, and U2 be the box axes. Each
// input point is of the form X = C + y0*U0 + y1*U1 + y2*U2. The
// following code computes min(y0), max(y0), min(y1), max(y1), min(y2),
// and max(y2). The box center is then adjusted to be
// C' = C + 0.5*(min(y0)+max(y0))*U0 + 0.5*(min(y1)+max(y1))*U1 +
// 0.5*(min(y2)+max(y2))*U2
// get first valid vertex
Vector3<Real> kDiff;
Real fY0Min = (Real)0.0, fY0Max = (Real)0.0;
Real fY1Min = (Real)0.0, fY1Max = (Real)0.0;
Real fY2Min = (Real)0.0, fY2Max = (Real)0.0;
int i;
for (i = 0; i < iQuantity; i++)
{
if ( abValid[i] )
{
kDiff = akPoint[i] - rkBox.Center();
fY0Min = kDiff.Dot(rkBox.Axis(0));
fY0Max = fY0Min;
fY1Min = kDiff.Dot(rkBox.Axis(1));
fY1Max = fY1Min;
fY2Min = kDiff.Dot(rkBox.Axis(2));
fY2Max = fY2Min;
break;
}
}
for (i++; i < iQuantity; i++)
{
if ( abValid[i] )
{
kDiff = akPoint[i] - rkBox.Center();
Real fY0 = kDiff.Dot(rkBox.Axis(0));
if ( fY0 < fY0Min )
fY0Min = fY0;
else if ( fY0 > fY0Max )
fY0Max = fY0;
Real fY1 = kDiff.Dot(rkBox.Axis(1));
if ( fY1 < fY1Min )
fY1Min = fY1;
else if ( fY1 > fY1Max )
fY1Max = fY1;
Real fY2 = kDiff.Dot(rkBox.Axis(2));
if ( fY2 < fY2Min )
fY2Min = fY2;
else if ( fY2 > fY2Max )
fY2Max = fY2;
}
}
rkBox.Center() += (0.5f*(fY0Min+fY0Max))*rkBox.Axis(0)
+ (0.5f*(fY1Min+fY1Max))*rkBox.Axis(1) +
(0.5f*(fY2Min+fY2Max))*rkBox.Axis(2);
rkBox.Extent(0) = 0.5f*(fY0Max - fY0Min);
rkBox.Extent(1) = 0.5f*(fY1Max - fY1Min);
rkBox.Extent(2) = 0.5f*(fY2Max - fY2Min);
return true;
}
Box3<Real> Wml::MergeBoxes (const Box3<Real>& rkBox0,
const Box3<Real>& rkBox1)
{
// construct a box that contains the input boxes
Box3<Real> kBox;
// The first guess at the box center. This value will be updated later
// after the input box vertices are projected onto axes determined by an
// average of box axes.
kBox.Center() = ((Real)0.5)*(rkBox0.Center() + rkBox1.Center());
// A box's axes, when viewed as the columns of a matrix, form a rotation
// matrix. The input box axes are converted to quaternions. The average
// quaternion is computed, then normalized to unit length. The result is
// the slerp of the two input quaternions with t-value of 1/2. The result
// is converted back to a rotation matrix and its columns are selected as
// the merged box axes.
Quaternion<Real> kQ0, kQ1;
kQ0.FromRotationMatrix(rkBox0.Axes());
kQ1.FromRotationMatrix(rkBox1.Axes());
if ( kQ0.Dot(kQ1) < 0.0f )
kQ1 = -kQ1;
Quaternion<Real> kQ = kQ0 + kQ1;
Real fInvLength = Math<Real>::InvSqrt(kQ.Dot(kQ));
kQ = fInvLength*kQ;
kQ.ToRotationMatrix(kBox.Axes());
// Project the input box vertices onto the merged-box axes. Each axis
// D[i] containing the current center C has a minimum projected value
// pmin[i] and a maximum projected value pmax[i]. The corresponding end
// points on the axes are C+pmin[i]*D[i] and C+pmax[i]*D[i]. The point C
// is not necessarily the midpoint for any of the intervals. The actual
// box center will be adjusted from C to a point C' that is the midpoint
// of each interval,
// C' = C + sum_{i=0}^2 0.5*(pmin[i]+pmax[i])*D[i]
// The box extents are
// e[i] = 0.5*(pmax[i]-pmin[i])
int i, j;
Real fDot;
Vector3<Real> akVertex[8], kDiff;
Vector3<Real> kMin = Vector3<Real>::ZERO;
Vector3<Real> kMax = Vector3<Real>::ZERO;
rkBox0.ComputeVertices(akVertex);
for (i = 0; i < 8; i++)
{
kDiff = akVertex[i] - kBox.Center();
for (j = 0; j < 3; j++)
{
fDot = kDiff.Dot(kBox.Axis(j));
if ( fDot > kMax[j] )
kMax[j] = fDot;
else if ( fDot < kMin[j] )
kMin[j] = fDot;
}
}
rkBox1.ComputeVertices(akVertex);
for (i = 0; i < 8; i++)
{
kDiff = akVertex[i] - kBox.Center();
for (j = 0; j < 3; j++)
{
fDot = kDiff.Dot(kBox.Axis(j));
if ( fDot > kMax[j] )
kMax[j] = fDot;
else if ( fDot < kMin[j] )
kMin[j] = fDot;
}
}
// [kMin,kMax] is the axis-aligned box in the coordinate system of the
// merged box axes. Update the current box center to be the center of
// the new box. Compute the extens based on the new center.
for (j = 0; j < 3; j++)
{
kBox.Center() += (((Real)0.5)*(kMax[j]+kMin[j]))*kBox.Axis(j);
kBox.Extent(j) = ((Real)0.5)*(kMax[j]-kMin[j]);
}
return kBox;
}
