MinBox3<Real>::MinBox3 (int numPoints, const Vector3<Real>* points,
Real epsilon, Query::Type queryType)
{
// Get the convex hull of the points.
ConvexHull3<Real> kHull(numPoints,(Vector3<Real>*)points, epsilon, false,
queryType);
int hullDim = kHull.GetDimension();
if (hullDim == 0)
{
mMinBox.Center = points[0];
mMinBox.Axis[0] = Vector3<Real>::UNIT_X;
mMinBox.Axis[1] = Vector3<Real>::UNIT_Y;
mMinBox.Axis[2] = Vector3<Real>::UNIT_Z;
mMinBox.Extent[0] = (Real)0;
mMinBox.Extent[1] = (Real)0;
mMinBox.Extent[2] = (Real)0;
return;
}
if (hullDim == 1)
{
ConvexHull1<Real>* pkHull1 = kHull.GetConvexHull1();
const int* hullIndices = pkHull1->GetIndices();
mMinBox.Center =
((Real)0.5)*(points[hullIndices[0]] + points[hullIndices[1]]);
Vector3<Real> diff =
points[hullIndices[1]] - points[hullIndices[0]];
mMinBox.Extent[0] = ((Real)0.5)*diff.Normalize();
mMinBox.Extent[1] = (Real)0;
mMinBox.Extent[2] = (Real)0;
mMinBox.Axis[0] = diff;
Vector3<Real>::GenerateComplementBasis(mMinBox.Axis[1],
mMinBox.Axis[2], mMinBox.Axis[0]);
delete0(pkHull1);
return;
}
int i, j;
Vector3<Real> origin, diff, U, V, W;
Vector2<Real>* points2;
Box2<Real> box2;
if (hullDim == 2)
{
// When ConvexHull3 reports that the point set is 2-dimensional, the
// caller is responsible for projecting the points onto a plane and
// calling ConvexHull2. ConvexHull3 does provide information about
// the plane of the points. In this application, we need only
// project the input points onto that plane and call ContMinBox in
// two dimensions.
// Get a coordinate system relative to the plane of the points.
origin = kHull.GetPlaneOrigin();
W = kHull.GetPlaneDirection(0).Cross(kHull.GetPlaneDirection(1));
Vector3<Real>::GenerateComplementBasis(U, V, W);
// Project the input points onto the plane.
points2 = new1<Vector2<Real> >(numPoints);
for (i = 0; i < numPoints; ++i)
{
diff = points[i] - origin;
points2[i].X() = U.Dot(diff);
points2[i].Y() = V.Dot(diff);
}
// Compute the minimum area box in 2D.
box2 = MinBox2<Real>(numPoints, points2, epsilon, queryType, false);
delete1(points2);
// Lift the values into 3D.
mMinBox.Center = origin + box2.Center.X()*U + box2.Center.Y()*V;
mMinBox.Axis[0] = box2.Axis[0].X()*U + box2.Axis[0].Y()*V;
mMinBox.Axis[1] = box2.Axis[1].X()*U + box2.Axis[1].Y()*V;
mMinBox.Axis[2] = W;
mMinBox.Extent[0] = box2.Extent[0];
mMinBox.Extent[1] = box2.Extent[1];
mMinBox.Extent[2] = (Real)0;
return;
}
int hullQuantity = kHull.GetNumSimplices();
const int* hullIndices = kHull.GetIndices();
Real volume, minVolume = Math<Real>::MAX_REAL;
// Create the unique set of hull vertices to minimize the time spent
// projecting vertices onto planes of the hull faces.
std::set<int> uniqueIndices;
for (i = 0; i < 3*hullQuantity; ++i)
{
uniqueIndices.insert(hullIndices[i]);
}
// Use the rotating calipers method on the projection of the hull onto
// the plane of each face. Also project the hull onto the normal line
// of each face. The minimum area box in the plane and the height on
// the line produce a containing box. If its volume is smaller than the
// current volume, this box is the new candidate for the minimum volume
// box. The unique edges are accumulated into a set for use by a later
// step in the algorithm.
const int* currentHullIndex = hullIndices;
Real height, minHeight, maxHeight;
std::set<EdgeKey> edges;
points2 = new1<Vector2<Real> >(uniqueIndices.size());
for (i = 0; i < hullQuantity; ++i)
{
// Get the triangle.
int v0 = *currentHullIndex++;
int v1 = *currentHullIndex++;
int v2 = *currentHullIndex++;
// Save the edges for later use.
edges.insert(EdgeKey(v0, v1));
edges.insert(EdgeKey(v1, v2));
edges.insert(EdgeKey(v2, v0));
// Get 3D coordinate system relative to plane of triangle.
origin = (points[v0] + points[v1] + points[v2])/(Real)3.0;
Vector3<Real> edge1 = points[v1] - points[v0];
Vector3<Real> edge2 = points[v2] - points[v0];
W = edge2.UnitCross(edge1); // inner-pointing normal
if (W == Vector3<Real>::ZERO)
{
// The triangle is needle-like, so skip it.
continue;
}
Vector3<Real>::GenerateComplementBasis(U, V, W);
// Project points onto plane of triangle, onto normal line of plane.
// TO DO. In theory, minHeight should be zero since W points to the
// interior of the hull. However, the snap rounding used in the 3D
// convex hull finder involves loss of precision, which in turn can
// cause a hull facet to have the wrong ordering (clockwise instead
// of counterclockwise when viewed from outside the hull). The
// height calculations here trap that problem (the incorrectly ordered
// face will not affect the minimum volume box calculations).
minHeight = (Real)0;
maxHeight = (Real)0;
j = 0;
std::set<int>::const_iterator iter = uniqueIndices.begin();
while (iter != uniqueIndices.end())
{
int index = *iter++;
diff = points[index] - origin;
points2[j].X() = U.Dot(diff);
points2[j].Y() = V.Dot(diff);
height = W.Dot(diff);
if (height > maxHeight)
{
maxHeight = height;
}
else if (height < minHeight)
{
minHeight = height;
}
j++;
}
if (-minHeight > maxHeight)
{
maxHeight = -minHeight;
}
// Compute minimum area box in 2D.
box2 = MinBox2<Real>((int)uniqueIndices.size(), points2, epsilon,
queryType, false);
// Update current minimum-volume box (if necessary).
volume = maxHeight*box2.Extent[0]*box2.Extent[1];
if (volume < minVolume)
{
minVolume = volume;
// Lift the values into 3D.
mMinBox.Extent[0] = box2.Extent[0];
mMinBox.Extent[1] = box2.Extent[1];
mMinBox.Extent[2] = ((Real)0.5)*maxHeight;
mMinBox.Axis[0] = box2.Axis[0].X()*U + box2.Axis[0].Y()*V;
mMinBox.Axis[1] = box2.Axis[1].X()*U + box2.Axis[1].Y()*V;
mMinBox.Axis[2] = W;
mMinBox.Center = origin + box2.Center.X()*U + box2.Center.Y()*V
+ mMinBox.Extent[2]*W;
}
}
// The minimum-volume box can also be supported by three mutually
// orthogonal edges of the convex hull. For each triple of orthogonal
// edges, compute the minimum-volume box for that coordinate frame by
// projecting the points onto the axes of the frame.
std::set<EdgeKey>::const_iterator e2iter;
for (e2iter = edges.begin(); e2iter != edges.end(); e2iter++)
{
W = points[e2iter->V[1]] - points[e2iter->V[0]];
W.Normalize();
std::set<EdgeKey>::const_iterator e1iter = e2iter;
for (++e1iter; e1iter != edges.end(); e1iter++)
{
V = points[e1iter->V[1]] - points[e1iter->V[0]];
V.Normalize();
Real dot = V.Dot(W);
if (Math<Real>::FAbs(dot) > Math<Real>::ZERO_TOLERANCE)
{
continue;
}
std::set<EdgeKey>::const_iterator e0iter = e1iter;
for (++e0iter; e0iter != edges.end(); e0iter++)
{
U = points[e0iter->V[1]] - points[e0iter->V[0]];
U.Normalize();
dot = U.Dot(V);
if (Math<Real>::FAbs(dot) > Math<Real>::ZERO_TOLERANCE)
{
continue;
}
dot = U.Dot(W);
if (Math<Real>::FAbs(dot) > Math<Real>::ZERO_TOLERANCE)
{
continue;
}
// The three edges are mutually orthogonal. Project the
// hull points onto the lines containing the edges. Use
// hull point zero as the origin.
Real umin = (Real)0, umax = (Real)0;
Real vmin = (Real)0, vmax = (Real)0;
Real wmin = (Real)0, wmax = (Real)0;
origin = points[hullIndices[0]];
std::set<int>::const_iterator iter = uniqueIndices.begin();
while (iter != uniqueIndices.end())
{
int index = *iter++;
diff = points[index] - origin;
Real fU = U.Dot(diff);
if (fU < umin)
{
umin = fU;
}
else if (fU > umax)
{
umax = fU;
}
Real fV = V.Dot(diff);
if (fV < vmin)
{
vmin = fV;
}
else if (fV > vmax)
{
vmax = fV;
}
Real fW = W.Dot(diff);
if (fW < wmin)
{
wmin = fW;
}
else if (fW > wmax)
{
wmax = fW;
}
}
Real uExtent = ((Real)0.5)*(umax - umin);
Real vExtent = ((Real)0.5)*(vmax - vmin);
Real wExtent = ((Real)0.5)*(wmax - wmin);
// Update current minimum-volume box (if necessary).
volume = uExtent*vExtent*wExtent;
if (volume < minVolume)
{
minVolume = volume;
mMinBox.Extent[0] = uExtent;
mMinBox.Extent[1] = vExtent;
mMinBox.Extent[2] = wExtent;
mMinBox.Axis[0] = U;
mMinBox.Axis[1] = V;
mMinBox.Axis[2] = W;
mMinBox.Center = origin +
((Real)0.5)*(umin+umax)*U +
((Real)0.5)*(vmin+vmax)*V +
((Real)0.5)*(wmin+wmax)*W;
}
}
}
}
delete1(points2);
}
Box3<Real> ContMinBox (int iQuantity, const Vector3<Real>* akPoint,
Real fEpsilon, Query::Type eQueryType)
{
Box3<Real> kBox;
// Get the convex hull of the points.
ConvexHull3<Real> kHull(iQuantity,(Vector3<Real>*)akPoint,fEpsilon,false,
eQueryType);
int iHDim = kHull.GetDimension();
int iHQuantity;
const int* aiHIndex;
if (iHDim == 0)
{
kBox.Center = akPoint[0];
kBox.Axis[0] = Vector3<Real>::UNIT_X;
kBox.Axis[1] = Vector3<Real>::UNIT_Y;
kBox.Axis[2] = Vector3<Real>::UNIT_Z;
kBox.Extent[0] = (Real)0.0;
kBox.Extent[1] = (Real)0.0;
kBox.Extent[2] = (Real)0.0;
return kBox;
}
if (iHDim == 1)
{
ConvexHull1<Real>* pkHull1 = kHull.GetConvexHull1();
aiHIndex = pkHull1->GetIndices();
kBox.Center = ((Real)0.5)*(akPoint[aiHIndex[0]]+akPoint[aiHIndex[1]]);
Vector3<Real> kDiff = akPoint[aiHIndex[1]] - akPoint[aiHIndex[0]];
kBox.Extent[0] = ((Real)0.5)*kDiff.Normalize();
kBox.Extent[1] = (Real)0.0;
kBox.Extent[2] = (Real)0.0;
kBox.Axis[0] = kDiff;
Vector3<Real>::GenerateComplementBasis(kBox.Axis[1],kBox.Axis[2],
kBox.Axis[0]);
WM4_DELETE pkHull1;
return kBox;
}
int i, j;
Vector3<Real> kOrigin, kDiff, kU, kV, kW;
Vector2<Real>* akPoint2;
Box2<Real> kBox2;
if (iHDim == 2)
{
// When ConvexHull3 reports that the point set is 2-dimensional, the
// caller is responsible for projecting the points onto a plane and
// calling ConvexHull2. ConvexHull3 does provide information about
// the plane of the points. In this application, we need only
// project the input points onto that plane and call ContMinBox in
// two dimensions.
// Get a coordinate system relative to the plane of the points.
kOrigin = kHull.GetPlaneOrigin();
kW = kHull.GetPlaneDirection(0).Cross(kHull.GetPlaneDirection(1));
Vector3<Real>::GenerateComplementBasis(kU,kV,kW);
// Project the input points onto the plane.
akPoint2 = WM4_NEW Vector2<Real>[iQuantity];
for (i = 0; i < iQuantity; i++)
{
kDiff = akPoint[i] - kOrigin;
akPoint2[i].X() = kU.Dot(kDiff);
akPoint2[i].Y() = kV.Dot(kDiff);
}
// Compute the minimum area box in 2D.
kBox2 = ContMinBox<Real>(iQuantity,akPoint2,fEpsilon,eQueryType,
false);
WM4_DELETE[] akPoint2;
// Lift the values into 3D.
kBox.Center = kOrigin + kBox2.Center.X()*kU + kBox2.Center.Y()*kV;
kBox.Axis[0] = kBox2.Axis[0].X()*kU + kBox2.Axis[0].Y()*kV;
kBox.Axis[1] = kBox2.Axis[1].X()*kU + kBox2.Axis[1].Y()*kV;
kBox.Axis[2] = kW;
kBox.Extent[0] = kBox2.Extent[0];
kBox.Extent[1] = kBox2.Extent[1];
kBox.Extent[2] = (Real)0.0;
return kBox;
}