public void ComputeVertices(ref Vector2dTuple4 vertex)
{
Vector2d extAxis0 = Extent.x * AxisX;
Vector2d extAxis1 = Extent.y * AxisY;
vertex[0] = Center - extAxis0 - extAxis1;
vertex[1] = Center + extAxis0 - extAxis1;
vertex[2] = Center + extAxis0 + extAxis1;
vertex[3] = Center - extAxis0 + extAxis1;
}
// ported from WildMagic5 Wm5ContBox2.cpp::MergeBoxes
public static Box2d Merge(ref Box2d box0, ref Box2d box1)
{
// Construct a box that contains the input boxes.
Box2d box = new Box2d();
// 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.
box.Center = 0.5 * (box0.Center + box1.Center);
// The merged box axes are the averages of the input box axes. The
// axes of the second box are negated, if necessary, so they form acute
// angles with the axes of the first box.
if (box0.AxisX.Dot(box1.AxisX) >= 0)
{
box.AxisX = (0.5) * (box0.AxisX + box1.AxisX);
box.AxisX.Normalize();
}
else
{
box.AxisX = (0.5) * (box0.AxisX - box1.AxisX);
box.AxisX.Normalize();
}
box.AxisY = -box.AxisX.Perp;
// Project the input box vertices onto the merged-box axes. Each axis
// D[i] containing the current center C has a minimum projected value
// min[i] and a maximum projected value max[i]. The corresponding end
// points on the axes are C+min[i]*D[i] and C+max[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}^1 0.5*(min[i]+max[i])*D[i]
// The box extents are
// e[i] = 0.5*(max[i]-min[i])
int i, j;
double dot;
Vector2d diff = new Vector2d();
Vector2d pmin = Vector2d.Zero;
Vector2d pmax = Vector2d.Zero;
Vector2dTuple4 vertex = new Vector2dTuple4();
box0.ComputeVertices(ref vertex);
for (i = 0; i < 4; ++i)
{
diff = vertex[i] - box.Center;
for (j = 0; j < 2; ++j)
{
dot = diff.Dot(box.Axis(j));
if (dot > pmax[j])
{
pmax[j] = dot;
}
else if (dot < pmin[j])
{
pmin[j] = dot;
}
}
}
box1.ComputeVertices(ref vertex);
for (i = 0; i < 4; ++i)
{
diff = vertex[i] - box.Center;
for (j = 0; j < 2; ++j)
{
dot = diff.Dot(box.Axis(j));
if (dot > pmax[j])
{
pmax[j] = dot;
}
else if (dot < pmin[j])
{
pmin[j] = dot;
}
}
}
// [min,max] 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 extents based on the new center.
box.Extent[0] = 0.5 * (pmax[0] - pmin[0]);
box.Extent[1] = 0.5 * (pmax[1] - pmin[1]);
box.Center += box.AxisX * (0.5 * (pmax[0] + pmin[0]));
box.Center += box.AxisY * (0.5 * (pmax[1] + pmin[1]));
return(box);
}
