//Static Functions
AglOBB AglOBB::constructMinimum(vector<AglVector3> p_vertices, vector<unsigned int> p_indices)
{
//Compute area of the mesh and centroid of the mesh
float areaH = 0; //areaH = areaHull
AglVector3 centerH(0, 0, 0); //centerH = centerHull
for (unsigned int i = 0; i < p_indices.size(); i+=3)
{
AglVector3 v1 = p_vertices[p_indices[i]];
AglVector3 v2 = p_vertices[p_indices[i+1]];
AglVector3 v3 = p_vertices[p_indices[i+2]];
AglVector3 cross = AglVector3::crossProduct(v2-v1, v3-v1);
float area = cross.length() * 0.5f;
areaH += area;
centerH += (v1 + v2 + v3) * area / 3;
}
centerH /= areaH;
//Compute the covariance matrix
float** covariance = new float*[3];
covariance[0] = new float[3];
covariance[1] = new float[3];
covariance[2] = new float[3];
for (unsigned int i = 0; i < 3; i++)
{
for (unsigned int j = 0; j < 3; j++)
{
float val = 0;
for (unsigned int k = 0; k < p_indices.size(); k+=3)
{
AglVector3 p = p_vertices[p_indices[k]];
AglVector3 q = p_vertices[p_indices[k+1]];
AglVector3 r = p_vertices[p_indices[k+2]];
AglVector3 m = (p + q + r) / 3;
AglVector3 cross = AglVector3::crossProduct(q-p, r-p);
float area = cross.length() * 0.5f;
val += (area / 12) * (9*m[i]*m[j] + p[i]*p[j] + q[i]*q[j] + r[i]*r[j]);
}
val = val / areaH - centerH[i]*centerH[j];
covariance[i][j] = val;
}
}
AglVector3 e1, e2, e3;
FindSymmetricEigenVectors(covariance, e1, e2, e3);
float minX, maxX, minY, maxY, minZ, maxZ;
maxX = minX = AglVector3::dotProduct(e1, p_vertices[0]);
maxY = minY = AglVector3::dotProduct(e2, p_vertices[0]);
maxZ = minZ = AglVector3::dotProduct(e3, p_vertices[0]);
for (unsigned int i = 0; i < p_vertices.size(); i++)
{
maxX = max(AglVector3::dotProduct(e1, p_vertices[i]), maxX);
maxY = max(AglVector3::dotProduct(e2, p_vertices[i]), maxY);
maxZ = max(AglVector3::dotProduct(e3, p_vertices[i]), maxZ);
minX = min(AglVector3::dotProduct(e1, p_vertices[i]), minX);
minY = min(AglVector3::dotProduct(e2, p_vertices[i]), minY);
minZ = min(AglVector3::dotProduct(e3, p_vertices[i]), minZ);
}
AglVector3 boxCenter = AglVector3(minX+maxX, minY+maxY, minZ+maxZ) * 0.5f;
boxCenter = e1 * boxCenter.x + e2 * boxCenter.y + e3 * boxCenter.z;
AglMatrix w = AglMatrix::identityMatrix();
w.SetTranslation(boxCenter);
w.SetRight(e1);
w.SetUp(e2);
w.SetForward(e3);
delete[] covariance[0];
delete[] covariance[1];
delete[] covariance[2];
delete[] covariance;
return AglOBB(w, AglVector3(maxX-minX, maxY-minY, maxZ-minZ));
}
//------------------------------------------------------------------------------
Rect& Rect::center (const Rect& rect)
{
centerH (rect);
return centerV (rect);
}
