/// <summary>
/// Check if the polys are similar to within a tolerance (Doesn't include reflections,
/// but allows for the points to be numbered differently, but not reversed).
/// </summary>
/// <param name="poly1"></param>
/// <param name="poly2"></param>
/// <returns></returns>
public static bool PolygonsAreSame2D(IList<Point2D> poly1, IList<Point2D> poly2)
{
int numVerts1 = poly1.Count;
int numVerts2 = poly2.Count;
if (numVerts1 != numVerts2)
{
return false;
}
const double kEpsilon = 0.01;
const double kEpsilonSq = kEpsilon * kEpsilon;
// Bounds the same to within tolerance, are there polys the same?
Point2D vdelta = new Point2D(0.0, 0.0);
for (int k = 0; k < numVerts2; ++k)
{
// Look for a match in verts2 to the first vertex in verts1
vdelta.Set(poly1[0]);
vdelta.Subtract(poly2[k]);
if (vdelta.MagnitudeSquared() < kEpsilonSq)
{
// Found match to the first point, now check the other points continuing round
// if the points don't match in the first direction we check, then it's possible
// that the polygons have a different winding order, so we check going round
// the opposite way as well
int matchedVertIndex = k;
bool bReverseSearch = false;
while (true)
{
bool bMatchFound = true;
for (int i = 1; i < numVerts1; ++i)
{
if (!bReverseSearch)
{
++k;
}
else
{
--k;
if (k < 0)
{
k = numVerts2 - 1;
}
}
vdelta.Set(poly1[i]);
vdelta.Subtract(poly2[k % numVerts2]);
if (vdelta.MagnitudeSquared() >= kEpsilonSq)
{
if (bReverseSearch)
{
// didn't find a match going in either direction, so the polygons are not the same
return false;
}
else
{
// mismatch in the first direction checked, so check the other direction.
k = matchedVertIndex;
bReverseSearch = true;
bMatchFound = false;
break;
}
}
}
if (bMatchFound)
{
return true;
}
}
}
}
return false;
}
