public bool isLegal(PatternId from_, Dir4 dir, PatternId to_)
{
int i = from_.asIndex;
int j = to_.asIndex;
if (i > j)
{
// swap the the patterns so that i <= j
i = i + j; // a + b
j = i - j; // (a + b) - b (=a)
i = i - j; // (a + b) - a (=b)
// and invert the direction
dir = dir.opposite();
}
return(this[i, (int)dir, j]);
}