lpetrich
Contributor
I'll return to regular solutions {k,m0+m*k} and calculate the effects of various symmetries.
A line along an axis: {k,m0} and {m0,k}
So in that case:
- rot 0d - {{1,0},{0,1}} - {0,0}
- rot 90d - {{0,-1},{1,0}} - {n-1,0}
- rot 180d - {{-1,0},{-1,0}} - {n-1,n-1}
- rot 270d - {{0,1},{-1,0}} - {0,n-1}
- rfl ax1 - {{-1,0},{0,1}} - {n-1,0}
- rfl ax2 - {{1,0},{0,-1}} - {0,n-1}
- rfl dg1 - {{0,1},{1,0}} - {0,0}
- rfl dg2 - {{0,-1},{-1,0}} - {n-1,n-1}
A line along an axis: {k,m0} and {m0,k}
- rot 0d - (1,2) k -> k, m0 -> m0
- rot 90d - (1->2) k -> k, m0 -> n-1-m0 ; (2->1) k -> n-1-k, m0 -> m0
- rot 180d - (1,2) k -> n-1-k, m0 -> n-1-m0
- rot 270d - (1->2) k -> n-1-k, m0 -> m0 ; (2->1) k -> k, m0 -> n-1-m0
- rfl ax1 - (1) k -> n-1-k, m0 -> m0 ; (2) m0 -> n-1-m0, k->k
- rfl ax2 - (1) k -> k, m0 -> n-1-m0 ; (2) m0 -> m0, k ->n-1-k
- rfl dg1 - (1->2, 2->1) k -> k, m0 -> m0
- rfl dg2 - (1->2, 2->1) k -> n-1-k, m0 -> n-1-m0
So in that case:
- No flip - rot 0d, rot 180d, rfl ax1, rfl ax2
- Flip - rot 90d, rot 270d, rfl dg1, rfl dg2