You are right, something is not as it should be here. (So thank you for reporting it!) hlalfN gives a 4-step orthogonal move, while hrarfN gives a 4-step diagonal one. While logically they should just be each other's mirror image.
I will have to figure out why exactly this happens. My first suspicion is that I added code to swap the meaning of l and r after a left-handed chirality-breaking step. At an early stage of designing the notation I thought this would be helpful, because it means that you could simply write afrN to mean hrafrNhlaflN. But later I realized that the modifiers q and z could be used in continuation legs as placeholders for l or r, meaning deflection in the same or in the opposit direction as the previous leg. This would be a natural generalization of the original Betza meaning of circular and zig-zag.
I suspect that in implementing the latter, I somehow interfered with the original idea of making the meaning of l and r itself in continuation legs dependent on context. I will check this out.
Anyway, the recommended notation for what you wanted to do would be aqfN, a first Knight step, followed by a 45-degree bend in the same direction. Where the original direction was defined by the way the oblique move was bending when you consider it an orthogonal move followed by a diagonal one.
You are right, something is not as it should be here. (So thank you for reporting it!) hlalfN gives a 4-step orthogonal move, while hrarfN gives a 4-step diagonal one. While logically they should just be each other's mirror image.
I will have to figure out why exactly this happens. My first suspicion is that I added code to swap the meaning of l and r after a left-handed chirality-breaking step. At an early stage of designing the notation I thought this would be helpful, because it means that you could simply write afrN to mean hrafrNhlaflN. But later I realized that the modifiers q and z could be used in continuation legs as placeholders for l or r, meaning deflection in the same or in the opposit direction as the previous leg. This would be a natural generalization of the original Betza meaning of circular and zig-zag.
I suspect that in implementing the latter, I somehow interfered with the original idea of making the meaning of l and r itself in continuation legs dependent on context. I will check this out.
Anyway, the recommended notation for what you wanted to do would be aqfN, a first Knight step, followed by a 45-degree bend in the same direction. Where the original direction was defined by the way the oblique move was bending when you consider it an orthogonal move followed by a diagonal one.