Kind of like a bluish or white energy that's flowing. It's sorta sharp at one end and generally has a sword shape in my mind
Materializing thoughts... somehow. Depending on your thoughts about what your "sword" is will be reflected to your materialized intent. Say, you practice in a fast, highly-penetrating, and destructive sword technique, I imagine that the sword intent will look like a long and thin grain ( as in rice grain, size is relative to your level) that has a reddish hue and keeps on vibrating.
Transparent force that kind surrounds figure and sword and is very sharp! Cant see it but can def feel it (if that makes sense ah)
sword shape vibration at high frequency and have very sharp chainsaw like chains that moves at a very high speed
Sword intent is your materialized knowledge about the sword. F.e. you know about the air movement, after a certain slash with the sword etc.
Yeah same, you can't see it but you can feel it like a very sharp wind. All intents or kind of like that, like feeling killing intent is probably like suddenly being drenched in icy water, and having a suffocating pressure applied to you that gives you a feeling of dread and terror.
Depends. Some stories make it seem like an aura blade, surrounding the sword. Others I've read use it as a sort of formless pressure that can be exerted on the surroundings at will.
Some kind of semi-invisible aura around the cultivator that looks fierce and sharp (can be seen through air currents)
How to define sword intent? The first thing first is how you see it. Some people will see something akin to a white aura that surrounds the user or/and the blade. It is formless but at the same time, it had the shape of a sword. How do you feel it? When you touch something icy, you will feel cold. When you are close to something burning you will feel the hotness. It is the same for sword intent. It gives off a feeling of sharpness, that will make you feel as if you were being cut in the piece if you get too close. It feels dangerous. How do you understand it? Sword intent is gained by acquiring an understanding of sword mastery. The simple immersion in it for a long enough time can reforge you into a swordman if you survive. How does it defines you? The sword's intent reflects the heart of his owner whether he is a saint or a demon
To me it's really just gibberish and sometimes even the translators are confused with the order of the evolution of sword(/martial) intent / will or the like. But in general i try to see it as a process starting with no visual effect at all except a shean that glides over the blade like it was of highest quality. Increasing how light reflects on the clean metal surface and strengthening the material. And as you train it gradually increases to a dim glow on the weapon held. After reaching some threshold there's also a strenghtened impact on the surrounding, aided by a layer of cutting wind surrounding the blade, following its movements and growing in ferocity with the cultivation. Depending on the cultivation stage i imagine the previous clear wind and dim glow to transform into lighting effect befitting of the stage. Like when it says the qi of a [random cultivation stage]-expert is blue then i imagine the light effect to be blue as well, influenced by the qi used.