I think this is an interesting, but difficult question to answer.
Hemispatial neglect patients do not typically have problem with visual pathways per se. Wikipedia suggests that the disorder is most closely linked to damage of the temporo-parietal junction and posterior parietal cortex, areas associated with attention. Thus, the sensation (e.g. on the retina, and in early visual pathways) should be similar in patients and non-patients.
Let me make an analogy to the inattentional blindness literature. You may have seen a famous video by Daniel Simons and Christopher Charis. If you haven't, go watch it now before continuing... (I'll wait.)
Now how would you paint a picture of how that video 'looks' to someone? Does that picture include a gorilla? It seems even normal perception has blindspots. In fact, much of our perception is not strictly bottom-up, but is a mixture between bottom-up and top-down processes.
I would argue comparing a hemispatial neglect patient to a control is (very loosely) like comparing someone watching the inattentional blindness video for the first time to someone who has seen it before.
One might argue that hemispatial neglect patients do not 'see' things any differently than us, only that they 'perceive' it differently. So you could possibly create a caricature of how these patients 'see' the world, but it would be just that: a caricature.
One thing for certain is that hemispatial neglect patients do not 'perceive' that half of their visual field is missing (e.g. leaving half the page blank). When prompted, these patients typically do not report that anything is out of the ordinary.
All that being said, this is not my area of expertise, so please feel free to post a better answer if you think this analogy is misleading...