Images mapped on polygons

[DustyPorViva]

Well, I was messing around with polygons, and I noticed something. I haven't dug deep into 3D enough to know how mapping textures on polygons work and what not, so excuse my ignorance...
Either way, take note of my attachments. The first image is of an image mapped on a 3 point polygon. See how clear and sharp the resize is? It's almost like a vector image... then add another point to the polygon, and see the difference.
Someone just tell me if this is possible or not, I'd like the same texturing method done with 4 point polygon's as done with the 3 point. The mapping is so much clearer and appealing to the eye on the first attachment. I take it though, that this is all being done the same way a 3D engine handles mapping and polygons, so I don't know if it's possible to change this.