Vanishing points are a form of linear perspective that is used to create foreshortening or a sense of depth to an object. Here are a couple of examples as to how vanishing points work. With cylindrical shape, the seemingly parallel edges of the cylinder would meet at a point in the distance. The front of the cylinder would be a circle. The back edge of the cylinder should arc as if the back end was a circle also. So what in 3-dimensions is two same sized circles connected by two parallel lines becomes in a 2-dimensional drawing two different sized circles connected by two lines that eventually meet at a point. These are two very different things, but one represents what is while the latter represents what we see.
The second example is that of a cube. This gets a little trickier because there are two vanishing points -- one on both sides of the cube. Again, the seemingly parallel sides actually meet at a point away from the cube. The vertical lines of a cube that is sitting on a horizontal surface will always be completely vertical. Of course, if the cube is on a slope or some non-horizontal surface, the verticals will tip one way or the other, but they will always be parallel to each other. That's just a little tip about linear perspective. If you are going to use angular geometric shapes, such as buildings, boxes, fish tanks, yoga bricks, desks, dumpsters (I think you get the idea) and such, in your composition, linear perspective can be helpful. If your objects are biomorphic or non-linear, then linear perspective is not very helpful. There are other ways to create perspective in those situations. But that is for another time.
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