There are 3 main versions of perspective in artwork, and while all are useful in certain circumstances, they represent an increase in complexity. The first, is one-point perspective.
This involves drawing all objects in relation to one dimension of depth. There is a 'vanishing point', which is a point on a horizon where all depth lines would eventually converge. This method of perspective is very simple, and is usually the first to be taught to art students. It is usually ideal for depicting environments containing relatively simple objects.
The second type of perspective is two-point perspective.
It adds considerably more complexity to environments depicted this way, but they also appear more believable. There are more faces that are scaled according to depth, and depending on the position of the faces, the lines point towards one of two vanishing points.
The third type is three-point perspective.
Three point perspective adds depth to all three geometric dimensions. The third vanishing point is usually towards the top or bottom of the environment, and most vertical lines converge there. While this is the most complex perspective method to plot, it is great for depicting dramatic scenes that greatly emphasise sheer scale and depth.
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