One vanishing point is typically used for roads, railroad tracks, or buildings viewed so that the front is directly facing the viewer. Any objects that are made up of lines either directly parallel with the viewer's line of sight or directly perpendicular (the railroad slats) can be represented with one-point perspective.
One-point perspective exists when the painting plate (also known as the pixture plane) is parallel to two axes of a rectilinear (or Cartesian) scene — a scene which is composed entirely of linear elements that intersect only at right angles. If one axis is parallel with the picture plane, then all elements are either parallel to the painting plate (either horizontally or vertically) or perpendicular to it. All elements that are parallel to the painting plate are drawn as parallel lines. All elements that are perpendicular to the painting plate converge at a single point (a vanishing point) on the horizon.
Two-point perspective can be used to draw the same objects as one-point perspective, rotated: looking at the corner of a house, or looking at two forked roads shrink into the distance, for example. One point represents one set of parallel lines, the other point represents the other. Looking at a house from the corner, one wall would recede towards one vanishing point, the other wall would recede towards the opposite vanishing point.
Two-point perspective exists when the painting plate is parallel to a Cartesian scene in one axis (usually the z-axis) but not to the other two axes. If the scene being viewed consists solely of a cylinder sitting on a horizontal plane, no difference exists in the image of the cylinder between a one-point and two-point perspective.
Three-point perspective is usually used for buildings seen from above (or below). In addition to the two vanishing points from before, one for each wall, there is now one for how those walls recede into the ground. This third vanishing point will be below the ground. Looking up at a tall building is another common example of the third vanishing point. This time the third vanishing point is high in space.
Three-point perspective exists when the perspective is a view of a Cartesian scene where the picture plane is not parallel to any of the scene's three axes. Each of the three vanishing points corresponds with one of the three axes of the scene.
One-point, two-point, and three-point perspectives appear to embody different forms of calculated perspective. The methods required to generate these perspectives by hand are different. Mathematically, however, all three are identical: The difference is simply in the relative orientation of the rectilinear scene to the viewer.
Text Reference:
http://en.wikipedia.org/wiki/Perspective_(graphical)
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