Linear perspective is based on the observation that parallel lines will converge to a common vanishing point on the horizon line. There are three types of linear perspective: One point, two point, and three point.
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One point occurs when the observer is directly facing the object, such as a cube. When this cube is right in front of you at eye level, you will only see a square. As the cube moves up from your eye level, you will begin to see more and more of the bottom face. The two vertices on the sides of the bottom face should converge at a vanishing point located on the horizon line aligned with the center of the cube. The single line that indicates the back side should be parallel to the bottom of the side facing you. The same thing occurs when the cube is moved below your eyelevel, except that you will see the top side instead. The lines will converge to the same vanishing point as the cube above your eyelevel. As the cube moves farther up or down, the bottom or the top side will seem to increase in area. To see this, take a cube-shaped object and move it up and down to observe what can be seen.
Two point perspective occurs when at least two sides are visible at eyelevel. This one has two vanishing points instead of just one. Here, the two vanishing points are at the two far ends of the page. Once again, all the parallel lines converge to the vanishing points, and the vertical edges are straight up and down since they do not go off in the distance. In a side to side motion, the lines continue to converge at the same vanishing points and the only thing that makes it look like it is turning is the position of the object.
Activity: On a 14"/355mm long sheet of paper, try drawing a box in motion by drawing a horizon line in the middle and placing vanishing points on the two ends of the line (note: have the 14" side horizontal so that the paper is 14" wide and put the vanishing points on the edge). Then, making sure you have enough room, draw seven boxes across the page, with their lines converging to the two vanishing points. Draw lightly at first so that it can be easily erased if needed. When you're done that, modify them so that the box is changing for each one until you have the final product at the seventh box. Be creative!
Finally, three point perspective is only visible at either great heights, or great depths, say when you're looking up at a skyscraper from the entrance. In this case, there will be another vanishing point above in addition to the ones in the two point perspective. If, say, you're flying above them, the vanishing point will be way below you. This perspective is not as common, although it can be seen quite often in comic books.
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