Linear perspective

Linear perspective is the art of representing three-dimensional constructions on a two-dimensional surface. It presupposes a fixed viewpoint and a desire to create an "objective" recording of one's visual experience - two conditions which have been the most dominant in the Western art of the past half-millennium.

2nd kind of vanishing points

If the lines have angles to the painting plate, they would vanish in the other vanishing points. There are lot of vanishing points homologous to different angles. But all vanishing points should be located in the same horizontal line with the focus.

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In other words, two-point perspective is derived from one-point perspective by yawing the line of vision so that the line of vision will be at an acute angle away from the focus. Then the lines which used to be horizontal and parallel will now be concurrent, intersecting at the horizon. Interpreted according to projective geometry, the horizontal parallel lines of one-point perspective are actually concurrent, intersecting at the point at infinity . When the head is turned by a slight angle, these lines no longer intersect at an ideal point, but at an affine point on the horizon, so they are no longer parallel.

Related Topics:
Projective geometry - Point at infinity

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More precisely, two-point perspective exists when the painting plate is parallel to a "Cartesian scene" (a scene composed entirely of linear elements intersecting only at right angles) in one axis (usually the z-axis) but not parallel 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.

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