The perspective image of an infinite checkerboard. It can be constructed starting from any triangle Δ O X Y, where O X and O Y form the near corner of the floor, and X Y is the horizon. If O Y_1 P_(1, 1) X_1 is the corner tile, the lines Y_1 P_(1, 1) and P_(1, 1) X_1 must be parallel to O X and O Y respectively. This means that in the drawing they will meet O X and O Y at the horizon, i.e., at point X and point Y respectively. This property, of course, extends to the two bunches of perpendicular lines forming the grid. The adjacent tile P_(1, 1) X_1 X_2 P_(2, 1) can then be determined by the following conditions: 1. The new vertices X_2 and P_(2, 1) lie on lines O X and Y_1 P_(1, 1) respectively.
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