disobey the law of conservation of energy. An extreme example is depicted in the film Inception, where by a forced perspective trick an immobile stairway changes its connectivity. The video game Fez uses tricks of perspective to determine where a player can and cannot move in a puzzle-like fashion. Perspective projection Perspective projection or perspective transformation is a nonlinear projection where three dimensional objects are projected on a picture plane. This has the effect that distant objects appear smaller than nearer objects. It also means that lines which are parallel in nature (that is, meet at the point at infinity) appear to intersect in the projected image. For example, if railways are pictured with perspective projection, they appear to converge towards a single point, called the vanishing point. Photographic lenses and the human eye work in the same way, therefore perspective projection looks most realistic. Perspective projection is usually categorized into one-point, two-point and three-point perspective, depending on the orientation of the projection plane towards the axes of the depicted object. Graphical projection methods rely on the duality between lines and points, whereby two straight lines determine a point while two points determine a straight line. The orthogonal projection of the eye point onto the picture plane is called the principal vanishing point (P.P. in the scheme on the left, from the Italian term punto principale, coined during the renaissance). Two relevant points of a line are: its intersection with the picture plane, and its vanishing point, found at the intersection between the parallel line from the eye point and the picture plane. The principal vanishing point is the vanishing point of all horizontal lines perpendicular to the picture plane. The vanishing points of all horizontal lines lie on the horizon line. If, as is often the case, the picture plane is vertical, all vertical lines are drawn vertically, and have no finite vanishing point on the picture plane. Various graphical methods can be easily envisaged for projecting geometrical scenes. For example, lines traced from the eye point at 45° to the picture plane intersect the latter along a circle whose radius is the distance of the eye point from the plane, thus tracing that circle aids the construction of all the vanishing points of 45° lines; in particular, the intersection of that circle with the horizon line consists of two distance points. They are useful for drawing chessboard floors