Figure 2.

Transformations between physical and perspective shapes. (a) A two-dimensional grid in physical space (blue) is located at a certain distance from the observer (indicated by arcs at the right side). Each point of the grid defines a direction (the black dotted lines are examples). Each point also defines a line parallel to the viewing direction (blue dotted lines) intersecting with the frontal plane of the observer. The parallels in physical space converge to the vanishing point VP in perspective space (red dotted lines). Intersections between directions and vanishing lines define points of the grid in perspective space. Together the intersections form a deformed grid (red). Transformation from physical to perspective space affects shape, size and distance of the grid. A physical grid is shown whose lines are parallel or orthogonal to the viewing direction. (b) The same physical grid is shown but rotated clockwise by 30° about its center. Note that the computed perspective grids of (a) and (b) are not rotated versions of each other. (c) The parallels in perspective space converge to a vanishing point VP in physical space lying behind the observer.