Issues of Perspective



Constructing solids in perspective is an exercise in judgement. Although I discussed Doblin's system of two-point perspective with its measuring points and the ability to lay out an indexed grid, the system represents an approximation of reality.

The first issue to cover is the nature of drawing in perspective which, in many ways, is the most complicated aspect to understand. In reality, perspective seems obvious and without distortion because we observe space in three dimensions (horizontal, vertical, and depth or, in mathematical terms, the x, y, and z axes). Translating this phenomenon to two dimensions requires a graphic understanding of the shape of objects in space and the related visual changes as space recedes in distance.



Fig.01 - Doblin, J. (1956), p.8 - A view of the picture plane

 The Picture Plane is the surface of a plane on which all 3-dimensional objects we view beyond are represented 2-dimensionally. The Picture Plane is usually represented by the pad of paper (or computer screen) on which we depict the objects. See Fig.01 for Doblin's illustration. Please note that his drawn visualization of the observer ( geometrically pear-shaped with a bow-tie and pointed shape for a head), as distracting as it may be, is purely for understanding the context.

The nature of our vision is 3-dimensional, however, so, unless the picture plane is infinitely large to depict all space in our front view to the periphery, we restrict our recorded view to an area known as the Cone-of-Vision. This idea is best represented by the analogy of a camera lens: the camera can only see to a certain angle away from the center of vision.

If one sets up a two-point perspective drawing it becomes apparent that a square grid on the ground plane changes shape depending both on the distance from the viewer and on the proximity to the outer boundaries of the cone-of-vision.


Fig.02 - Doblin, J. (1956), p.18 - The 'Cone of Vision' - Note the distortion near to and beyond the boundaries.

 In Figure 02, note the distortion in the shape of a square footprint near and beyond the boundary of the Cone of Vision. According the to the perspective grid, the shape of a square would have angles less than 90 degrees, an impossibility. This phenomenon may often be observed in architectural photography where images are distorted due to the prismatic nature of the wide-angle lenses used on the camera. For industrial design, however, drawings of form would confuse the observer if distortion was included in the visualization. In Fig. 2, squares A1 and B appear to be in proportional perspective. This area could be termed a 'sweet spot' for accurate visualization. Moving away from this area uses perspective grids that become progressively distorted.


Fig. 03 - 30-60 two-point perspective. Note the difficulty in matching a template ellipse for the cone base while maintaining a vertical minor axis.


 In Figure 03, the 'sweet spot' for accurate perspective is near the picture plane and origin, the cube shows the least distortion. Moving away to the left, however, one notices that the ellipses used in the cone and cylinder do not coincide completely with the foot prints of the outline parameter cubes. With all vertical center lines and surfaces kept perpendicular to the ground plane, ellipse guides (true perspective with no distortion) become unreliable and don't fit the square footprints.
Observing the same view in Maya, however, the software has the sophisticated ability to adjust both ellipses and vertical lines to a 3rd vanishing point (Fig.04).


Fig.04 - Screenshot of four solids in Maya. Note the 3rd point perspective for vertical lines.



If one introduces a third-point in the drawn perspective the template ellipses work much better (Fig.05) The implications are, however, that a 3-point perspective system must be used to depict larger visualizations to avoid distortion.


Fig. 05 - 3-point perspective shows deviation of vertical lines from y-axis


Interestingly, one can document the mathematical precision of the Maya visualization software by observing the change in perspective comparing an ellipse on the screen and an ellipse from a template. As any particular point in space recedes into the distance, the angle of view changes incrementally. Ellipse templates only give an approximation every 5 degrees and are symmetrical front to back. Maya, conversely, is able to accurately predict the exact elliptical angle at any point in space - thus, the deviation shown from matching the front half of a template to the screen image to the back half in Figure 06.


Fig. 06 - Comparison of ellipse template and Maya-generated ellipse. Note the gap at the rear/top of the two ellipse representations.

 As capable as Maya is at depicting many variations of perspective there lie hidden traps for the less-than-expert user. If one selects the Camera icon from the sub-menu, a host of variables are offered for adjustment: Angle of View, Focal Length, Camera Aperture, Film Aspect Ratio, and Camera Scale are among several that may be fine-tuned. Note the differences between the perspective views of Figures 07 and 08 which result mostly from changes in just the aperture.


Fig. 07 - Super 16mm - note the foreshortening in the foreground.



Fig.08 - 70 mm Projection - note the wide-angle distortion in the perspective

As shown in figures 07 and 08, the impact of a single image can change dramatically with just a few adjustments to the software viewing set-up. This represents a risk for the designer who may not fully understand the implications of the power of modeling/rendering software.

Although dramatic, the implications of forced perspective shown in figure 08 can be illustrated another way. Doblin explains that the angle of a horizontal square intersection visualized in a 2-dimensional plane can never be 90 degrees because it would require the viewer to be looking down from directly above plane or object. See figure 09. In design, one has to balance inspiring the client and risking confusion from images that don't represent reality.


Figure 09 - Doblin, J. (1956), p. 19. What distorted perspective means to the viewer.