The development of rendering algorithms has largely been devoted to achieving a resemblance to the sorts of surfaces depicted by photography. Lansdown and Schofield (1995) however list some of the attempts that have been made in other directions, including Schofield's own Piranesi renderer. They document the attempts which have been made in both 3D rendering and paint systems to replicate the materials traditionally used by artists, but point out that this is in its own way a limiting view. What is required, they argue, is not just the facility to imitate familiar rendering styles, but techniques to make more expressive representations. They do not use this primarily to refer to emotional expressiveness, but to the ability that some drawings, for example, have to 'speak' to us more directly of the forms they depict than could a photograph. One of the most profound skills of drawing is the use of mark-making as a form of explanation the marks take on the status of a form of language, helping the user to 'read' the forms depicted. This is why drawings, paintings and sketches often contain marks which do not directly correspond to any observed edge or tonal difference in the scene but instead, for example, establish the spatial relationships of objects to one another, or the dominant directions of a surface. In fact, many kinds of drawing freely mix marks with obvious direct referents in the observed scene, such as the edges of objects, with other marks of more schematic kinds. The person skilled in drawing is able to combine in one artefact the traditions of verisimilitude to the retinal image and those of schematic representation.
[Painters] were enabled to 'capture' aspects of that world in a wholly unprecedented form of synthesis, which owed as much to science and mathematics as it did to the earlier practices of pictorial art.
We cannot deal here with the vexed question of whether three-point perspective (the one we normally think of as 'perspective') is in a special sense, correct. However, we can look at the status of 'perspective' and ask ourselves whether it is the only system we would want to use to project our virtual realities.
When three-dimensional cartesian data is stored in a computer system, this implies almost nothing about what the user will see. Assuming that the eyes are the user s means of sensing the three-dimensional model, then it is unavoidable that the three-dimensional data will be mapped onto two-dimensional surfaces, whether a conventional desktop monitor, projection screen, miniature LCDs in a headset, or even the retinae themselves. A 3D to 2D transformation must be applied, and what this transformation may be is dictated by the rendering system, not by the model.
In a graphics rendering system, any consistent model of perspective can be applied (it could even be inconsistent if we chose to make it so). It is a simple matter to render cartesian three-space in any of the standard projection systems: orthographic, axonometric, isometric, two-point or three-point perspective. However, VR systems are normally assumed to map the three-dimensional data using three-point perspective. Arguably we are back to a question of definition, since some would certainly want to define VR as based on three-point perspective projection. We would argue however that the essential qualities of spatiality and virtuality are present even when other perspective systems are chosen. In addition as we shall briefly see, even the adoption of 3-point perspective leaves many questions undecided.
A theme of this report is the recurrent question, 'Does it work?' In evaluating the role of VR in Higher Education, we have chosen to look above all at effectiveness. Therefore we must ask for a given projection system, not 'Is it correct?' but 'Does it serve our purpose?' Clearly there will not be a right answer for all cases.
The relationship between what we see and what we know is never settled.
One point to note immediately is that in the mass of the world s visual representations, 3-point perspective is unusual. In the past it has been supposed that the acquisition of knowledge about how to use these systems is symptomatic of the essential superiority of post-Renaissance European culture over all others, and there are probably residues of this opinion current now. The core of such an idea is that other cultures would have made use of three-point perspective if only they had been fortunate or clever enough to invent it.
There has been much speculation about why the system was invented/ discovered (even the choice of word is loaded) at the time and place it was, and arguments have included chance, the rise of the property-owning class, a shift away from a theocentric view of creation, and many more.
Because we are brought up with 3-point perspective, it seems natural not just the obvious choice, but the one we would instinctively choose. In some senses however, 3-point perspective seems not to be natural at all, and perhaps this is why it is so uncommon as a form of representation. Teaching drawing (in the West) involves inculcating the process of capturing on paper the three-dimensional world from a single viewpoint according to the rules of 3-point perspective, and it turns out to be an extraordinarily difficult to do. Some learners never manage the essential skill of seeing the top of a rectangular table as a trapezoid at a particular angle to the line of sight: they can only see what they 'know is there', a viewpoint-less view. Following an ecological line of argument, it is interesting to speculate why it might be that (1) seeing in perspective is an unnatural skill acquired by most people only with substantial difficulty and (2) it is very uncommon in the history of the world s cultures. We might begin to suspect that, from an ecological point of view, it is somehow 'unnecessary', or 'unproductive'.
Until the invention of photography (which in its usual form produces images in three-point perspective), the application of 3-point perspective to images was almost entirely in the field of Fine Art painting. Even after photography, there has been a continuous outpouring of images which do not use 3-point perspective. The representations favoured by architecture, product design, engineering, magazine advertising and many other image-using trades and professions use 3-point perspective as the exception rather than the rule. This is not because of a lack of technical capability, but because in more cases than not the 3-point perspective image would not serve the valuable purpose that (for example) an orthographic image does. It would not be capable of conveying the necessary information. It is too easy to assume that 3-point perspective is a sort of superset of projections which contains more than each of the lesser projections individually, but of course the ambiguities of 3-point perspective can often only be avoided by adopting some simpler projection altogether.What value do we get out of a 3-point perspective image? We might be able to answer this question by separating images into those generated by photography and those constructed by other means:
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