AGOCG logo
Graphics Multimedia VR Visualisation Contents
Training Reports Workshops Briefings Index
This report is also available as an Acrobat file.
Back Next Contents
The Design of Virtual Environments with particular reference to VRML

The uses of spatiality

Fundamentals of spatial organisation

The process of perception is not of merely scientific interest. It is regrettable that so many visual artefacts of all kinds are created in ignorance of important theories about perception and cognition: many designs are based on inherited, ill-founded beliefs. However there are also many traditional practices in design which do seem to reflect well-founded principles of spatial organisation. These are broadly consonant with the approach of Gestalt psychology, and include the following important principles of perceptual organisation - anyone embarking on the design of spatial artefacts should be aware of these possibilities and constraints. Some of these findings seem like 'common sense' (for example in relation to Proximity) while others are surprising (Orientation), or unfamiliar (Symmetry).

Smooth continuation

We group together in a single structure those parts which seem to align or continue smoothly. Thus, in Figure 1, we see two curved lines crossing at right angles (as in Figure 2) rather than two V-shaped forms meeting at a point as in Figure 3. This principle is also known in some texts as 'good continuation'.

Fig 1 Smooth continuation of lines

Fig 2 Preferred visual grouping of lines

Fig 3 This visual grouping of lines is normally rejected (even though it was the grouping that was used to create Fig 1)

Perhaps this feature derives from our experience of the 'objectness' of things. Thus, we see objects as a whole even when they are partially occluded by other things because we know that they do not break up when they disappear from view, as Figure 4 shows. Objects overlaying others have continuous outlines. The overlaid objects have interrupted outlines but, by the principle of smooth continuation, we can deduce continuity behind the overlaying object. Kellman and Spelke (1983), however, show that 3-4 month old infants only appreciate this if the objects are moving relative to one another.

Fig 4 Smooth continuation contributes to our feeling of 'objectness' and allows us to judge that the thin rectangle might be a complete object behind a rectangle in front

Presumably we learn to judge the still-image situation from experience although, as Figure 5 illustrates, our tendency to accept objectness through the principle of smooth continuation can sometimes mislead us.

Fig 5 Sometimes objectness overrides smooth continuation and gives us the mistaken impression that lines continue when they do not. Not only is the diagonal rectangle in the left hand side of the figure not continuous, the two diagonal rectangles (as can be seen in the figure to the right) do not even align


We group together those parts that are closest together. As can be seen in Figure 6, we perceive the group (a) as three vertical lines of dots and the group (b) as three horizontal lines of dots. The dots in (c) are equally spaced and do not suggest an orientation.

Fig 6 The principle of proximity determines our interpretation of the groups

Obviously proximity and the size of the elements that make up the pattern are related factors here (Zucker and Davis 1988).


We group together those parts that appear 'similar'. Hence in Figure 7, we see separate white diagonal lines and black diagonal lines rather than vertical or horizontal lines of black and white dots.

Fig 7 The principle of similarity determines our interpretation of the groups in this case and thus we tend to see diagonal lines

Sometimes, similarity can override proximity as the organising principle (Figure 8).

Fig 8 The principle of similarity ensures that we group the dots in vertical columns


We group together items which are arranged in a vertical or horizontal orientation in preference to those orientated on different axes. Thus orientation seems often to be a stronger grouping principle than similarity (Figure 9).

Fig 9 We group together items having similar orientations rather than similar shapes

Orientation, as we shall see later when we look at relationship to frame, also affects our interpretation of a shape.


We group together parts that give the appearance of closed shapes (Figure 10).

Fig 10 The principle of closure determines that we see these interrupted lines as forming closed figures

Thus it is often possible to suggest a virtual frame around a figure by only drawing its corners. The organisational principle of closure seems to come to the fore when we interpret sketch drawings - which are often incomplete but which we normally have little difficulty in understanding (Figure 11). See also Productive ambiguities in drawing p66.

Fig 11 Closure comes into play in our recognition of sketches

Relative size: figure and ground

Given two superimposed areas, we will tend to see the smaller as a figure against the larger background rather than vice versa (Figure 12).

Fig 12 We tend to read this image as a white square on a black one rather than a black square with a hole in it

When there is little difference in the size of the parts, ambiguity can result and we are unable to fix exactly which is the figure and which is the ground. Sometimes this ambiguity can be exploited for art purposes. Figures 13 illustrate this.

Fig 13 Two versions of an image in which the relative sizes of the parts are similar so that it is difficult to distinguish figure from ground (based on a CND poster)

In cases like these we can chose arbitrarily which is the figure and which is the ground. One choice allows us to perceive one meaning, the alternative choice allows us to perceive a different meaning. This effect is the basis of a number of well-known optical illusions such as the faces/vase illusion of Figure 14.

Fig 14 Different information arises depending on whether we take the black or the white to be the ground

Part of the ambiguity of Figure 14 seems to derive from the mixture of convexity and concavity of the black and white parts. Kanizsa and Gerbino (1976) show that shapes that are symmetrical about a vertical axis are usually seen as figures against ground but that this is not always the case if the forms are concave. Carrying out experiments with diagrams similar to those shown in Figure 15, they discovered that over 92% of people tested see the convex shapes as the figures and the concave ones as ground. This is independent of whether the convex shapes are black as in (a) and the concave ones white, or vice versa as in (b).

Fig 15 In general it is the convex shapes that are seen as figures against ground

To check whether the matter is influenced by degree of symmetry rather than convexity/concavity, Kanizsa and Gerbino (1976) went on to test subjects using diagrams similar to those in Figure 16 in which the concave shapes are symmetrical about the vertical and horizontal axes but the convex figures are only symmetrical about the horizontal axis. Once again the overwhelming majority of subjects saw the convex shapes as the figures whether they were drawn in black, as in Figure 16 (a) or in white, as in Figure 16 (b).

Fig 16 Here again, the convex shapes are seen as figures on a ground of the opposite colour

This seems to confirm an innate preference for convexity in two-dimensional shapes. It is not clear, though, that this preference transfers to a preference for convexity in the third dimension (although this can probably be inferred).

As with the other grouping principles, the figure/ground, relative size principle can sometimes be overridden by a different preference: in this case for certain orientations (as in Figure 17 where, in both images it is the upright one that dominates).

Fig 17 Our perception of what is figure and what is ground changes with the orientation of the figure suggesting that orthogonal relationships are preferred


We group together symmetrically arranged items and find it easier to make sense of symmetrical groupings than asymmetrical ones (Figure 18).

Fig 18 Symmetry is a strong grouping principle. It is very much easier to make sense of the top line of the figure than the bottom one

It is known that we make less eye movements when dealing with symmetrical figures and it is probable that they take less cognitive resources to process.

Like all the principles, symmetry can also be upset by context. Thus the dot in the centre of the square in Figure 19 can appear not to be in the centre when an additional off-centre square is added.

Fig 19 The addition of an off-centre square upsets our perception of the central dot

Familiarity and context

Familiarity with a scene and its context affects our grouping - sometimes bringing about substantial changes in our understanding of what we see (Figure 20).

Fig 20 This familiar image is hard to recognise in this orientation. Turning the image through 90 degrees clockwise allows us to view it in 'correct' orientation

Our sense of 'objectness' often comes into play: knowing that we are looking at a partially occluded object immediately affects our ability to group. This is strikingly illustrated in Figures 21 and 22

Fig 21 It is difficult to make sense of this image . . .

Fig 22 . . . until one realises it is partially occluded text

The context with which we frame a drawing is also significant. The squares and diamonds in Figure 23 are perceived differently according not, as might be supposed, to their relation to some absolute frame of reference, but to their placement within the drawing frame. This has obvious implications for the design of Virtual Environments, where the user's frame of reference - the sense for example of 'right way up' - is all too easily lost.

Fig 23 The relationship of the internal figure to the orientation of the frame determines whether we will perceive it as a square or a diamond

Palmer (1992) has shown that context is also significant in allowing us to orientate ambiguously pointing shapes such as equilateral triangles. When seen alone, an equilateral triangle can appear to point in any of three directions (In Fig 24 a the triangle can be seen as pointing to 3 o'clock, 7 o'clock or 11 o'clock). When seen grouped in company with similarly orientated triangles, all seem simultaneously to point in one or other of these directions (Fig 24b). The preferred direction of pointing changes when the triangles are aligned along an axis (Fig 24c). When they are aligned along one of their sides, they seem to point in a direction at right angles to the alignment (Fig 24d).

Fig 24 Equilateral triangles have ambiguous orientations that can be directed by appropriate grouping

Note the even more ambiguous effect of arranging similarly orientated triangles around a circle (Fig 25).

Fig 25 It is hard to perceive these equilateral triangles as having the same orientation

Common Fate

Items that move together are grouped together. This organising principle cannot be adequately illustrated in a still picture but requires animation or movies to be fully appreciated. One of the most impressive manifestations of the principle of common fate was performed by Johansson (1973a, 1975) who attached lights to joints of a black-clad actor and filmed him as he moved across a darkened room. When the actor was stationary, no pattern could be discerned in the lights. But, as soon as he walked, it was easily possible to identify the very sparse pattern as that of a moving figure. Pavlova (1992) has shown that, when children aged 3-5 years were tested with animated cartoons consisting of moving dots attached to the main joints of an invisible man and an invisible animal moving as if on a treadmill, the 3-year olds were able to recognise the moving displays and the 5-year old's performance was as good as adults. Static versions of the display however were not recognised. Familiarity and context must also play a part here.
Back Next Contents

Graphics     Multimedia      Virtual Environments      Visualisation      Contents