Alistair B. Fraser


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Drag the air parcel towards the ground. Air diverges horizontally in response to vertical convergence.

Position

Sometimes one wants to illustrate the way in which something changes with position. (This is not spacial modeling in the sense used earlier where one wished to explore the special structure of a scene or object, say as viewed with different orientations.) The  Shockwave  model to the right illustrates the continuity equation (a fluid-dynamics description of mass conservation) by allowing the viewer watch the response as an air parcel approaches the ground.

The background image shows a summer shower which spreads as it reaches the ground to produce a foot. The falling rain can pile up on the ground, but the air it drags down with it cannot, so the descending air parcels must diverge horizontally as they converge vertically. The air flowing outwards drags some raindrops with it and the shower gains a foot. In class, this is used to illustrate both the basic behavior, but also the way in which the continuity equation describes this behavior.

Drag horizontally to look around; drag vertically to change form; or click on it and use arrow keys.

Arbitrary

It was worth featuring parametric models of position (above) owing to their importance, but the parameter could be anything at all. The visualization then allows the viewer to change a parameter and observe what is often a complex response. This is, of course, what is being being shown when one plots a function, but usually the only things which can be plotted are simple (one variable) responses to either simple (one variable) or complex (multiple variables) input. Here one can observe a complex response to an input.

Shown is a two-axis QTVR object movie. This technology was illustrated earlier in the discussion of three-dimensional spacial models, but on that occasion, both axes were used to change the view (in azimuth and elevation) of a single object. The really striking thing about QTVR objects is that an axis can represent anything. Here, the horizontal axis is used to change view (azimuth), while the vertical axis varies a parameter which varies the form of the structure. The two-axis (arbitrary parameter) movie is a capability of QTVR objects which is lacking in other systems which offer spacial objects (such as Metastream), yet the price one pays for this greatert versatility is larger files.

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