Fig. 3. A space-time path (Source Miller, H. J. (2017)

Ochungo; JERR, 21(5): 61-80, 2021; Article no.JERR.74936

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Fig. 4. A space-time prism (Source Miller, H. J. (2017)
In Fig. 4 we see an illustration of a space-time prism with the space of movement being cast down on a dimensional plane. They- axis demarcates the possible locations for the space- time path within a time budget and is therefore a direct measure of a person’s accessibility to the environment and activities. Fixed activities anchor a spacetime prism since by definition these allow only one spatial possibility during their duration. For example, the first anchor in Fig. 4 could be the person’s home while the second anchor could be their workplace. At sometime during the time interval between when the home activity ends and the work activity begins, the person wishes stop at some location to conduct an activity, e. g, shop at a store. The available time interval is the time budget for the travel and activity episode. Given these anchoring activities, the time budget, a maximum velocity of movement and the required activity participation time, the prism determines the locations in space and time that are available to the person. The region inside the prism comprises locations where an individual could beat different times during that episode. An activity is not accessible to this person during this episode unless its location and duration intersects with the prism to a sufficient degree, with this determined by the minimum time required to conduct the activity. Similarly, two people cannot meet unless their prisms intersect to a sufficient degree. The projection of the prism to the two-dimensional plane is the potential path area this comprises the region in geographic space where the person can be during the entire time interval.

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