Some Types of Physical-Spatial Problems

Here are a few categories of such problems:

Fitting

Fitting problems. A space planner may work on fitting desks, conference rooms, reception areas, offices, and other rooms into a commercial office floor plan, as if packing a suitcase.

The floor plan below is called a “test fit,” drawn most often to determine whether a company’s office needs will “fit” in a given property they’re considering leasing. The rules for drawing a proper test fit attempt to satisfy many spatial goals: ensuring the right number of program elements (desks, offices, conference rooms, etc.), elements are sized properly in terms of floor area, fire codes are met, important guests can be shepherded directly from the entrance to reception to the largest conference room swiftly, that wheelchairs can navigate properly, corner offices have great views, and more.

Fit is also a problem of mathematics and geometry, often presenting as “close packing” or “tiling,” but also as dynamic problems like the counterintuitively challenging “moving sofa problem,” which is still unsolved.

This fundamentally depends on a notion of space that can be consumed by its occupants, either solid or otherwise.

Way-Finding and Way-Signaling

A two major classes of everyday problems are way-finding and way-signaling. If people walk into a building unfamiliar to them, how do they find their way around? How do they know where to go and how to get there? Do they use a map, posted signs, spoken directions from someone, conventions (every commercial office building likely has a security desk in the lobby), etc? Where are they not allowed to go and how do they know?

Then, in what ways should architects, who must ask and answer such questions before a building is constructed, signal the way to future occupants the knowledge they need to know? What spatial cues can they design into the form of a building? What conventions should they employ?

Crowd Management

Managing crowds of people, whether unruly or not, is an important spatial problem for a variety of places, including large-event venues like stadiums, high-traffic zones like airports, but also farms that manage hundreds of livestock. “Crowd control” is the defensive version of crowd management, a set of techniques used by law enforcement agencies to ensure safety and compliance during parades and protests.

Related, ever wonder why Disney World is the way it is, not necessarily the fantastical imagery, but customers waiting in long winding single-file lines for hours? And given that, why do some venues keep the crowd disorganized on one side of a crosswalk, only to divide them into parallel queues on the other side?

In US airports, does the TSA Pre-Check line really go faster than the regular security line? And do you notice there’s a third line for aircraft crews?

“Queueing” is a class of solutions that address how to coordinate crowds of people in an organized manner through some procedure, like boarding a ride at Disney World, ordering and getting fast food, entering/exiting a stadium, or going to the DMV. Queueing employs a combination of environmental fixtures or architecture itself (like the layout of an airport that separates people with ticket counters, security checkpoints, and terminal gates) in service of a set of corresponding operational processes and systems.

“Crowd simulation” and algorithms of “collective intelligence” can simulate crowd behavior and thus help plan for different scenarios.

Geopositioning

Geopositioning is the process of finding the geographic position of a person, place, or object in relation to the globe or a known mapped geography. This brings up a few questions, like what do “place,” “geography,” “map,” “local” or “location,” and “position” mean?

Localization

Related to geopositioning is localization, or determining an object’s position within an environment (like a room or street) or frame of reference (like the bookshelves of a library). This is particularly helpful for augmented and mixed reality headsets that intermingle virtual objects with the physical world. Some of the latest algorithms from research teams like Meta AI are making localization and object tracking much more efficient and accurate.

Navigation

Navigation covers a category of spatial problems involving planning and controlling the movements of vehicles, everything from ships on the sea, automobiles on a road network, airplanes through airspace.

Designing Spatial Connectivity

A major task in architectural design is the planning of circulation paths throughout a building, a kind of physical spatial connectivity problem for the flow of people, constrained by a building’s program, governing codes, and design concepts.

For example, courthouses requires strict separation between judges, attorneys, defendants, and the general public (including members of the press), except for the formal, controlled settings where they’re intended to meet as part of civil or criminal procedure (e.g., the courtroom).

Then, as complicated as all of that is, an architect designs so that everyone can reach an exit in the event of an emergency, which may create paths and connections that cut across the original topology of strict separation. And an architect will also ensure proper access for all individuals using wheelchairs.

More than this, there are forms of spatial connectivity that aren’t necessarily about physically moving people or things through a building. Visual connectivity (a fancy way to say opportunities for people to see stuff) is important to way-finding, but also to situations in which physical spatial connectivity isn’t desired, like the audience of a theatrical production. Audiences need to see the actors but be discouraged from walking on stage.