We are all familiar with **3-dimensional** representations that align along
the x, y and z axes, the Cartesian coordinates that help us orient ourselves
in the physical world. But a “dimension” can also refer to an aspect, feature
or characteristic
of the object we are trying to describe. Parametric modeling
systems allow us to integrate data into the model so that, in addition
to its spatial orientation, the 3-dimensional representation also contains
and can display any characteristic we can describe mathematically or link
to through the cloud.

For example, we might represent a simple, box-shaped structure like the drawing on the right.

Then we might add a rule that says: this is a shed, and for sheds all surfaces along x and y axes shall be wood, and the “top” surface shall be a shed roof angled at 12° and covered with roofing shingles. The model will tilt the top and make all the other adjustments required to comply with that rule, like the drawing on the left.

If we have given the model a chart that lists the standards of construction
(for example, studs shall be 24 inches apart), the procedures (for example,
first frame the wall flat on a working platform using jigs, then remove
the jigs, raise the wall and connect it to another at a 90° angle) and
the average time needed to execute the procedures (10 minutes to set each
stud in a wall and 30 minutes to raise and connect each wall), it can calculate
how much time it will take to build this shed. This gives us a **4–dimensional
model** in which the fourth “dimension” is time, which is often illustrated
as a Gantt chart.

It can also provide us with a bill of materials (this is a common feature
of enhanced 3-dimensional models) that specifies the dimensions and material
of each component, taking into account, for example, that two of the walls
will have to have slanted tops to meet the slanted roof. If we have also
attached a chart that lists the cost of materials, the model can calculate
the cost of the shed matching the bill of materials to the cost chart.
This gives us a **5–dimensional model** in which the fifth
“dimension” is cost.

## Making the Model Virtual and Integrated

If we have placed the shed into its geographical context using web technology that allows the viewer to circle around and enter into the shed, we call it a virtual image of the shed. The fourth and fifth dimension can be represented by labels on the virtual shed, but since the model is integrated, clicking on those labels will trigger the underlying Gantt chart, bill of materials and cost catalogs, as well as the markup calculation used to generate the selling price.

A 3-dimensional model is an image; as soon as the fourth dimension is added it becomes an information model. Integration means that all the dimensions are dynamically connected, so that a change in one dimension triggers corresponding changes in all the others. For example, if we change the floor size of the shed from 5' x 8' to 6' x 11', time, cost and price will all change, the bill of materials will be refreshed to reflect the additional materials required and the Gantt chart will be refreshed to reflect the additional time required.

Five dimensional models are relatively simple to program and understand. Multi- dimensional models draw us into the realm of simulation, for they add the dimension of workflow or activity. An additional dimension for a model of a watershed with its flow control structures, for example, might be rainfall and the resulting water flow. The rules that govern that dimension are a projection from the historical rainfall averages and the formulae of hydraulic engineering that tell us how water moves once it has reached the ground. In our shed, the addition of workflow models can tell us what size shed will be required to allow a weekend gardener or a dedicated handyman to comfortably work in that space, what kinds of interior surfaces and storage spaces are needed, etc.

There are few limits on the nature and the amount of additional information that can be integrated into a multi-dimensional model — it might reach 12 or 24 dimensions if the data is available and the rules can be defined. For example, a model of a school can calculate room volume and square footage on the fly, match it to classroom space requirements and air quality standards by grade, and cost each room individually. A model of a development might act as a visual portal through which any authorized user can access real time information about any lot, identified visually or by keying in a lot number, and drill down to the plat, the building permits, information about the contractor and sub-contractor, and profit and loss calculations on that individual lot. From there, the user might drill back up to the financials for the entire development. Here at IDEAS, we believe the most important dimension in a multi-dimensional model is the workflow, and we reserve the sixth dimension for it. You can read about our integrated 6-dimensional virtual models here.