Grid indicators

Constructions have properties, such as construction and demolish costs, construction time, amount of floor space. Sometimes, a property can influence the surroundings. You might want to be able to measure this influence. Additionally, influences of multiple constructions may overlap.

Let's say I want to measure the attractiveness of a particular area and project it in an overlay. I can give each construction a parameter Attractiveness. Not every construction will be attractive, but I am interested in the average Attractiveness of any location on the city map. For this situation, a Grid Indicator comes in handy.

Let's consider a subsection of the city map. A construction is situated in the middle. The construction has a quantified attractiveness of 5. In order to measure the average, we map to polygon to a grid. You can do this in many ways, most often the average of intersections on a tile. However, also the mean, max or min can be considered.

For simplicity, I chose to multiply the overlap fraction of a grid square with the polygon, and multiply that with the attractiveness factor of the polygon. I rounded this number to make the image more readable.

Now that the polygon(s) have been mapped to a grid, a filter can be applied to that grid.

Since I want to know the average attractiveness of a location, I will use an average filter. My average filter will spread 1 extra grid tile in each direction. The following 3 by 3 uniform average filter will suffice:

A filter can be applied to the grid, resulting in the following averaged grid:

Next, an average value can be calculated for a zone, by consulting the grid tiles within a zone. This average score can then be used to calculate an indicator score to measure improvements made. Furthermore, an overlay can be generated using the filtered grid and adding a color mapping to it. For now, we only allow a linear color mapping, but it might be expanded in the future. The image below shows a linear color mapping from 0 to 5 with a ramp from blue to green.

In stead of calculation an average score of a zone, you can also measure the amount or percentage that scores above or below a threshold value. As an example, let's define a rule that every house in the city should be within 2 miles of a police department. We can give the policedepartment a coverage value, apply a large average filter with a range of 2 miles and set the threshold to >0. Measuring the amount of grid cells with a value below the threshold will lead to the percentage that is not covered by a police department.