There are multiple solutions for the requirement of “wrapping around the edges”. Depending on the background of your participants, they might have different understandings of the coordinate system. Previous experience doing this kata shows that misunderstandings, e.g. participants arriving with different mental models, can easily derail the kata and deflect from testing and designing. For facilitators, we recommend you work towards the participants aligning on which model to go by.

It is most helpful to work with visualizations and spend some structured time exploring the problem and the options the participants present and highlight how they can all be valid solutions.

Torus/Donut: Retaining euclidian geometry

Similar to games (think snake, pacman), where the player vanishes on the top and reappears on the bottom (vis versa for left & right), this might be a solution someone with a mental model based in maths/topology or games arrives at.

The implementation does not produce any new edge cases, but the mental model might be hard to align on.

Example:

In a 4x4 grid (x ∈ { 1, 2, 3, 4 }, y ∈ { 1, 2, 3, 4 }) the following table shows the resulting position for a movement on the grid:

Credit to @drpicox for providing an explanation for this model.

Polar coordinate system: Thinking in maps and planets

This interpretation of the grid system lends itself to the concept of latitude and longitude. The sphere is sliced into an even number of latitudes (equidistant lines) and longitudes (evenly spaced lines from North to South pole)

In this model, X and Y become abstract representations of longitudes and latitudes.

While the model might be the first one people arrive at if they’re coming from the mental models of planets and maps, it produces some significant edge cases that make this solution rather challenging:

Some potential challenges:

• The distance between two points of the grid is no longer the actual distance. (two points close the poles are closer to each other than two points on the equator)
• If the Poles can be represented through the coordinates, the behaviour at that point is undefined. E.g. at the North pole, the Mars Rover always faces South (by definition), but the direction it would move forward to is informed by the longitude it is facing. (e.g. (x, 1) for all x ∈ {1, 2, 3, 4} describes the same point, but a different point the mars rover will end on if it moves forward.)
• The geometry at the poles is no longer euclidian, e.g. the path you take at the pole to arrive back at the same position has three corners, where everywhere else it has four.

This interpretation is vastly more complex, but can be tamed by constraining the solution to the following aspects:

• The number of latitudes and longitudes is the same and a multiple of 2
• x and y are positive integers. Positions not on the grid can not exist.
• The poles are not “on the grid”. The rover moves “over” the pole but never rests on them.

Example

In a 4x4 grid (x ∈ { 1, 2, 3, 4 }, y ∈ { 1, 2, 3, 4 }) the following table shows the resulting position for a movement on the grid: