Not necessarily. In 3D graphics, it is common to represent points with homogeneous coordinates, where points in N-dimensional space are represented by N+1 real numbers. Using 4x4 matrices [0] to describe affine transformations of 3D points is very convenient.
(Agreed with your overall point though. Just goes to show how different some fundamental perceptions/definitions can be.)
It actually is. It's generally assumed to be equal to one, but it need not be.
> isn’t necessary to store to apply a 4x4 matrix
...if you assume it is equal to one, yes.
However, actually representing the fourth component is both mathematically sound and occasionally useful. For example, the midpoint of two affine points, such as (1, 2, 3, 1) and (3, 6, 9, 1) is actually just their sum: (4, 8, 12, 2), which represents the same 3D point as (2, 4, 6, 1). The fourth component can also be zero, in which case you describe a point at infinity in the given direction.
But yes, if you only use homogeneous coordinates for chaining 3D transformations, storing the extra component it pointless.
This is the first time I’ve come across this definition of a point. Geometrically point is defined as a zero dimensional shape (or something similar) if I recall correctly.
Besides, I don’t see how it’s intuitive at all! It isn’t to me at least.
Larger point being, if you pick such random domain without calibration you will run into such argument/discussions during an interview. Not sure what data point could be derived from such discussion when you are looking for someone who can write a decent maintainable code.
I must say that I’m terrible with geometry/graphics which hasn’t stopped me from creating value through software development in my domain, online payments.
If your intention is to gather signal for collaboration then I suggest picking something you are likely to collaborate on a day to day basis. Let’s say code review or architecture review. You could discuss why such and such an architectural pattern is useful, under what conditions, what are the pitfalls to watch out for etc etc.