Suppose I have a (twisted) line, for example

```
2-x==y && x< 1
3-2x == y && 1.5>=x>= 1
```

I want to take this crooked line and represent it discretize it (that is, I want to show points along this line)

I can do this with discretize region, for example

```
r=ImplicitRegion(2-x==y && x<1 , {x,y});
r2=ImplicitRegion(3-2x == y && 1.5>=x>= 1,{x,y});
DiscretizeRegion(RegionUnion(r,r2))
```

This will give me a graph of the line and some discrete points (I would rather not include the line here, but that is not too important)

- How can I show how these points are determined?
- How can I control how these points are determined?

I suppose there is a mesh function or something similar, and if so, I could control how the points are determined by specifying the mesh, but I could not solve this.

Alternatively, perhaps it is better to use something like MeshRegion?

An explanation of what I want to do:

I want to take a function (a twisted line in this case, but the function doesn't really matter).

So, I want to build a grid **consisting of points generated by the intersection of vertical and horizontal grid lines, spaced at size intervals $ d $**

Next, I want to find the intersection of these points and the function, and show only these points, as well as the underlying grid that generated them

- (I'm fine if I don't visualize the grid if it gets in the way of the visualization, as long as I can generate a separate chart that shows the grid that was used. Basically, I want to be able to visualize how the points are selected)

I realize that I can write a custom code to do this. If this is the route you want to suggest, I'd rather try to write the code myself to improve in math, unless I have a particularly elegant (or short) solution to suggest.

I also realize that I could do the above with a mesh, where the mesh cells are points. If this is possible, I would like to see how to do it, since I don't understand well enough how the mesh works (and the mesh cells, etc.).