Rectangle Surface Primitive and Integration with Box

[hervasa2]

Definition and plotting for Rectangle Surface Primitive. Rectangles are restricted to have normal vectors on x, y, or z

• Functions: in(), sample()
• Pending: distance_to_surface(). To be added along with that of prism surfaces.
• Pending: sample() with ticks

Box now has get_decomposed_surfaces(). It gets decomposed into two of each: Rectangle{T, Val{:x}}, Rectangle{T, Val{:y}}, Rectangle{T, Val{:z}} unless one of the dimensions is zero.

[fhagemann]

Nice! 👍

Some comments:

• I find the surface primitives Square from RegularPrism and Rectangle from Box quite similar. People might think that a square Rectangle might be a Square, so we should discuss whether we want to rename Square then.
• For the Rectangle constructors: what do you think about introducing aliases
  (e.g. RectangleX = Rectangle{<:Any, Val(:x)})?
  Because I do not think it is the user-friendliest option to use Val(:x) as input for Rectangle.
  Also, it would allow getting rid of most of the Val(:x) in the code.

[fhagemann]

Can you remove AbstractSurfacePrimitive before the [?
Julia will know that this is a Vector{Rectangle} and convert it to a Vector{AbstractSurfacePrimitive}, e.g. when determining the decomposed surfaces of contacts.

[hervasa2]

We've had this conversation before. This also happens with the Sphere and in some other specific cases. The AbstractSurfacePrimitive is there for consistency. This is still a pending issue that deserves its own PR

[fhagemann]

I added the sample functions with CartesianTicksTuple and CylindricalTicksTuple.

The sampling with CartesianTicksTuple is extremely straightforward.
The Rectangles are sampled at their edges and all the grid ticks in between:

The sampling with CylindricalTicksTuple is a bit more tricky.
For each φ, the intersections with the four edges of the Rectangle at positive radii are determined. This can be zero (no intersection), one (the Rectangle includes the origin of the coordinate system), or two (the Rectangle has an offset and does not include the origin of the coordinate system). Then, all ticks in r between the intersection points are sampled with the grid spacing as step size:

Especially the sampling with CartesianTicksTuple might need some nice polishment but it should work for now.

[fhagemann]

I would like the sampling of Rectangle to also sample intersections of r ticks with the edges and not only the intersection of the φ ticks. This would result in more samples on the blue lines in this figure (especially the top left of the Rectangle):

Let me work on this before we merge.

[fhagemann]

Sampling with CylindricalTicksTuple now also includes sample points at r-ticks on the edges:

Sampling only at r ticks

Combined sampling

The corners of a Rectangle are not explicitly sampled. However, when creating the Grid, the "important points" of the Rectangle will be added such that the corners will "naturally" be sampled at a specific r and φ tick.