Constructive solid Geometry in functional programming

Question

I'm implementing CSG in a haskell program. When I did that in an OOP lahguage I was inspired by the Composite Patron.

I had an abstract class "Object", some concrete objects (Sphere, plane, etc), and a concrete class "CompositeObject" whith an operator and two pointers to Object.

To implement the CSG tree in that way in Haskell I was thinking in a recursive datatype:

data Shape = Sphere (..some types here..)
           | ..other primitive objects..
           | Composite Shape Op Shape 

Then I define the functions over objects by pattern matching. The problem here, is that all objects must be in this module. All objects are concentrated in a monolith.

I think that is a good idea having a typeclass for objects:

class Shape a where
  intersection :: Ray   -> a -> [Points]
  normal       :: Point -> a -> Vector
  ...

Now I define instances for Sphere, plane, cilinder, etc.

But what about composite objects? How can I create a type constructed from two types of a class, with the class functions depending on the constructors, or something like that?

Answer 1

The usual pattern is to skip the class and just make it data, like this:

data Shape = Shape
    { intersection :: Ray -> [Point]
    , normal       :: Point -> Vector
    }

Then you would have functions like sphere that took a position and a radius and produced a Shape; or a composite object that took two Shapes and did something with them.