Sven,
Am Montag, 4. Mai 2009 13:33:33 schrieb David Duke:
Decoupling basic primitives for geometric modelling from OpenGL would be
useful. [...]
Even just data constructors and instances of these within Functor and
Applicative are a useful starting point. [...]
This leads me to the conclusion that I should only lift the data types for
vectors and matrices out of the OpenGL package, including only instances for
standard type classes like Eq, Ord, Functor, etc. This means that the new
package will *not* include type classes for things like scalars, vector
spaces, etc. These can be defined by the other packages in their own "type
class language".
That seems a reasonable step. If and when consensus does emerge on
packaging vector & matrix operations, that could be added as a further
package.
Regarding Functor/Applicative: The obvious instances for e.g. a 2-dimensional
vertex are:
data Vertex2 a = Vertex2 a a
instance Functor Vertex2 where
fmap f (Vertex2 x y) = Vertex2 (f x) (f y)
instance Applicative Vertex2 where
pure a = Vertex2 a a
Vertex2 f g <*> Vertex2 x y = Vertex2 (f x) (g y)
They fulfill all required laws, but are these the only possible instances? If
not, are they at least the most "canonical" ones in a given sense? And
finally: Does somebody have a real-world example where the Applicative
instance is useful? Usages of the Functor instance are much more obvious for
me.
The Vertex constructor and Applicative operators don't seem to admit
anything different that is also sensible (unless someone has a use for
<*> with function and/or args permuted). As to real-world example, if
you interpret a vertex as a (position) vector and want to apply that to
another vertex, liftA2 (+) is neat. For working with sampled data, we
have something like
class Interp b where
interpolate :: Float -> b -> b -> b
with suitable instances for types in the numeric hierarchy, and then
instance (Interp a, Applicative f) => Interp (f a) where
interp t = liftA2 (interp t)
If vertex is an instance of applicative, we then immediately have
interpolation between coordinates (we use it in contour and surface
extraction, others may find it useful in animation or distortion).
David
--
Dr. David Duke E: d...@comp.leeds.ac.uk
School of Computing W: www.comp.leeds.ac.uk/djd/
University of Leeds T: +44 113 3436800
Leeds, LS2 9JT, U.K.
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