Not sure if I understand your problem.
Is it the verbosity of extracting coordinates? (rect-one :x1)
Or is the problem with increasing the dimensionality?
Anyhow I would define the types as following:
(def point [1 2 3])
(def rect [point point])
(defn point-in-rect? [p [[r1 r2]]]
(every? true? (map <= r1 p r2)))
(defn overlap-rect? [a b]
(or (some #(point-in-rect % a) b)
(some #(point-in-rect % b) a)))
this should work for n-dimensions I think.
If you want to more closely follow your original code:
(with-destructured-rects rect-one rect-two
(and
(>= r1x1 r2x0)
(>= r2x1 r1x0)))
2011/5/29 Brian Watkins
> I often write code that deals with geometric coordinates and similar
> ordered n-tuples on homogenous bases. Lots of times I face the
> situation where I want to write a condition that says, "if these two
> regions overlap, then do something," or "if this function is satisfied
> over an axis ax+by=c or over an axis bx+ay=c then do something."
>
> The issue is that the x and y (and z and z' ... ) coordinates are
> often interchangeable and the condition needs to be satisfied over any
> one of them or all of them.
>
> Here, for instance, is a check that two rectangles, rect-one and rect-
> two, with corners [:x0 :y0] and [:x1 :y1] overlap. This is vastly
> simplified, of course. I'm sure you can imagine that when the
> combinations of axes and desired conditions become more and more
> complex, the code gets more and more repetitive and awful.
>
> (and
> (>= (rect-one :x1) (rect-two :x0))
> (>= (rect-two :x1) (rect-one :x0))
> (>= (rect-one :y1) (rect-two :y0))
> (>= (rect-two :y1) (rect-one :y0)))
>
>
> Problem is that code is awful and repetitive. I can shrink it in
> various one-off ways but I wonder if anyone has general advice or
> experience in writing a readable condition function. I think it
> should be reduced with multiple axes substituted into a function
> somehow but I don't know a good idiom to make it clear.
>
> Maybe an experienced lisper or wise code craftsman can help me out.
>
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