change-your-points-of-view

Change your Points of View

We want to define the location x, y of a point on a two-dimensional plane where x and y are positive integers.

Our definition of such a point will return a function (procedure). There are several possible functions to do that.

Possible form of point:

... complete with the type of your function ... point(int a, int b) {
  // your code
}
The return type of point(a, b) is "java.util.function.Function"

Of course we need to be able to extract from our point the two coordinates x and y.

The function fst must return the first element x and our function snd must return the second element y.

We will also write a function sqr-dist which returns the square of the distance between two points point1 and point2.

Last function to write line:

Given two points foo and bar this function return a list (l m n) or [l, m, n] where l, m, n are the coefficients in the general equation l*x + m*y + n = 0 (1) of the straight line through the points foo and bar.

Equation k*l*x + k*m*y + k*n = 0 is equivalent to (1) and the tests consider that they define the "same" line.

Examples:

 foo = point(3, 5)
 typeof(point(3, 5)) === "function" -> true
 fst(foo) -> 3
 snd(foo) -> 5
 sqr-dist(point(22, 55), point(75, 66)) -> 2930
 line(point(20, 22), point(29, 10)) -> [12, 9, -438] ([4, 3, -146] is a good answer too)

Note:

• Please ask before translating: some translations are already written and published when/if the kata is approved.