```rslt ← {c←1} ##.kball p         ⍝ Relationship between point and k-ball.

Supplied  by  Steve Mansour, this function determines the relationship between a
point and a k-ball. For background, see Steve's paper Arithmetic Boundary Check-
ing [abc].

For k=1, this is a line segment
k=2, this is a circle
k=3, this is a sphere
k=4, this is a hypersphere, etc.

c:  Left argument is a scalar or vector
First item of c is the radius
Remaining items are the coordinates of the center (default is origin)
If left argument is not specified, it represents the unit ball centered
at the origin.

p:  Vector or matrix
If p is a k-vector it is the coordinates of a point in k-space
If p is a k×n matrix, each column represents the coordinates of a point

rslt:  A scalar or vector of length n corresponding to the rows of p
indicating the region to which it belongs as indicated in the
diagram below:

┌───────────────────────────────────────────────────────────────────────┐
│                                                                       │
│       Outside (1)                                                     │
│                            *     *     *                              │
│                                                Boundary (0)           │
│                     *                       *   |                     │
│                                                 ∨                     │
│                 *                               *                     │
│                                                                       │
│                                                                       │
│             *                                       *                 │
│                                                                       │
│                       r                                               │
│             *<----------------->*                    *                │
│                                 c                                     │
│                                                                       │
│             *                                       *                 │
│                             Interior (-1)                             │
│                                                                       │
│                 *                               *                     │
│                                                                       │
│                     *                       *                         │
│                                                                       │
│                           *     *     *                               │
│                                                                       │
│                                                                       │
└───────────────────────────────────────────────────────────────────────┘

Examples:

5 kball 2 3                     ⍝ Inside the circle.
¯1
5 kball 3 4                     ⍝ On the boundary.
0
5 kball 5 6                     ⍝ Outside the circle.
1
5 1 2 kball 2 3, 4 6, ⍪9 9      ⍝ Radius 5; center at (1,2).
¯1 0 1

13 kball 5 6 7                  ⍝ Inside the sphere.
¯1
13 kball 3 4 12                 ⍝ On the surface.
0
13 kball 6 8 12                 ⍝ Outside the sphere.
1

See also: abc kcell ksphere

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```