[OT] Poll: What does it mean for 1 rect to be 'within' a certain distance of another rect?

[Alex Tweedly]

On 15/02/2021 23:21, Sean Cole (Pi) via use-livecode wrote:
> Hi,
> No point reinventing the wheel..

But most of those links actually did not have this particular wheel, or 
anything like it.

The exception was the last one (programmerssought.com) which had an 
ugly, inefficient and lengthy (45 lines in Python) solution. [OK, that 
45 includs blank and comments :-) !!

For me, a more precise problem specification is:

Given two rectangles (in regular Livecode format), the distance between 
them is :

  - if they touch or overlap, distance is zero.

  - otherwise, it's the smallest distance from any point in R1 to any 
point in R2.

Which leads to a simple solution

> function rdist R1, R2
>    local DX, DY
>    put max( item 1 of R1 - item 3 of R2, item 1 of R2 - item 3 of R1, 
> 0) into DX
>    put max( item 2 of R1 - item 4 of R2, item 2 of R2 - item 4 of R1, 
> 0) into DY
>    return sqrt( DX*DX + DY * DY)
> end rdist
>
Alex.


> Lots of other way. Distance between two near or far edges. distance between
> corners, distance to centers, or area median, area of space between,
> overal usage area minus the area used by the two rectangles. Math is fun.
> Keeps us in business.
>
> Google (distance between two rectangles):
>
> https://stackoverflow.com/questions/4978323/how-to-calculate-distance-between-two-rectangles-context-a-game-in-lua
>
> https://math.stackexchange.com/questions/2724537/finding-the-clear-spacing-distance-between-two-rectangles
>
> https://www.wyzant.com/resources/answers/583373/finding-the-distance-between-two-rectangles
>
> https://www.programmersought.com/article/44554760896/
>
> etc
>
> On Mon, 15 Feb 2021 at 22:53, Paul Dupuis via use-livecode <
> use-livecode at lists.runrev.com> wrote:
>
>> This is an Off Topic informal poll of sorts, but related to LiveCode as
>> I am writing a LiveCode expression to determine if 2 arbitrary
>> rectangles (r1,r2) are with some distance d (in px) of one another. In
>> considering this problem, the questions comes up: What is meant by
>> rectangles being within a distance d of one another. What is the 'd'
>> measured from?
>>
>> center to center? Easiest is many ways, but I don't think this is what
>> most people would think of.
>>
>> adjacent edge to adjacent edge? This is harder (I think), but I think
>> this is what more people intuitively think of. To me, implicit in the
>> visual concept of 2 rects being within some distance of one another is
>> that they are NOT overlapping, but that some gap exists between the
>> nearest adjacent edges?
>>
>> Something else? What does 2 rects  being 'within' d pixels of one
>> another mean to you, if not one of the two above options?
>>
>> Maybe there is a exact mathematical definition of what 2 rectangles
>> being within distance d of one another is, but, if there is, I am
>> unfamiliar with it.
>>
>>
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