Re: Discuss Digest, Vol 37, Issue 7

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Re: Discuss Digest, Vol 37, Issue 7

jim_klessig
Troberg said
"This just gave me an idea. When doing odd shapes, hull is good for doing
convex corners, but not as good for concave corners.

With negative objects, this could be solved. Where a positive object
"stretches the surface" outside it, the negative object would instead
stretch it so that the object is outside the resulting object"

I do not see how that can work. For a quote negative space quote with hull.  It would have to "know" which way you wanted the deformation to go.

Hull looked at in two dimensional space, is essentially a minimum energy solution to surrounding the items with a rubber band. For any set of objects included in the hull, there is a single solution.
But with the "negative" space added, there is no longer a single solution. 
Again looking at 2d.  If we have  2 circles and hull them we get a "worm". If we add a +3rd, equally spaced we get a billards racking triangle. If that 3rd is - rather than +, there are at least 2 solutions, one is our original worm, and the other wraps around  the outside of the 3rd (making a nonmanifold result) .

If you add a 4th circle, with all 4 + you get a "round cornered square", a single solution. With two circles that are "-" (in opposite corners) you get the original worm, an "S" shape, a "Z" shape, and two different Boomerang shapes. 


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Re: Discuss Digest, Vol 37, Issue 7

nophead
>But with the "negative" space added, there is no longer a single solution.

I think there is if you hull all the positive objects first and then process the negative objects. Imagine a band around the positive objects and then introduce the negatives ones from the outside. You could get a conflict of they overlap though. That would be an error.

On 8 December 2017 at 17:28, jim.klessig <[hidden email]> wrote:
Troberg said
"This just gave me an idea. When doing odd shapes, hull is good for doing
convex corners, but not as good for concave corners.

With negative objects, this could be solved. Where a positive object
"stretches the surface" outside it, the negative object would instead
stretch it so that the object is outside the resulting object"

I do not see how that can work. For a quote negative space quote with hull.  It would have to "know" which way you wanted the deformation to go.

Hull looked at in two dimensional space, is essentially a minimum energy solution to surrounding the items with a rubber band. For any set of objects included in the hull, there is a single solution.
But with the "negative" space added, there is no longer a single solution. 
Again looking at 2d.  If we have  2 circles and hull them we get a "worm". If we add a +3rd, equally spaced we get a billards racking triangle. If that 3rd is - rather than +, there are at least 2 solutions, one is our original worm, and the other wraps around  the outside of the 3rd (making a nonmanifold result) .

If you add a 4th circle, with all 4 + you get a "round cornered square", a single solution. With two circles that are "-" (in opposite corners) you get the original worm, an "S" shape, a "Z" shape, and two different Boomerang shapes. 


Sent from my U.S. Cellular® Smartphone

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