# Euclidean approach to mesh offsetting

(Aris Nikolopoulos) #21

man, you still don’t get me! can you pls answer me the following question?
(which is the subset that meets the demands and what are the prequisites)

(Aris Nikolopoulos) #22

All of your answers are like “squaring the circle” your approach is that you can approximate it with astronomically close proximity. My question is ‘what is the ABSOLUTE’ solution.
(and so far, I am convinced that there is an absolute solution)

But if this:

can being “reformed” (with a physics engine you silly, he he) to that:

What makes you believe that I can’t get you? (The Lord knows what you want before even you think of it). But … the question is: since you are a fellow Greek (and the Lord helps Greeks) what I’m trying to tell you?

Option A: It’s just a mind trap > avoid.
Option B: Addressable … but not with things/means that you can handle > avoid.

Note: We are engineers > there’s no absolute (only the Absolute Vodka qualifies). Even thinking or searching for that > it’s a crime > bad boy > prison for life.

(Aris Nikolopoulos) #24

since we bring Greekness into the matter (although math has no country, it is absolute and eternal) I will answer you with the last passage of Ithaka (the poem):

“And if you find her poor, Ithaka hasn’t fooled you.
now that you became wise with so much experience
you should have already understood what Ithakas mean”

my delusional (?) trip has already brought me a lot of insight into how planes behave. What if I don’t find the answer I’m looking for? what you call a rabit hole I call the trip to ithaka!

Still I am convinced my intuition is right: with approximation you can only have an solution to any given problem at hand but you cannot have imergence…

See that freaky fella over there ?: he spend all of his time trying to solve the following puzzle: given a gazillion of atoms (of thin air) in a room > make clusters with co-planar atoms (where 0 is 0.00000000000000000000000000000001)…

See that other fella over here ? He writes some lines (well … maybe some “more”) then gets a Coffee Lake CPU (cores aplenty) on some X299 mobo and squeezes the start button.

Moral: Ithaka can fool you some times (in fact most of times)

(Aris Nikolopoulos) #26

I doubt it will be me, but at some point some guy is going to give you a simple formula and your code lines will be reduced to the equivalent of just a cupful of coffee (ideally, frape!)

That’s impossible. Why?

Well … is like claiming that you can outline (theoretically) the ideal fuel injection map (+ the paraphernalia: correction tables et all) for a given thermal engine

Since non rational conditions vary constantly (engine wear, circuit glitches, sensor health, fuel quality, air quality etc etc) the only thing that you can do is to write down the code that adapts to all that (and pray).

Exactly what’s happening in the rectangle with the hole thingy as above: Instead of trying to create rules (fruitless and restrictive = the art of pointless since these days ANY form should being solvable [triangles, mind, not quads]) you dismiss ANY rule, set sky as the limit and approach the problem the physics engine way (should I call it: a self learning process?): tiny changes to this node (in relation with the others etc) applied a gazillion times yield a big thing that can been made by not flexible THICK and HEAVY plywood “stripes” ( that make self supporting triangular “frames”) … and that is 0 planarity for me (and should be OK for you as well).

This fundamental difference is all what computers serve (but I hate computers, he he). Anyway … before AI arrives to the masses (the end of days).

Moral: free your mind, forget determinism .

And this … well … it’s a classic thingy on that matter by Daniel using K1 (a bit old but still …classy). Daniel is to Kangaroo what David is to GH. Torsion free means “planar” (green), mind. Spot that changes in the geometry happen (that’s obvious anyway) but who cares? and who should? (nobody who understands a thing or two about the true essence of computers [and physics engines])

Insofar I hesitated to post it because you are searching things the entirely wrong way (by actually forgetting what computers are) … but … well … you know Greeks … never give up etc etc, he he.

torsionfree.gh (25.3 KB)

(Aris Nikolopoulos) #29

emergence…

evanescence most likely (but who’s counting?).

BTW: a cat who become a Buddhist monk spots a freezing baby sparrow . ASAP puts the bird deep into some horse #%@##. Baby is happy: warm/safe et all. The next day a dog who become a Buddhist monk spots the bird. Thinks: WTF > let’s give the poor bird some clean air. But a hawk (who failed to become a Buddhist monk) spots the bird and does what hawks do.

Moral: obvious

Added the freaky part: Is it truth out there ?

torsionfree_withPlanarityCalcs_V1.gh (131.1 KB)
:

(Aris Nikolopoulos) #31

btw, we disagree strongly on the approach but I bow to your knowledge and the gold you posting!

You are trapped in an ominous pendulum: Only the Lord (the Merciless King of SardineLand) can save you.

Salvation:Sign the paper (Imagine what the rest of my defs (~10+K) do). Sell soul > get slavery > be a happy bunny

just_sign.pdf (35.4 KB)

(Aris Nikolopoulos) #33

hahahahaha the LOD hasn’t shown me not even a glimpse of what I’m looking for. even if I was willing to give away my soul, I haven’t seen any proof that the aforementioned skills would give me the capablility to achieve my goal. Therefore the offer is deemed of highly questionable outcome and is hence kindly rejected!

#34

Wow, this thread - the last half of it anyway - reminds me of Usenet in the 90’s.

Well that unwise rejection reminds me the tale of an alligator (who become a Buddhist monk). One day he … blah, blah.

See this? (MeshMashine > Physics engine > random relaxed blob > 6 methods to pick naked/clothed anchors (+ an interactive one as we discussed in the phone) > then do this, that (and that)). If all the black (LoD’s official color) things are planar (like the green things as above) within a very small tolerance (say 1-2 millimeters) and therefor 100% doable … what is the meaning of all the rest?

Answers: the alligator, district 9 , apartment 666, north pole.

(Daniel Piker) #36

To cautiously step in here…

@anikolo - Based on what you write in your first post, it sounds like what you are looking for is what is often referred to as a face/face offset mesh.

So both the inside and outside, and all the sides of your cells are planar, the inner and outer mesh have the same number of vertices, and the inside and outside face pairs are all at the same distance from each other.
If just looking at the sides of the cells as beams, this is also an example of a structure with torsion free nodes.

A quad mesh has this property if it is conical - which means all the faces around each vertex are tangent to a common cone.
Closely related are circular meshes, where the vertices of each face lie on a common circle.
Circular meshes can also be offset to another planar mesh, and still ‘node out’ with torsion free nodes, but instead of having constant distance between corresponding face pairs, they have constant distance between node pairs.
You can convert back and forth between circular and quad meshes, and it is sometimes easier to create a circular mesh first and go from that to a conical one.

Also - regarding approximation, when you are modelling anything more complex than a simple orthogonal shape on a computer, there will always be some deviation from geometric rules in the ‘strict Platonic sense’ due to the finite precision used in calculations. We usually don’t worry too much about this, because these deviations will typically be many orders of magnitude less than practical construction tolerances (easily less than the radius of individual atoms).

There are ways of generating face-face offset meshes for certain simple types of geometry through simple short sequences of geometric operations, but for more complex shapes, generally the only way we have is to use some sort of iterative/numerical/optimisation based method.
These methods do change the nature of the design process somewhat, and in cases where a simple non-iterative geometric construction exists it often makes sense to use that, but if used correctly you can use iterative methods to generate far more varied shapes and still meet given geometric constraints to a degree of accuracy that can be considered exact for all practical purposes.

(Aris Nikolopoulos) #37

Daniel, now we’re talking!!!
I have been studying on the subject the past few days and thanks to Ander’s post I’ve found extensive literature (which I’m still going through).

The reason I’m insisting on (let’s call it) the Platonic approach is this: Although I’ve already found the tools to practically turn almost any polysurface into a tortion free offset mesh by approximation, I haven’t so far found what the prequisites are for a set of joined faces to be conical. It is an instinct that if I understand HOW conical faces behave I could discover ‘emergent’ forms.
for example: It was a very joyfull moment for me to discover that triangular offset faces can only (platonically) give you a sphere! If I followed Peter’s approach I would have gone forward into making any blob I want but I would never have discovered the sphere! Now with Quadrilateral faces what is the range of forms you can ‘legitimately’ achieve?
I am sure this knowledge exists, I just haven’t found it so far.

I don’t know if I am making myself clear, but as I search into the geometry of the conical faces, I see that they behave in a specific way(they limit what you can do and often I have found that a limitation is just an apparition of a deeper harmony that you just don’t understand yet.)
and that is the point of our (very interesting) disagreement with Peter, because his position is:
“give me any surface and I can turn it into a -PRACTICALLY- torsion free offset mesh” when my question is:
“if you respected in absolution, the rules that govern conical faces, what forms can you get?”

I don’t even know if it is a valid question, I just have a hunch that it is… and I admit to a limited knowledge on the matter but I’m posing those questions in the hope that somebody will point out my misconceptions or give me answers…

(Aris Nikolopoulos) #38

oh and by the way, I’m conscious that it is annoying when somebody is exposing his ignorance so ‘shamelessly’ but it’s worth it! your answers guys have sped up my education on the subject dramatically!
(thank you very much!)

BTW: In relation with yesterday’s conversation and taking a break from theoretical exploitation(s) [I hate that] … see this (static) thingy:

RealLife.zip (2.0 MB)

2 “planarized” (compare size VS planarity tolerance: realistically 0) beam like meshes (tri-quads) plus 666 instance definitions of some very simple human figures plus some truss axis lines. It’s a hybrid LBS with a MERO KK system and beams that in fact are carbon fiber double C combos. It’'s related with a WIP project - some future EXPO thingy (a bit oversized as the owners vanity, mind).

state of things before the magic:

If such primitive stuff yields a 7 MB Rhino file … imagine what happens if you advance a bit things and invite real objects to the party.

Moral: All king’s horses and all king’s men … blah, blah.

(Aris Nikolopoulos) #40

wow!!! still not what I’m looking for but wow!!! (and I liked the 666 instances hahahaha)
Appart from showing off though,have you found any bibliography for me ?