Trilobe hatch pattern

[eldon]

Not wanting the brain to atrophy over the holiday season. I thought to post a hatch pattern that I have called Trilobe-E. I expect others can make a hatch pattern faster with various tools, but I like to use Autocad and trigonometry (in a spread sheet). It was based on a unit sized hexagon.

As the grid is a hexagonal one instead of an orthogonal one, the brain was given good exercise.

 

I am posting the text of the file as well as the pattern file.

 

*Trilobe-E, trilobe pattern
307.589089469,3,3,12.1236363414,0.1320676359,0.15069,-19.521625573
322.410910531,3.0919,2.8806,9.6409374243,-0.2287478555,0.15069,-11.2071266916
337.589089469,3.2113,2.7887,9.6409374243,0.2287478555,0.15069,-11.2071266916
352.410910531,3.3506,2.7312,12.1236363414,-0.1320676359,0.15069,-19.521625573
7.589089469,3.5,2.7113,12.1236363414,0.132067636,0.15069,-19.521625573
22.410910531,3.6494,2.7312,9.6409374243,-0.2287478555,0.15069,-11.2071266916
37.589089469,3.7887,2.7887,9.6409374243,0.2287478555,0.15069,-11.2071266916
52.410910531,3.9081,2.8806,7.5486792315,0.132067636,0.15069,-19.521625573
112.410910531,4,3,12.1236363414,-0.132067636,0.15069,-19.521625573
97.589089469,3.9425,3.1393,-9.6409374243,-0.2287478555,0.15069,-11.2071266916
82.410910531,3.9226,3.2887,9.6409374243,-0.2287478555,0.15069,-11.2071266916
67.589089469,3.9426,3.438,12.1236363414,0.132067636,0.15069,-19.521625573
52.410910531,4,3.5774,7.5486792315,0.132067636,0.15069,-19.521625573
37.589089469,4.0919,3.6968,9.6409374243,0.2287478555,0.15069,-11.2071266916
22.410910531,4.2113,3.7887,9.6409374243,-0.2287478555,0.15069,-11.2071266916
7.589089459,4.3506,3.8461,12.1236363414,0.132067636,0.15069,-19.521625573
67.589089469,4.5,3.866,12.1236363414,0.132067636,0.15069,-19.52162557
82.410910531,4.5575,4.0053,9.6409374243,-0.2287478555,0.15069,-11.2071266916
97.58908946,4.5774,4.1547,9.6409374243,0.2287478555,0.15069,-11.2071266916
112.410910531,4.5574,4.3041,12.1236363414,-0.132067636,0.15069,-19.52162557
127.589089469,4.5,4.4434,7.5486792315,-0.132067636,0.15069,-19.52162557
142.410910531,4.4081,4.5628,9.6409374243,-0.2287478555,0.15069,-11.2071266916
157.589089469,4.2887,4.6547,9.6409374243,0.2287478555,0.15069,-11.2071266916
172.410910531,4.1494,4.7121,7.5486792315,0.132067636,0.15069,-19.52162557
*eldon fecit MMXXIII

 

Trilobe-E.pat

[SWDivad]

Very interesting pattern and works perfectly in SolidWorks as well...

 

FYI, I have tried to get ChatGPT to create some patterns while in search of creating hatches to simulate perforated sheet... ChatGPT failed in all attempts so far to create a hatch pattern of dodecagons... For that, I have not attempted it, but it does seem to be a simple exercise.

 

Do you think it's an easy exercise to create dodecagon hatch patterns with different percentages of open area?

[eldon]

@SWDivad, I am glad the pattern works for you.

 

The trouble I see with using a hatch pattern for your need , is that at the edges, there would be part holes. So the hatch would not be able to reproduce your picture above. If it were easy to do, then I expect there would be plenty of hatches available!

 

The secret in writing hatch definitions is to accurately calculate the exact position of the next node in the direction of a line, and slightly alter the angle to give a perfect landing. With the limitations of significant figures and the limitation of the number of characters in a single line, there can be a variation of the position of the lines when far from the origin - have a look at the AutoCAD concrete hatch pattern.

 

Anyway, this topic might be of interest to you. But why limit the "circle" to 12 sides? I wrote a pattern for a 32 sided "circle" (icosidodecagon or triacontadigon). It took time and I don't know whether the eye could appreciate the difference. If such a porosity pattern were to be written, I see no problem in scaling certain linear parts of the definition as the angular numbers would be the same.

[BIGAL]

I have a lisp called zigzag it takes a shape and draws it with a stagger like what you want, but its not a hatch, you can enter space values. You need multi getvals.lsp so save into a support path.

 

; https://forums.autodesk.com/t5/visual-lisp-autolisp-and-general/rectangular-array-creating-every-other-row-offset/td-p/9667120
; array rows a 1/2 x spacings
; Enter -ve values to change direction.
;By AlanH info@alanh.com.au Aug 2020

(defun c:zigzag ( / ent ss ans hor ver numx numy x )
(setq ent (entsel "\nSelect object to array"))
(setq ss (ssadd))
(ssadd (car ent) ss)
(if (not AH:getvalsm)(load "Multi Getvals.lsp"))
(setq ans (AH:getvalsm (list "Enter spacings " "Horizontal  " 7 6 "100" "Vertical" 7 6 "50" "Num X " 7 6 "3"  "Num Y" 7 6 "3")))
(setq hor (atof (nth 0 ans)))
(setq ver (atof (nth 1 ans)))
(setq numx (atoi (nth 2 ans)))
(setq numy (atoi (nth 3 ans)))
(setq x 1.0)
(repeat (- numx 1)
(command "copy" ent "" (list 0.0 0.0) (list  (* x hor) 0.0) )
(ssadd (entlast) ss)
(setq x (+ x 1))
)
(setq x 1.0)
(while (< x numy)
(command "copy" ss "" (list 0.0 0.0) (list (* 0.5 (- hor)) (* x ver)))
(setq x (+ x 2))
)
(setq x 2.0)
(while (< x numy)
(command "copy" ss "" (list 0.0 0.0) (list 0.0 (* ver x)))
(setq x (+ x 2))
)
(princ)
)
(c:zigzag)

 

 

 

Multi GETVALS.lsp

 

[eldon]

I will start a new thread on Perforated Plate Patterns when I have calculated a few examples.