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#51

Mr Magoo
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Joined: 04 May 2014
Posts: 225
Member
26 August 2016 10:49 pm

Interested for sure. Although no sure if I'll get it. Can you at least PM it? I have not done the maths. Just been testing Gem CAD which seems to me, work.

2 users like this post: AtomRat, Nena

#52

Nena
Member
From: Hoogeveen (NL)
Joined: 03 July 2016
Posts: 222
Member
27 August 2016 05:54 am

The Calculation big_smile sorry for the long math big_smile lol. But i done it!

Pavilion Build:

Getting my 16 triangles

360* / 16 = 22,5*

Cutted Total Width = 1.0"

1 / 2 = 0.5 (half)

Calculating first triangle: I know the degrees and the lengt of 2 sides of the triangle .500" i need to
calculate the 3th side.

A Side Length = 0.5
B Side Length = 0.5
C side Length = ?
A Angle = 22.5

2x 0.5 square root = 0.25

0.25 + 025 - 2 * 0.5 * 0.5 * cos(22.5) = 0,03806023374435662193590840530161 square root = 0,19509032201612826784828486847703

C Side Length: 0,19509032201612826784828486847703 (REMEMBER!!)

We now can calculating the angle of the sides B & C

We have:

A Side: 0.5
B Side: 0.5
C Side: 0,19509032201612826784828486847703

(sqr(0,19509032201612826784828486847703) + sqr(0.5) - sqr(0.5)) / (2 * 0,19509032201612826784828486847703 * 0.5) = 0,19509032201612826784828486847703
cos-1(0,19509032201612826784828486847703) = 78,75*

Now i can calculate the height of the triangle:

0,5 * sin(78,75) = 0,49039264020161522456309111806712

Remember: 0,49039264020161522456309111806712

Now we need to calculate the height with the 41 angle this is what we got:

A side: 0.5
A angle: 41*
A angle: 90*

90* - 41* = 49*

0.5 / tan(49) = 0,43464336890811333110004781935197

With the awnser of that we create a new triangle with the remembered calculation we need to get the length
of the triangle this is what we got:

A side: 0,49039264020161522456309111806712 (remembered)
B Side: 0,43464336890811333110004781935197 (Heigth of pavilion with the 42.1 degrees)
A Angle: 90*

sqr(0,49039264020161522456309111806712) + sqr(0,43464336890811333110004781935197) = 0,42939979969970514285074057912462

0,42939979969970514285074057912462 square root = 0,65528604418200845951299818907049 (REMEMBER SECOND TRIANGLE)

if we devide the awnser we have a midpoint from a rectangle and between 2 triangles. And we can now calculate
the first angle of the cut a way piece.

0,65528604418200845951299818907049 / 2 = 0,32764302209100422975649909453525

we remembered the 0,195 from the beginning we now devide that one to in 2.

0,19509032201612826784828486847703 / 2 = 0,09754516100806413392414243423852 REMEMBER!!

A Side = 0,32764302209100422975649909453525
B side = 0,09754516100806413392414243423852
A Angle = 90*

We need to calculate the angle of the triangle

0,32764302209100422975649909453525 / 0,09754516100806413392414243423852 = 3,3588854506469852220206832501572

tan-1(3,3588854506469852220206832501572) = 73,420794479222064121318415104858* degrees

Our cutting Angle is: 73,420794479222064121318415104858* Degrees

Almost there big_smile

We now need to calculate the angle of the square (double triangle) where we divide the awnser from
we now need the full length to get the angle.

We use the same diveded line width from the last triangle calculation

We have:

A Side: 0,65528604418200845951299818907049
B Side: 0,09754516100806413392414243423852 Remembered!!
A Angle: 90

0,65528604418200845951299818907049 / 0,09754516100806413392414243423852 = 6,7177709012939704440413665003143

tan-1(6,7177709012939704440413665003143) = 81,533186488604028574831045002464

We can now calculate our meetpont with those two triangles!!! I now need to calculate one side length to
get the tip of the triangle that indicates our MEETPOINT!

We got the following:

Side A: 0,19509032201612826784828486847703 Remembered from the beginning!
Angle A: 73,420794479222064121318415104858
Angle B: 81,533186488604028574831045002464

Get the 3th angle

180 - 73,420794479222064121318415104858 - 81,533186488604028574831045002464 = 25,046019032173907303850539892678

Now i can calculate te length of Side B to calculate the heigth of the triangle:

sin(73,420794479222064121318415104858) * 0,19509032201612826784828486847703 / sin(25,046019032173907303850539892678) = 0,44167099778293711698181581067354

Height of the angle:

0,44167099778293711698181581067354 * sin(81,533186488604028574831045002464) = 0,43685736278800563967533212604698

Pfiew! big_smile Took a complete day to get that point.

Exact Meetpoint: 0,43685736278800563967533212604698

degrees_k.jpg

Measured from the girdle the beginning of the pavilion! And on the angle from the 42.1* cut. The meetpoint is at the outher side of the cut.

Dont use the picture for calculating! I used it only as a guide big_smile

Greets

Christian

Last edited by Nena (27 August 2016 06:43 am)

1 user likes this post: AtomRat

#53

kawman
Member
From: Taree, NSW
Joined: 11 July 2013
Posts: 935
Member
27 August 2016 07:38 am

that is a brain buster.. yikes

#54

AtomRat
Member
From: Katazone, VIC
Joined: 22 May 2014
Posts: 5,080
Member
27 August 2016 09:59 am

Does that Autodesk support scripts like 3dsmax? Bloody interesting to watch!
Is the above just one polygon / facet made from two faces ( 6 vertices ) from the code, or is it split further again to get a meetpoint, or is there a small amount of code missing to make all 16 triangles? Supplied image doesn't help no lol lol Top job


Wisdom is knowing how little you know

#55

Nena
Member
From: Hoogeveen (NL)
Joined: 03 July 2016
Posts: 222
Member
27 August 2016 08:06 pm

It is now possible to calculate all 16 meetpoints and use the height and with to make a 3d code drawed image. By setting up an array with only points. The only thing you need to do is drawing from point to point.

Mr Magoo

I posted it online becouse i could not find any information about getting a meetpoint. If im rigth it shoult work with different stones. Otherwise i need to do some recalculations from the midpoint of the 41* degree cut.

There a some mistakes in my text by the way!

> B Side: 0,43464336890811333110004781935197 (Heigth of pavilion with the 42.1 degrees)
Must be 41* Degrees.

>Measured from the girdle the beginning of the pavilion! And on the angle from the 42.1* cut.
Is also 41* Degrees.

I will make a little program out of it to calculate it with different stone measurements. If im oke this calculation should also work for the Crown. Im not shure yet, didnt test it yet big_smile

AtomRat

No Autodesk inventor does not support scripts. Its like Autocad and is not made for these drawings. I cannot draw it perfect in Inventor. The above image is the facet next to the facet that is cutted with the 41* degrees. The image is only to see if im doing my math rigth smile It does not include all the math from the beginning.

I now need to program it and i will make a new set of images to show you what the calculations do. Or something like it!? It are all triangle calculations. The complex thing of calculating is that you need to do 3 axis math.

#56

Mr Magoo
Member
Joined: 04 May 2014
Posts: 225
Member
27 August 2016 10:01 pm

Dude I'm not getting it. sad

From what point to what point are you getting

Exact Meetpoint: 0,43685736278800563967533212604698

Is it the edge length or height from girdle 0?
I'm assuming it's an edge length as it's larger than the depth of the pavillion.

Can you mark it on an image of the stone with a width of 1?

#57

Nena
Member
From: Hoogeveen (NL)
Joined: 03 July 2016
Posts: 222
Member
27 August 2016 10:13 pm

Hi Mr Magoo,

Its at the 41 degree facet, measured from the begin of the pavilion.

degrees_l.jpg

Im going to recalculate and also draw it all over again to beshure of all. For every thing i do i will make a image to be correct. Im already started with programming so i need to do every thing again smile

Last edited by Nena (27 August 2016 10:21 pm)

1 user likes this post: AtomRat

#58

Mr Magoo
Member
Joined: 04 May 2014
Posts: 225
Member
27 August 2016 10:30 pm

OK. That makes sense. Just wasn't sure. I'm going to test it.

I believe Gem CAD is getting it right as far as I can tell.

Last edited by Mr Magoo (27 August 2016 10:30 pm)

#59

Nena
Member
From: Hoogeveen (NL)
Joined: 03 July 2016
Posts: 222
Member
28 August 2016 03:07 am

I have made a recalculation with making a little program. I also checked all of the awnsers of the calculation and i it worked big_smile

My results (awnsers) of the calculations:

# 0 = 0.5
# 1 = 0.195090322016128
# 2 = 0.490392640201615
# 3 = 0.434643368908113 # Heigth of Pavilion
# 4 = 0.655286044182008
# 5 = 0.327643022091004 # Midpoint
# 6 = 0.0975451610080642
# 7 = 73.4207944792221
# 8 = 81.533186488604
# 9 = 25.0460190321739
# 10 = 0.441670997782937

Meetpoint = 0.436857362788006

meetpoint_calc_a.jpg
meetpoint_calc_b.jpg
meetpoint_calc_c.jpg
meetpoint_calc_d.jpg
meetpoint_calc_e.jpg
meetpoint_calc_f.jpg

Mr Magoo

Dit you check the calculation with GC?!

Last edited by Nena (28 August 2016 03:32 am)

1 user likes this post: AtomRat

#60

Nena
Member
From: Hoogeveen (NL)
Joined: 03 July 2016
Posts: 222
Member
28 August 2016 04:08 am

Im starting to think its not correct sad thinking about something that i should use. But didnt use! We will see! I will draw a new drawing, otherwise ill draw it in Bryce.

Last edited by Nena (28 August 2016 04:31 am)

#61

Nena
Member
From: Hoogeveen (NL)
Joined: 03 July 2016
Posts: 222
Member
28 August 2016 07:35 am

Im certainly shure it is not the meetpoint! Its the .137 as you said (mr Magoo) I redraw the stone. Took an hour or 2 big_smile and im now shure of the measurements. But need to do some recalculation. sad i shall work my way to that point big_smile not giving up!

#62

Nena
Member
From: Hoogeveen (NL)
Joined: 03 July 2016
Posts: 222
Member
28 August 2016 09:09 am

Pfiew!

Thougth i never find it! But i have a new chance! Checked it 1000 times and it should be correct for now! Never saw that bevore! The calculation is more simpler than i wrote yesterday! But it is stranger! big_smile Im going to work to the .137 becouse that is the correct awnser!

Sorry for all the above standing trouble and confusing!

But one thing about the calculation, i need to confirm if its correct. But i already saw that it uses all measurements.

Ill make the calculation tomorrow/today big_smile 9 hour shift, i go to bed now but im now pretty shure about the case!

#63

Mr Magoo
Member
Joined: 04 May 2014
Posts: 225
Member
28 August 2016 11:44 am

Mr Magoo
Dit you check the calculation with GC?!

I did and as you have found out it wasn't favorable. The trouble is I can't prove GC wrong, and I doubt it is. So I'm just pondering how to do it without GC. As I said great learning opportunity. smile

#64

Nena
Member
From: Hoogeveen (NL)
Joined: 03 July 2016
Posts: 222
Member
28 August 2016 11:41 pm

Ok!

I did some calculations, im wonder if it is correct! I cant test it anymore, my GC has expired (trail version) But you can big_smile

Measured from the tip of the pavilion: Z is down, X is from mid to left.

Width: 1.000
Z: 0.137043598057487
X: 0.170639807539304

I made a random if you change

42.1 to: 35.10*
41* to: 32.30*
and the width to: 2.400

The results from my calculation are:

Width: 2.400
Z: 0.416872866002222
X: 0.713759363060057

Please let me know!!!

#65

Nena
Member
From: Hoogeveen (NL)
Joined: 03 July 2016
Posts: 222
Member
29 August 2016 06:19 am

Mr Magoo?

How did you get the .137? Can you please tell me beqouse i dont get it anymore. Im verry confused. If i draw the stone in autodesk inventor and make slices i get the good measurements but if i calculate what GC does im not shure anymore...

If i do a slice the meetpoints are lower then in the GC program and i dont no why. Please tell me how you get the 137 mayby i can see why!?

Thnx

Christian

#66

Nena
Member
From: Hoogeveen (NL)
Joined: 03 July 2016
Posts: 222
Member
29 August 2016 10:12 am

I found what i did wrong. I have made a new drawing width 5 numbers after the point and have it exacly the same as in GC now! I will try again, 3 times is shipright isnt it?! Ill check the drawing and its calculations again and will see if i get something right this time big_smile

#67

Mr Magoo
Member
Joined: 04 May 2014
Posts: 225
Member
29 August 2016 03:34 pm

That 0.137 is a mistake. Wrong figures used. 0.117 is still favorite.

#68

Nena
Member
From: Hoogeveen (NL)
Joined: 03 July 2016
Posts: 222
Member
29 August 2016 07:15 pm

GC Meetpoint is:

girdle: 0.06959048
meetpoint: -0.63607389
punt/tip: -0.7996821

0,06959048 = 0
-0,63607389 = -0,56648341
-0,7996821 = -0,73009162
-------------------------------------

-0,16360821 / 2 = -0,081804105 Meetpoint.

Just installed GC on my second computer big_smile 30 days left big_smile lol But i have made a new drawing, this time it is correct. Now finding a solution to get my meetpoint.

Greets

#69

Mr Magoo
Member
Joined: 04 May 2014
Posts: 225
Member
29 August 2016 07:25 pm

Yes! I concur.

I have no idea where I got 0.117 from. It's busting my brain cell this.

It's 0.082 as from a couple of pages back. Which works with maths and a radial position of 0.102

There's something being over looked but what is itttttttt!!!!! mad mad mad mad

1 user likes this post: AtomRat

#70

Nena
Member
From: Hoogeveen (NL)
Joined: 03 July 2016
Posts: 222
Member
29 August 2016 07:29 pm

Found already some interesting mesurements. But didnt found any logic for now but ill try, didnt look for long now big_smile

#71

Nena
Member
From: Hoogeveen (NL)
Joined: 03 July 2016
Posts: 222
Member
30 August 2016 07:46 am

Made a new prog! But i dont know why i have a slightly differents in the results by comparing the two?! Mayby i should ask GemCad. I Realy dont know what that is. Also in the drawing it gives a small differents. Now i got 3 different numbers... But now it comes to: Who has it right big_smile lol

Here are some results of what i have tested:

# Width: 1.0000
# 41 = 41
# 42.1 = 42.1
# MP GC: 0.081804105
# My PR: 0.0817735821883434

# Width: 1.000
# 41 = 32.30
# 42.1 = 33.31
# MP GC: 0.059493205
# My PR: 0.0595510861076159

# Width: 2.5472
# 41 = 32.30
# 42.1 = 33.31
# MP GC: 0,151541095
# My PR: 0.151688526533319


My PR = My program big_smile
MP = Meetpoint smile

Greets

Last edited by Nena (30 August 2016 07:50 am)

#72

Nena
Member
From: Hoogeveen (NL)
Joined: 03 July 2016
Posts: 222
Member
30 August 2016 07:32 pm

Whehehe!

My calculation is exactly the same as in Autodesk Inventor 2016 big_smile LOL

meetpoint_new_a.jpg
meetpoint_new_b.jpg

# Width: 1.0000
# 41 = 41
# 42.1 = 42.1
# MP GC: 0.081804105
# My PR: 0.0817735821883434

#73

Mr Magoo
Member
Joined: 04 May 2014
Posts: 225
Member
30 August 2016 10:10 pm

congratualtions-smiley.gif

My brain cell is still shaking in the corner. loosing-it-smiley.gif

So what measurement/angle was the key that unlocked the box.

2 users like this post: kawman, Nena

#74

Nena
Member
From: Hoogeveen (NL)
Joined: 03 July 2016
Posts: 222
Member
30 August 2016 11:42 pm

Hi Mr Magoo,

First i need to confirm the second two measurements before i do anything big_smile I already contacted GemCad and he confirmed me that i was right! And that the problem was in the GEM file from facetdiagrams has something todo with a another software and hand calculations?!. He also send me a new drawing, i uploaded to my server at: http://www.88i.nl/images/work.gem If i got my math confirmed to be correct you may email me and ill send the math to you under one restriction big_smile I won't post it on the forum.

Greets,

Christian

Last edited by Nena (30 August 2016 11:43 pm)

#75

Nena
Member
From: Hoogeveen (NL)
Joined: 03 July 2016
Posts: 222
Member
31 August 2016 05:11 am

I Also have CONFIRMED the 3th test angles!!! I have drawed a drawing on the random angles and width! And it confirms that MY MATH is CORRECT! big_smile Yeah!!!!

# Width: 2.5472
# 41 = 32.30
# 42.1 = 33.31
# MP GC: 0,151541095
# My PR: 0,151688526533319
# Diff: -0,000147431533319

meetpoint_confirm_a.jpg
meetpoint_confirm_b.jpg

Greets,

Christian


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