Some help from you drafters/math guys please...

[daltoncalford]

Ok, I am trying to put a hex grid in a isometric bounding box, a sort of pseudo 3d subsector grid.

Now, here is my difficulty, I need the translation vector for the grid.

Here are the details,

Hexagon A is a closed polygon defined by the following six points A1,A2,A3....

A1 = 0.00x, 0.86y
A2 = 0.50x, 0.00y
A3 = 1.50x, 0.00y
A4 = 2.00x, 0.86y
A5 = 1.50x, 1.72y
A6 = 0.50x, 1.72y

The interesting thing is, I need to change the universal 60degree angles into different angles due to the translation, but, the length of the sides need to remain constant.

For example line A1,A2 needs to be congruant to line A4,A5 while line A2,A3 needs to be congruent to line A5,A6. (This has to go together as a grid)

Now, an isometric translation causes a 30degree rotation to occur, while compressing the top by an unknown factor.

Anybody got a class full of bright kids you can dump this on as a homework project????



Anyways, any help would be appreciated as I am being overwhelmed with other editing work.

It's getting so bad I had to cancel gaming tonight.

best regards

Dalton

 

[TheEngineer]

Hi Dalton !

Maybe I did not understand the problem correctly...

Do You need the transformation formulars themself to get a pretty isometric view ?

If so, You might use a sequence of x axis rotation - y axis rotation - x axis rotation.
X axis rotation can be done with
X' = X
Y' = Y*cos(x angle) - Z*sin(x angle)
Z' = Y*sin(x angle) + Z*cos(x angle)

and Y axis rotation via
X' = X*cos(y angle) - Z*sin(y angle)
Y' = Y
Z' = X*sin(y angle) + Z*cos(y angle)

So a - 90 degree x axis rotatition, a say 20 degree y axis rotation and a concludiing 30 degrees x axis rotation results in a pretty iso view....

But as I said, I perhaps did not get the actual problem...

Regards,

Mert

 

[daltoncalford]

Hi Mert,

Looks like you know what I need, but, I do not follow your math (I left school at the age of 16 due to a stroke, and everything I know is self taught)

Could you do me a huge favour, useing the xypoints I have given you, could you give me the final points.

It would be great if you showed your work but, that would be over and beyond my immediate needs.

Thanks

Dalton

 

[TheEngineer]

Hi !

OK

Here is a set of numbers as a result of the transformation of Your xy-point .(-90x, 20y and 30x rotation)..

0,29+0,59*x 0,40+0,81*y
0,47+0,59*x -0,09+0,81*y
1,41+0,59*x -0,26+0,81*y
2,17+0,59*x 0,06+0,81*y
2,00+0,59*x 0,55+0,81*y
1,06+0,59*x 0,72+0,81*y

Does it work ?
I will figure out a general and simplyfied calc in a little while

If You would like to have the spreadsheet give me a PM.

regards,

Mert