K3DSurf forum

denisc · Joined: 24 Apr 2013 Posts: 92

thank very much

for the cube that work, if you write
min(min(1-abs(x) ,1-abs(y)),1-abs(z) )
or ( if you write min(min(abs(1-x),abs(1-y)),abs(1-z)) that work also, but
just for x=y=z=- +1 )

not if you write
min(1-abs(x) ,1-abs(y) ,1-abs(z) ) !
a detail
for the suite i am begin to calculate the 6xn of dodecaedron
i supposed if
f1=
if X= ( 2, 2, 2)* (x ,y , z )
f1= R - abs(2x+2y+2z) ?

cheers
denis

inode · Joined: 27 Jan 2007 Posts: 127 Location: Austria

Hi all
There is a nice wine red Dodecahedron Variant with one hole through any side puplished by Stefan at http://forum.jotero.com/viewtopic.php?t=258&postdays=0&postorder=asc&start=0 (03.06.2010, 12:34).
Stefan created this shape with 'Shade'. Now it would be nice to create a algebraic surface formula for that shape! One idee to get a formula may be to combine 6 rotated hyperbolic cylinders with the rules of an dodecahedron...
Wink

Gerd

Furan · Posted: Thu May 02, 2013 1:20 pm Post subject:

Yes, that is the scalar product of two vectors
f= R - abs(X * n) = R - abs(x*nx + y*ny + z*nz)

denisc · Joined: 24 Apr 2013 Posts: 92

hello all

here the detail for all n, for dodecaedron

it's if i make some mistake?

centre

he pink vertex at [f,0,-1/f]
The orange vertices at [1,1,-1] and [1,-1,-1]
The green vertices at [0,1/f,-f] and [0,-1/f,-f]

n1 = 1/5 * [2+f, 0, -1/f-2-2*f] / R

droit

The orange vertices at [1,1,-1] and [1,1,1]
The pink vertex at [f,0,-1/f] and [f,0,1/f]
The blue vertex at [1/f,f,0]

n2 = 1/5 * [2+2*f+1/f, 2+f, -0] / R

n2 = 1/5 * [2+2*f+1/f, 2+f, -0] / (sqrt(5/2+11/10*sqrt(5)))/2

gauche

The orange vertices at [-1,1,-1] and [-1,-1,-1]
The pink vertex at [-f,0,-1/f]
The green vertices at [0,1/f,-f] and [0,-1/f,-f]

n3 = 1/5 * [-2-f, 0, -1/f-2-2*f] / R

n3 = 1/5 * [-2-f, 0, -1/f-2-2*f] / (sqrt(5/2+11/10*sqrt(5)))/2

dessus

The orange vertices at [1,1,-1] and [-1,1,-1]
The blue vertex at [1/f,f,0] and [-1/f,f,0]
The green vertices at [0,1/f,-f]

n4 = 1/5 * [0, 1/f+2+2*f, -2-f] / R

n4 = 1/5 * [0, 1/f+2+2*f, -2-f] / (sqrt(5/2+11/10*sqrt(5)))/2

dessous droit

The orange vertices at [1,-1,-1] and [1,-1,1]
The pink vertex at [f,0,-1/f] and [f,0,1/f]
The blue vertex at [1/f,-f,0]

n5 = 1/5 * [1/f+2+2*f, -2-f, 0] / R

n5 = 1/5 * [1/f+2+2*f, -2-f, 0] / (sqrt(5/2+11/10*sqrt(5)))/2

dessous gauche

The orange vertices at [1,-1,-1] and [-1,-1,-1]
The blue vertex at [1/f,-f,0] and [-1/f,-f,0]
The green vertices at [0,-1/f,-f]

n6 = 1/5 * [0, -1/f-2-2*f,-2-f] / R

n6 = 1/5 * [0, -1/f-2-2*f,-2-f] / (sqrt(5/2+11/10*sqrt(5)))/2

if i take

f=1,6
R=1.11
i hope it's not less.

n1 = [3.6/5.11, 1/5.11, -1.165/ 1.11 ]

i certainly finish for next day.

cheers

denisc · Joined: 24 Apr 2013 Posts: 92

perhaps, i do a mistake.

i write the formula, but the dodeca are not regular?

f1 = 1.11- abs(3.6/5.11*x+ 1/5.11*y -1.129/ 1.11*z )
f2 = 1.11- abs(1.129/1.11*x+3.6/5.11*y+ 1/5.11*z)
f3 = 1.11- abs(-3.6/5.11*x+ 1/5.11*y -1.129/1.11*z)
f4 = 1.11- abs(1/5.11*x+ 1.129 / 1.11*y -3.6/5.11*z)
f5 = 1.11- abs(1.129 / 1.11x -3.6/5.11*y +1/5.11*z)
f6 = 1.11- abs(1/5.11*x -1.129 / 1.11*y -3.6/5.11*z)

f(x,y,z)=
min(min(min(min(min(1.11- abs(3.6/5.11*x+ 1/5.11*y -1.165/ 1.11*z )
,1.11- abs(1.165/1.11*x+3.6/5.11*y+ 1/5.11*z) )
,1.11- abs(-3.6/5.11*x+ 1/5.11*y -1.165/1.11*z) )
,1.11- abs(1/5.11*x+ 1.165 / 1.11*y -3.6/5.11*z) )
, 1.11- abs(1.165 / 1.11*x -3.6/5.11*y +1/5.11*z) )
,1.11- abs(1/5.11*x -1.165 / 1.11*y -3.6/5.11*z ))

cheers

denisc · Joined: 24 Apr 2013 Posts: 92

hello all
's not 5.11 but 5.55
but, it's a same.

i don't know if the order of f1 , f2 ;;;;;

is important?

it's a beginning Wink

cheers

abdelhamid belaid · Joined: 13 Aug 2009 Posts: 170

Hello,
Yes Denis order is important generally.

you wrote:

denisc · Joined: 24 Apr 2013 Posts: 92

:)Hello Mr belaid

Great thanks for your answer and comment.

abdelhamid belaid · Joined: 13 Aug 2009 Posts: 170

I think we didn't finish, we have just began Smile

, for me the important is not this formula, there are many methods to reach one, for the dodecahdron all faces are the same (a plane), we have similarity here, I mean it's logical that there is a formula without max and min, imagine if we can creat it just starting with one plan(z-a=o for example), as you have seen I got five faces starting from one just writing "atan(tan(2.5*atan2(y,x)))/2.5" instead of "atan2(y,x)", the question is: How ?????
_________________
My YouTube channel

denisc · Joined: 24 Apr 2013 Posts: 92

i think exactly , the same.

it's for that , i had post my question in first .

((i hoped , someone andswer me a formula with no booléens.

but perhaps, it's a dream ))

Furan · Posted: Fri May 03, 2013 12:08 pm Post subject:

Well, using functions like atan(tan()) etc. does offer simple usage of various sawtooth waves, step functions etc., but it's "dirty". It's sadistic to force the cpu to calculate twice some form of Taylor series or similar operation, if you could just use some logical operations and modulo.
http://en.wikipedia.org/wiki/Modulo_operation
You can get sharp edges with veeeery high power
For example a cube:
x^n+y^n+z^n = (a/2)^n

I'm pretty sure you could get a dodecahedron by:
F(x,y,z) = f1 + f2 + f3 + ... + f6

f_i = R^n - (n_i * X)^n

Round edges for lower n. Try it.

denisc · Joined: 24 Apr 2013 Posts: 92

hello mr Furan

thanks for this new way.
what do you mean by ^n and Round edges for lower n ?
i cannot translate properly?
(for the moment, i try your first formula for the icosaedron)

cheers
denis

denisc · Joined: 24 Apr 2013 Posts: 92

for icosa
i take 1/3* for calculate the middle point ?
but it's more horrible that dodeca.

i'm look like a bad architect in asterix and result also!

Shocked

( funny write)

test by yourself

min(min(min(min(min(min(min(min(min(0.75- abs(4/9*y+4.8/3*z),
0.75- abs(-4/9*y+4.8/3*z)),
0.75 -abs(-10.4/9*x+10.4/9*y+10.4/9*z)),
0.75- abs(10.4/9*x+10.4/9*y+10.4/9*z)),
0.75- abs(-10.4/9*x-10.4/9*y+10.4/9*z)),
0.75- abs(10.4/9*x-10.4/9*y+10.4/9*z)),
0.75- abs(-4.8/3*x-4.08/3*y+4/9*z)),
0.75- abs( 4.8/3*x-4.08/3*y+4/9*z) ),
0.75- abs(-4/9*x-4.8/3*y-4.08/3*z) ),
0.75-abs(4/9*x-4.8/3*y-4.08/3*z))

abdelhamid belaid · Joined: 13 Aug 2009 Posts: 170

Hello,
thanks Furan, you have your own standards anyway.

Denis, if you want to make a dodecahedron using Furan's first way you would use my formula to avoid calculations and generate every plane formula easily:
an upper plane has a formula of the form sin(1.07498)*sqrt(x*x+y*y)*cos(atan(tan(2.5*atan2(y,x)))/2.5)+cos(1.07498)*z that means sin(1.07498)*sqrt(x*x+y*y)*cos(atan2(y,x)+n*2*pi/5)+cos(1.07498)*z such that n=-2, -1, 0, 1, 2

(n=0) plane number 1 formula is:
sin(1.07498)*sqrt(x*x+y*y)*cos(atan2(y,x))+cos(1.07498)*z = sin(1.07498)*x+cos(1.07498)*z

(n=1) plane number 2 formula is:
sin(1.07498)*sqrt(x*x+y*y)*cos(atan2(y,x)+2*pi/5)+cos(1.07498)*z =
sin(1.07498)*(x*cos(2*pi/5)-y*sin(2*pi/5))+cos(1.07498)*z

................etc
maybe this way is the fastest to get every plane formula Smile

_________________
My YouTube channel

denisc · Joined: 24 Apr 2013 Posts: 92

thank very much, Mr belaid for your help.

i try all , quickly.

Laughing