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ufoace
Joined: 11 Mar 2013 Posts: 46
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Posted: Sun Oct 13, 2013 9:35 am Post subject: 2D Polar Rose with z*z? |
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Hi, it is possible to make a spiral with:
F(): 0.5 - z*z - sin((sqrt(x*x+y*y) - 0.5*atan2(y,x)))^2
and i have failed to make the same style for a polar rose, is it impossible?
just these using z*z for depth?
the spiral:
F(): 0.5 - z*z - sin((sqrt(x*x+y*y) - 0.5*atan2(y,x)))^2
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denisc
Joined: 24 Apr 2013 Posts: 92
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Posted: Sun Oct 13, 2013 3:35 pm Post subject: |
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hello ufoace
With this formula, if you don't write x, y, and z limit
the result is very poor for me ,in K3Dsurf, a little slightly distorted ?
cheers |
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ufoace
Joined: 11 Mar 2013 Posts: 46
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Posted: Sun Oct 13, 2013 8:49 pm Post subject: |
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I had same in the pic, i rewrote it for a marching cubes engine and it was same. I'm silly because polar roses are parametric and i always work on isosurfaces. i can't believe that i didnt manage to emulate parametric for my marching cubes engine because normally you would run segments and += them to the total and i didnt! |
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denisc
Joined: 24 Apr 2013 Posts: 92
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denisc
Joined: 24 Apr 2013 Posts: 92
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Posted: Tue Oct 15, 2013 12:09 am Post subject: |
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hello uoface
For the moment, i am not a solution for more reasons.
When you try make tube with spiral, you are not intersection of segments.
When you try make tube with parametric formula in general
; When you are intersections of segments, the tube is not perfect.
With knoten torus perfect.
With treefold torus , i cannot round the model prefectly, for the moment
with lissajous , is a best
you can make a tube , but not all round when you try to flat him .
with of polar rose , i am a bubon of 6 part but not center
for n=3/2
it's a full model.
(I was looking for this for some time, so it is)
i try to model a TRIFOLIUM with isometric formula + the solution of
abdelhamid belaid.
dont work for this formula
(x^2+y^2)^2-x*(x^2-3*y^2)
in final
((y-((x^2+y^2)^2-x*(x^2-3*y^2)))*cos(atan((4*x+3)*y^2+4*x^3-
3*x^2)) )^2 +z^2-0.01
perhaps , it's a mistake?
a general formula exist for tube in a nb for mathematica, but my link is
dead and it's in french .
cheers
denisc |
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denisc
Joined: 24 Apr 2013 Posts: 92
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Posted: Tue Oct 15, 2013 12:31 pm Post subject: |
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hello uoface
here a view of quadrifolium .
it's possible on parametric , but is complicated a lot , because you must
calculed the formula of tube for each figure.
ex/ for trifolium and quadrifolium you are two different formule for the tube.
And I'm not as good as others for this.
cheers
ps:
(if you have enough of it you can use hexagon, ( It's free and there is a function to magnify the line.)
I am also well aware that this was not the initial request, but I hoped this helped a little anyway.
denisc |
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