Author Message
nextstep

Joined: 06 Jan 2007
Posts: 539

Posted: Tue Aug 14, 2007 8:12 pm    Post subject: How to make Isosurfaces with "tickness" ?

Hi all,
I've already talked about my formulas for generating "tick" surfaces. However, it's possible to extend this formulas to generate much more interesting surfaces.
I'll start with some explanations on how to use it and will show some "extra" use of it
The formulas is described like this :
 Code: G[x, y, z] = F[x, y, z] * F[x - (T/R)*dF()/dx, y - (T/R)*dF()/dy, z - (T/R)*df()/dz] Where : dF()/dx == partial derivative of F() to the variable x. R = sqrt[(dF()/dx)^2 + (dF()/dy)^2 + (dF()/dz)^2] T = Tickness value

To apply this formula , you should be able to calculate the derivative form of your original isosurface. If you don't know how to do it, take a look on these pages :
http://en.wikipedia.org/wiki/Derivative
http://mathworld.wolfram.com/Derivative.html
Once you're familiar with this notation, it's only a matter of minutes to calculate the derivative formula.
The first extension of this formulas can be obtained by generating isosurfaces with more that two successive parts. For example, to have three surfaces , we have only to vary the parameter T and use this formulas :
 Quote: H[x, y, z] = F[x, y, z] * F[x - (T/R)*dF()/dx, y - (T/R)*dF()/dy, z - (T/R)*df()/dz]* F[x - (T/2*R)*dF()/dx, y - (T/2*R)*dF()/dy, z - (T/2*R)*df()/dz]

when applied to the Schwartz formula, we obtain something like that :
 Quote: Name: TickIso_3 F(): (cos(x) + cos(y) + cos(z))* ((cos(x + sin(x)/(2*sqrt(sin(x)^2 + sin(y)^2 + sin(z)^2))) +cos(y + sin(y)/(2*sqrt(sin(x)^2 + sin(y)^2 + sin(z)^2))) +cos(z + sin(z)/(2*sqrt(sin(x)^2 + sin(y)^2 + sin(z)^2)))))* ((cos(x + sin(x)/(4*sqrt(sin(x)^2 + sin(y)^2 + sin(z)^2))) +cos(y + sin(y)/(4*sqrt(sin(x)^2 + sin(y)^2 + sin(z)^2))) +cos(z + sin(z)/(4*sqrt(sin(x)^2 + sin(y)^2 + sin(z)^2))))) [x]: -4 , 4 [y]: -4 , 4 [z]: -4 , 4 ;

Also, another interesting extra use for soon
_________________
Cheers,
Abderrahman
jotero

Joined: 27 Jan 2007
Posts: 153
Location: Germany Hannover

 Posted: Wed Aug 15, 2007 7:44 am    Post subject: hello all Very good work Taha thanks ciao torolf_________________Kontakte
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