Finding solution of a quartic "Visually".

[gaurav]

Hello folks,

It may look like i am asking for high school home work help.

But how many different ways can we find zeros of following attached(or any) polynoimal in houdini. if the solution exist.

As usual the method i come up first is not the most efficient one.

All ideas are welcome.

Cheers,

p.s. - Houdini will make a badass graphing calculator.

rootsOfPolynomial.hipnc

[gaurav]

Ah.. Forgot to attach the most obvious one.

[michaelw]

hi, just got two approaches. Clip SOP and Ray SOP

rootsOfPolynomial2.hipnc

[Andz]

Hei Vectorblur, I'm more comfortable using the isosurface for such things, it already has the bounds built in so you can clamp it to 0 in the Y and Z axis.

Yes, I use Houdini as a graphic calculator, specially for surfaces.

[gaurav]

Thanks guys,

Hi mike - nice ones

Hi Andz - Isosurface is Even better.. It never clicked me to use it as a function plotter.

I think one learns houdini faster seeing how other folks use it.

However I have few more questions.

1. What method isosurface sop is using to convert a surface from implicit representation ?

2. How would you go about graphing curves and surfaces which have parametric representations ?

3. I may be completely off on this one by asking "Can chops be used to find the intersection of ty with x axis.

I can barely spell chops at this point but some how it seems the right context to deal with graphing. Am i wrong ?

e.g. if i fetch the point sop in my first example using geometry chop. It samples the point position in Tx,Ty,Tz and returns graph of channels.

Can this info be used ?

Thanks,

[Andz]

2. How would you go about graphing curves and surfaces which have parametric representations ?

That's a good question, I have never had the need to use a parametric form. Can you give an example?

Edited January 16, 2012 by Andz

[gaurav]

That's a good question, I have never had the need to use a parametric form. Can you give an example?

Hi Andz,

We could probably take something as simple as an ellipse.

x($T ) = $WIDTH * Cos($T)

y($T) = $HEIGHT * Sin($T)

0<=$T<=2$PI

Whose implicit form will be ($X/$WIDTH)^2+($Y/$HEIGHT)^2 -1 =0

Now when i think about it. Doing it with pops makes more sense as to me.

e.g. A particles moving in ellipse, its velocity can be given as

V($T) = (- $WIDTH *sin($T),$HEIGHT cos($T) in terms of parameter $T.

Pls check the attached file to see if it makes sense.

Now how about a couple of curves in polar form like

Logarithmic spiral : r = e^0.20 , Henri's Butterfly : r = (sin40)^2+cos30

:)

Cheers,

parametric.hipnc

[Andz]

I'll give a look at the file tonight from home.

The only time I remember that I actually needed something in a parametric form (looking at it as an actual application wise) was due to software lack. I needed to have an arbitrary point of rotation for objects on a game engine that only recognized the top left corner of objects as it's centre of rotation.

Edited January 17, 2012 by Andz