Cubic bezier4 compound with 1st and 2nd derivative

[Daniel Brassard]

I made this compound to test cubic bezier curves. It's a modification of the factory bezier4 compound, I added the 1st and second derivatives as output.

EDIT

I removed the file because I updated the compound and created a few more. Go to the ICE compound section to download the most up to date.

Cheers!

Dan

[ActionArt]

That sounds so cool. I wish I knew what it meant

[Leo]

It should just give you the slope of the bezier curve at any given point (first derivative) and the slope of the function that gives the slope of the bezier curve at any given point (second derivative).

[Daniel Brassard]

The first derivative gives you the tangent vector at any point on the curve, useful for object sliding or following the curve. The tangent is also a parameter used to match two Bezier curves so that they join smoothly (C1 continuity or tangential continuity). Can be useful for extrusions as well.

Tangents are also used for Bezier surfaces (defined by curves in u and v) to determine the normal of the surface using the cross product.

The second derivative gives you the normal vector at any point on the curve. The second derivative is used to determine the curvature at any point on the curve. It is also used to ensure two Bezier curve that meet are smoother (C2 continuity or curvature continuity).

If you want to have an object follow the curve orientation (like a rocket following a trajectory), you would use the tangent and normal vector to orient the object along the curve(s).

There is other application of the derivatives (control twisting, etc). In most cases, the tangent is sufficient for Bezier4 (Cubic) curves. Maybe someone will have a use for this.

EDIT
BTW, The cross-product of the first and second derivative will give you the binormal vector (the UP vector). With these three vectors (tangent, normal and binormal), you can control the pitch, roll and yaw of an object moving along the curve.

Dan

[ActionArt]

Very interesting. You might want to contact Eugene Sares on the list. He's working on improving his curve tools and is trying to develop corner rounding which would be extremely useful. This might help.

http://www.keyvis.at/?page_id=671

[Eugen]

Hi guys!
Topo changes on Curves or Surfaces are not yet possible in ICE. I use plain old JScript.
Mailing list thread regarding this topic:
http://groups.google.com/group/xsi_list ... 461edecd3a

Guillaume Laforge (ICE Modelling developer):
"I know that we need better curve tools in Softimage. But we just can't add every possible modeling feature in ICE Modeling version 1.0 ! Nurbs (curve and surfaces) would be very useful using ICE Modeling for sure !"

So, let's wait and see.
Best,
Eugen

[Hirazi Blue]

That sounds so cool. I wish I knew what it meant

Just wanted to add belatedly, that I had exactly the same feeling...
This qualifies (IMHO) for a "Funny, because it's true"-Award....

[ActionArt]

I guess I've been out of school too long, I seem to have forgotten some of that stuff.

I'm glad SI might be adding more in the way of curves and surfaces in ice.

BTW, I like the new avatar Hirazi, did you render that?

[Hirazi Blue]

Me, rendering... anything? Nope...
Meanwhile I, sadly, had to remove the avatar ActionArt mentioned after I found out I misinterpreted its license