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Rekna 11-06-2004 03:41 PM

Quick Linear Algerbra question for you
 
Does the cross product of 2 normal vectors yield a normal vector? Or do I need to normalize the result to get a normal vector?

Polaris 11-06-2004 04:21 PM

No. The cross product of two normal vectors (of the same plane) will result in the zero vector.

However, the cross product of two vectors that exist in the same plane will give you a normal vector to that plane.

I'm not sure if that answers your question because I wasn't sure which normal vectors you were referring to.

a-j 11-06-2004 04:57 PM

The way it sounds like you are using "normal" is in reference to unit vectors, those with a magnitude of 1. If this is what you mean then the cross product of 2 unit vectors will only give you a unit vector if they are orthogonal. In fact the cross products magnitude is equal to the area of a parallelogram defined by the two vectors, in the case of orthogonal unit vectors the parallelogram is a square and the result would be a unit vector with magnitude ("area") 1.

fckm 11-06-2004 05:14 PM

Quote:

Originally Posted by Polaris
No. The cross product of two normal vectors (of the same plane) will result in the zero vector.

However, the cross product of two vectors that exist in the same plane will give you a normal vector to that plane.

I'm not sure if that answers your question because I wasn't sure which normal vectors you were referring to.


err. Any two vector always lie in the same plane.

daking 11-06-2004 06:59 PM

aj got it right !

Rekna 11-06-2004 11:34 PM

yeah sorry i think i missused the terms there. I have 2 normalized vectors T and N (tangent and normal) and I am crossing them to get B (binormal) I am wondering if I need to normalize B after I cross them. In the end I should have 3 vectors T, B, and N that define a new coordinate system.

I'm really beginning to hate all the linear algerbra in graphics... ;)

a-j 11-06-2004 11:45 PM

Rekna, its been so long since I did stuff with parametric curves and T, B, N. I think though that when you get T (tangent), and N (normal), they are almost always orthogonal to each other, so if they are normalized then you don't need to normalize B (binormal) when you take the cross-product.

fckm 11-07-2004 08:24 AM

If T and N are orthogonal, then you don't need to renormalize. In general, you do need to renormalize.

Thermopyle 11-07-2004 11:58 AM

Quote:

Originally Posted by fckm
If T and N are orthogonal, then you don't need to renormalize. In general, you do need to renormalize.

fckm found the crux

Rekna 11-07-2004 09:08 PM

In my case i'm pretty sure T and N are orthogonal so I shouldn't need to normalize. I believe I have everything working now I just need to work with a more extream normal map and my bump mapping should work.


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