Quick Linear Algerbra question for you - Tilted Forum Project Discussion Community

Rekna · 11-06-2004, 03:41 PM

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.

11-06-2004, 03:41 PM	#1 (permalink)
Rekna Junkie	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?

11-06-2004, 11:45 PM	#7 (permalink)
a-j Tilted	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. Last edited by a-j; 11-06-2004 at 11:49 PM.. Reason: Spoke too soon

11-06-2004, 04:21 PM	#2 (permalink)
Polaris Upright	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.

11-06-2004, 04:57 PM	#3 (permalink)
a-j Tilted	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.

11-06-2004, 06:59 PM	#5 (permalink)
daking Tilted	aj got it right !

11-06-2004, 11:34 PM	#6 (permalink)
Rekna Junkie	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...

11-07-2004, 08:24 AM	#8 (permalink)
fckm Insane Location: Ithaca, New York	If T and N are orthogonal, then you don't need to renormalize. In general, you do need to renormalize.

11-07-2004, 09:08 PM	#10 (permalink)
Rekna Junkie	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.