• Announcements

    • khawk

      Download the Game Design and Indie Game Marketing Freebook   07/19/17

      GameDev.net and CRC Press have teamed up to bring a free ebook of content curated from top titles published by CRC Press. The freebook, Practices of Game Design & Indie Game Marketing, includes chapters from The Art of Game Design: A Book of Lenses, A Practical Guide to Indie Game Marketing, and An Architectural Approach to Level Design. The GameDev.net FreeBook is relevant to game designers, developers, and those interested in learning more about the challenges in game development. We know game development can be a tough discipline and business, so we picked several chapters from CRC Press titles that we thought would be of interest to you, the GameDev.net audience, in your journey to design, develop, and market your next game. The free ebook is available through CRC Press by clicking here. The Curated Books The Art of Game Design: A Book of Lenses, Second Edition, by Jesse Schell Presents 100+ sets of questions, or different lenses, for viewing a game’s design, encompassing diverse fields such as psychology, architecture, music, film, software engineering, theme park design, mathematics, anthropology, and more. Written by one of the world's top game designers, this book describes the deepest and most fundamental principles of game design, demonstrating how tactics used in board, card, and athletic games also work in video games. It provides practical instruction on creating world-class games that will be played again and again. View it here. A Practical Guide to Indie Game Marketing, by Joel Dreskin Marketing is an essential but too frequently overlooked or minimized component of the release plan for indie games. A Practical Guide to Indie Game Marketing provides you with the tools needed to build visibility and sell your indie games. With special focus on those developers with small budgets and limited staff and resources, this book is packed with tangible recommendations and techniques that you can put to use immediately. As a seasoned professional of the indie game arena, author Joel Dreskin gives you insight into practical, real-world experiences of marketing numerous successful games and also provides stories of the failures. View it here. An Architectural Approach to Level Design This is one of the first books to integrate architectural and spatial design theory with the field of level design. The book presents architectural techniques and theories for level designers to use in their own work. It connects architecture and level design in different ways that address the practical elements of how designers construct space and the experiential elements of how and why humans interact with this space. Throughout the text, readers learn skills for spatial layout, evoking emotion through gamespaces, and creating better levels through architectural theory. View it here. Learn more and download the ebook by clicking here. Did you know? GameDev.net and CRC Press also recently teamed up to bring GDNet+ Members up to a 20% discount on all CRC Press books. Learn more about this and other benefits here.
Sign in to follow this  
Followers 0
Steve_Segreto

Orthonormalize Two Vectors

6 posts in this topic

I'm trying to implement something like Unity's Vector3.Orthonormalize() function.

Vector3.OrthoNormalize

Since the documentation for this function states that both vectors are normalized and then the second vector is made to be orthogonal to the first (i.e. 90 degrees angle between second and first vector), my question is whether I should even bother with G-S Orthonormalization or just use this:


Vector3 OrthoNormalize( Vector 3 normal, Vector3 tangent )
{
normal.normalize();
tangent.normalize();

return tangent.cross( normal );
}




So is the cross-product of two normalized vectors a third vector that has a 90 degree angle to the first one?
0

Share this post


Link to post
Share on other sites
Quote:

So is the cross-product of two normalized vectors a third vector that has a 90 degree angle to the first one?

Yes, but in general it won't have a magnitude of one. The magnitude of the cross product is the area of the parallelogram the two arguments form. And if these two vectors have unit length but are not perpendicular the magnitude will be less than one.
Also, I would let the function take the both tangents by reference, since the first one may have to be modified to get an orthonormal basis (and the second one may have to be constructed). Or, which I usually do, let it operate on a matrix.

EDIT:
To answer the first question: As far as I know you'd have to use either GS or two cross products + normalizations:

n.normalize();
v = cross(n,u);
v.normalize();
u = cross(v,n);



[Edited by - macnihilist on October 17, 2010 3:18:04 PM]
1

Share this post


Link to post
Share on other sites
How about this? Would this work to orthonormalize the tangent vector to the normal vector?


void D3DXVec3OrthoNormalize( D3DXVECTOR3 *normal, D3DXVECTOR3 *tangent )
{
D3DXVec3Normalize( normal, normal );
D3DXVec3Normalize( tangent, tangent );

D3DXVec3Cross( tangent, normal, tangent );
}


0

Share this post


Link to post
Share on other sites
Isn't it exactly the same logic as the code in your first post? Both your new code and the first don't work as already explained by macnihilist. I don't understand why you don't want to use GS ortho-normalization since it is cheaper and only slightly longer to write:

void D3DXVec3OrthoNormalize( D3DXVECTOR3 *normal, D3DXVECTOR3 *tangent )
{
D3DXVec3Normalize( normal, normal );

D3DXVECTOR3 proj;
D3DXVec3Scale( &proj, normal, D3DXVec3Dot( tangent, normal) );

D3DXVec3Subtract( tangent, tangent, proj );

D3DXVec3Normalize( tangent, tangent );
}



2

Share this post


Link to post
Share on other sites
Hey so, I found this and was thinking that I can help you if you can help me.

When you cross two orthonomal vectors together, you will always get another orthonormal vector (try crossing (1,0,0) and (0,1,0), which yields (0,0,1)).

Also note, that whenever a cross is performed you will always return a vector that is orthogonal (i.e. 90 degrees in between the two)to BOTH of the vectors that you crossed together.

You can prove this by doting the returned vector with the two input vectors, which will yield a 0 (Dot(a,b)=||a|| *||b|| Cos(angle between the two)) and since Cos(90) is 0, thus proved.

Sometimes you will get the 0 vector, this is technically orthogonal to every vector out there, which means that the two vectors you crossed together were similar (pointing in the same direction).

But as far as what I was wondering, I have been using this stuff in Physics, Statics, Calculus, etc and have been wondering how it can be applied to actual problems, so if you don't mind explaining why you were wanting to do this, that would be awesome :).

I have programmed for about a year and a half so I don't mind if you use programming terminoligy to explain.

Thanks :)

Petry
0

Share this post


Link to post
Share on other sites
Quote:
Original post by Petry
... why you were wanting to do this, ...


There are a number of 3D rendering algorithms that depend on local coordinates system explicitly, e.g. dynamic bump mapping and anisotropic lighting (e.g. WARD lighting model).

For a 3D model, the normals and the tangents are defined at vertices and are interpolated for the pixel operations. Although vertex normal and vertex tangent are orthonormal to each other, the interpolated normal and tangent are not orthonormal in general. So, when we try to form a local coordinates system using the interpolated normals and tangents, we need to make them orthonormal first.

By the way, we have a well-known solution for it already, i.e. Gram-Schmidt Orthonormalization, which was mentioned by Apatriarca along with source code.
0

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!


Register a new account

Sign in

Already have an account? Sign in here.


Sign In Now
Sign in to follow this  
Followers 0