Bitpacking Normal Vector

Chris · 02-27-2011 12:14 PM

Hi,

I'm using voxels, and each voxel has 4 bytes of data (32-bit). Previously I had my method working where a normal vector was packed into 3-bits, and the final bit stored some other data. But now I find that my paper can greatly be improved if I use 2 bits to encode the normal vector, and 2 bits for the other data.

So I need to crudely encode a Vec normal; (magnitude of 1) as just 2-bytes, then be able to do the inverse - from 2 bytes, get a Vec normal again.

This is my guess so far (using 5 bytes for x, 6 bytes for y, 5 bytes for z), but i'm not sure if it's correct - it's kinda hard to debug.

Code:

U16 nrmval =  (((U16)((in.normal.x+1)*16) << 11 ) & 0xFF) | (((U16)((in.normal.y+1)*16) << 6) & 0xFF) | ((U16)((in.normal.z+1)*16) & 0xFF);

// pack normal

Byte a = nrmval >> 8;

Byte b = nrmval & 0xff;

1. I'm sure this is wrong, any ideas how to do it correctly?
2. I'm also not sure how to do the inverse.

Chris · 03-02-2011 06:18 PM

*Bumps this* I changed the original question quite a bit.

rndbit · 03-02-2011 08:05 PM

maybe if you could explain it better.. i find hard time understanding exactly what you are trying to achieve. example in form of detailed expected input and output would help

Chris · 03-03-2011 12:41 AM

(03-02-2011 08:05 PM)rndbit Wrote: maybe if you could explain it better.. i find hard time understanding exactly what you are trying to achieve. example in form of detailed expected input and output would help

Okay:

Input: Vec (96-bits)
Output: Byte a; Byte b; (or a U16, it doesn't matter [16-bits])

The input is a normal vector, e.g. it has a length/magnitude of 1. This means that perhaps you can take advantage of it and use spherical coordinates:

http://mynameismjp.wordpress.com/2009/06...ordinates/
http://aras-p.info/texts/CompactNormalStorage.html

But in the above two links, they usually convert from Vec3 (96-bit) to Vec2 (64-bit), or from Half3 (48-bit), to Half2 (32-bit).

1. What I want to do is much more lossy & crude, encode from 96-bits to 16-bits, hopefully while taking advantage of the normal properties.

2. I'd like to also do the inverse; to decode from two bytes, to a Vec.

**Esenthel** · 03-03-2011 04:10 AM

Code:

Vec v; // v is normalized

Byte x=Round(Lerp(0,255,LerpRS(-1,1,v.x))), // 8-bit prec

     y=Round(Lerp(0,127,LerpRS(-1,1,v.y))); // 7-bit prec

if(v.z<0)y|=128; // encode z sign in last y bit

decode:

v.x=Lerp(-1,1,LerpRS(0,255,x    ));

v.y=Lerp(-1,1,LerpRS(0,127,y&127));

// length(v)==1 -> Sqrt(v.x*v.x + v.y*v.y + v.z*v.z)==1 -> v.x*v.x + v.y*v.y + v.z*v.z==1 -> v.z*v.z==1 - v.x*v.x - v.y*v.y -> v.z==Sqrt(1 - v.x*v.x - v.y*v.y)

v.z=Sqrt(Sat(1 - v.x*v.x - v.y*v.y));

if(y&128)CHS(v.z); // if encoded z sign bit in y is on then change sign of v.z

v.normalize();

Chris · 03-03-2011 01:54 PM

Thank you so much Esenthel, this is so wonderful smile

It works beautifully; can I ask how it works to know what to write about - how can you encode the z in just one sign bit? The quality seems very high.

**Esenthel** · 03-03-2011 02:20 PM

only X Y are encoded, while for Z only it's sign is encoded.
since you said that you need normal vector, then its length is 1, so having X Y you can calculate Z from following formula:

length(v)==1 -> Sqrt(v.x*v.x + v.y*v.y + v.z*v.z)==1 -> v.x*v.x + v.y*v.y + v.z*v.z==1 -> v.z*v.z==1 - v.x*v.x - v.y*v.y -> v.z==Sqrt(1 - v.x*v.x - v.y*v.y)
v.z=Sqrt(Sat(1 - v.x*v.x - v.y*v.y));

sqrt always gives positive value, but Z can be + or -, so we need to encode it's sign first (that's the last bit in 2nd byte for)

Chris · 03-03-2011 02:44 PM

Awesome! Such an elegant solution to the problem smile

Chris · 04-22-2011 09:45 PM

Hi, I updated my question with my latest development of the problem:

Here's what I have, a set of 3d vectors in a 3d flow.

But they face different directions in the flow (backwards and forwards, left and right). I need to generate a lookup table of n random colours for each possible normal vector within some degree of accuracy (e.g. a sphere of some resolution where each vertex contains a colour), where opposite normal vectors (e.g. change sign) have the same colour.

I then, idealistically (but not necessarily) need a function which finds the nearest normal vector & corresponding colour in this table, from a given normal vector.

Input: normal vector
Output: colour for corresponding closest normal vector
-> where all opposite vectors in the "lookup sphere" have the same colour.

Edit: Ah, nevermind - i've got this mostly working now.

Thanks,
Chris

Bitpacking Normal Vector
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