Hi,

Simple question - given two normal vectors (x,y,z is between -1 and 1), how can I compute the similarity between them in EE?

is that what AbsAngleBetween is for? or should I be doing it some other way than:

if (AbsAngleBetween(nrm1, nrm2) < PI/2) // does this mean they're within 180 degrees similarity?

1. I want to detect how much they're facing the same direction - but it's a bit hard to test if its working, so thought i'd make a post.

2. Less important: Is there a "best way" to make them, over time, make them join into one normal - or do I just keep lerping them towards the average of each other etc.

Thanks,
-Chris

1. yeah, absanglebetween is the right choice
2. lerping is simple but it's not mathematically correct, what you want is to compute Cross product between 2 vectors, and then rotate the 1 vector by the Cross direction.

Vec cross=CrossN(a,b); // get normalized cross
a*=Matrix3().setRotate(cross, angle); // or -angle, need to check which one to use

Awesome answers, thank you for your help.

1. Another thing; if I wanted to get the normal vector between a set of normals of size n, how do I mathematically correctly rotate it towards the set without using averages - or should I use them at one point (if so, i'm not sure where)?

2. Also how do you mean I check the -angle in your above comments - do I check which one is closer to the side of 180 somehow?

Thanks, i'm getting much better results with this.

1.
-calculate average normal of all normals
-for each normal compute cross between i-th normal and average, and rotate it
2. just check +angle and -angle, and see which works correctly, and use that version

Thanks for your fast reply:

1. So you mean something like:

Vec myNormal = // some normal
Vec avgnrm = 0;
UInt count = 0;

FREPA(normals) { // all normals in the set
avgnrm += normals[i];
count++;
}

-calculate average normal of all normals:
avgnrm /= count; // okay, next part:

-for each normal compute cross between i-th normal and average, and rotate it:
// just following your instructions like a machine:
FREPA(normals) {
Vec cross=CrossN(normals[i],avgnrm);
Vec temp = normals[i];
temp*=Matrix3().setRotate(cross, angle); // check +angle -angle etc later
}

- but now what? I don't want to rotate the set towards myNormal (hence creating temp) - I wan't to rotate myNormal towards the set.
- do you mean I should now sum temp and average temp?

Thanks - excuse "pseudo" code.

2. I think it was +angle as "nrm*=Matrix3().setRotate(cross, 0.2f);" - Q. what unit is 0.2f in for angle though - I originally tried "1" thinking it was degrees, but this messed it up quite alot

1. Please can you clarify the end of my averaging problem in the above post - i'm beginning to get amazing results now (so a big thank you!!) - but it needs to be done perfectly. How can I finish it:

"-calculate average normal of all normals
-for each normal compute cross between i-th normal and average, and rotate it"
what next?

I thought you mean move all normals towards the average

(12-12-2010 03:41 PM)Chris Wrote:  Q. what unit is 0.2f in for angle though - I originally tried "1" thinking it was degrees, but this messed it up quite alot

It should be in radians. So, 1 is ~57.3 degrees.

I would like to move myNormal (one normal) towards the "average" of the set. I guess I need to keep the magnitude to 1 - this is why moving them towards to average is resulting in eventually the normal becoming 0, as the magnitude of the cross isn't always 1. But I never learnt about normals - am not sure how to do this in EE.

Please could you help explain it; e.g. rotating myNormal towards the average of the set of normals, without affecting the magnitude?

Thanks.

do avg_normal.normalize(); instead of avg_normal/=count;

Vec cross=CrossN(myNormal,avg_normal);
myNormal*=Matrix3().setRotate(cross, angle); // check +angle -angle etc later

rotating doesn't change the vector length

You mean:

FREPA(normals) { // all normals in the set
avgnrm += normals[i];
}

avgnrm.normalise();

I just tried this - but the result is very wrong - sorry if i'm doing something very silly, I had a long day.

Edit: Oh, sorry I didn't even read the bit under it - thanks it works with:

avg_normal.normalize();
Vec cross=CrossN(myNormal,avg_normal);
myNormal*=Matrix3().setRotate(cross, angle);

I think i'll look at this deeper after sleeping,
Thank you very much for your help today.

Chris

Sorry to bring up something similar to this again, but there are several formulas for this and i'd like to know a efficient way to do it in EE (performance is quite important for this):

Suppose I have a Plane (Vec source, and Vec normal) and I have have another Vec pos infront of this plane. How can I calculate the AbsAngleBetween from the source to the pos, governed by the normal?

   
Attached is a diagram - how to find theta?

(I tried using a closest point on line segment function from pos to normal, and performing basic trig on the right angle triangle.. but it's very inefficient.)

What's a good way to do this in EE?

Thanks so much,
Chris

AbsAngleBetween(normal, pos-source);