Offset a vector by another vector

[Josh]

I have a vector in space. I want to make a ring of vectors that are offset from the original by a certain angle, so that they form a cone shape. I realize this can have multiple solutions. That's okay, as long as the resulting vectors form a cone around the original. How can this be done?

[TylerH]

In 2D:

angle *= rand() * 6.28; // Pi*2, rand() should be a float between 0 and 1

float cosa = cos(angle);

float sina = sin(angle);

return vec2(cosa * x - sina * y, sina * x + cosa * y);

 

In 3D:

(up should be the local up vector, or a vector perpendicular to the vector you are testing against)

 

// Rotate up vector by random amount around this

Quaternion q;

q.FromAngleAxis( rand() * 6.28, v );

up = q * up;

 

// Finally rotate this by given angle around randomised up

q.FromAngleAxis( angle, newUp );

return vec2(q * v);

 

 

(Slightly modified from OGRE)

 

NOTE: The above will give you deviant vectors that are offset by the angle, you can place some simple limits on the 0-1 random value to make it a cone shape, and then iterate a step function over however many segments of the cone you want to have (64 super precise, or 8 not so much).