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Hi,

i need a function, that creates a random vector. As parameters i give it a normal-vector, which would be the standard direction and an int (alpha), which would be the maximum deviation from the normal in degree (so if alpha=180° the vector could point everywhere).

I really canīt think of any good solution.

Thanks.

Jan.

Just FYI, this is more of a math question than an OpenGL question, so you might take some heat from posting here.

Why not just pick a random rotation axis (vector) then use your angle (alpha) and this axis to make a rotation matrix for your original vector? If you need to know how to build such a matrix, use google to look up the man pages for glRotatef( ).

-- Zeno

ScottManDeath

06-07-2002, 11:06 AM

Hi

why not following:

vec normal,random;

float angle;

do

{

vec[0]=rand();

vec[1]=rand();

vec[2]=rand();

}while ( dotproduct(normal,random) <= cos(angle))

normalize(vec);

Bye

ScottManDeath

jwatte

06-07-2002, 06:08 PM

ScottMan,

That function will generate vectors that cluster towards the corners of a "cube" surrounding the sphere.

You should use the function for an evenly distributed point on the shell of a sphere, and adjust it for only a slice of a sphere, where the slice height is one minus the cosine of the angle you want to use.

vector random_vector(float angle) {

float x = rand_closed(cos(angle),1);

float a = rand_half_open(-PI,PI);

float r = sqrtf(1-x*x);

float y = sin(a)*r;

float z = cos(a)*r;

return vector(x,y,z);

}

Proof that this generates a unit vector:

x = [-1,1]

r = sqrt(1-x*x)

y = cos(a)*r

z = sin(a)*r

x*x+y*y+z*z == 1

y*y/r*r+z*z/r*r == 1

y*y+z*z == r*r == 1-x*x

y*y+z*z+x*x == 1

Proof that this generates a uniformly distributed point on the shell of a sphere (or sphere slice) can be derived by looking at the surface covered by each sample in the quantized case for quantization approaching zero, i e through simple integration.

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