normal for analytical surface

Question

I'm calculating surface normal for my analytical surface. Some parts of normal i'm getting are correct but not all. Code is :

SurfaceVertices3f[pos] = i;
SurfaceVertices3f[pos+1] = j;
SurfaceVertices3f[pos+2] = (cos(i)*sin(j));

/*a and b hold the poutput of partial differentiation of vertices from above three lines.a is wrt i and b is wrt j */           
a[0]=1;
a[1]=0;
a[2]=-sin(i)*sin(j);

b[0]=0;
b[1]=1;
b[2]=cos(i)*cos(j);

normal_var=Vec3Df::crossProduct( a, b);
normal_var.normalize();

My output looks like this, right image is mine and left one i'm using as refrence . http://tinypic.com/view.php?pic=73l9co&s=5

Could anyone tell me what mistake i'm doing?

Answer 1

Your normal calculation is correct. The reference image has just a different way to map normals to colors.

If you have a look at the green ground color, you will see that the color's norm is not 1. But normals should have a norm of 1. If we assume another common mapping from normal to color like this one:

color.rgb = normal.xyz / 2 + 0.5

We see that this is no unit vector either. So either they used yet a different mapping or they just don't have unit length normals.