Use Perlin noise to render wood

Use Perlin noise to render wood

guys, I'm reading Shaders for Game Programming and Artists. In Chapter 13
"Building Materials from Scratch", the author introduced some render
techniques to simulate complex materials such as marble or wood by using
Perlin noise. But I'm puzzled by the wood rendering. To simulate the wood,
we need a function gives a circular value along a specific plane so that
we can create the rings in the woods. This is what the author said, "take
the dot product of two axes along a plane, creating the circular value on
that plane"
Circle = dot(noisetxr.xy, noisetxr.xy);
noisetxr is a float3, it's a texture coordinate to sample the noise
texture, I can't understand why the dot product will gives a circular
value
Here is the complete code(pixel shader in hlsl):
float persistance;
float4 wood_color; //a predefined value
sampler Texture0; // noise texture
float4 ps_main(float3 txr: TEXCOORD0) : COLOR
{
// Determine two set of coordinates, one for the noise
// and one for the wood rings
float3 noisetxr = txr;
txr = txr/8;
// Combine 3 octaves of noise together.
float final_noise = 0;
for(int i=0;i<2;i++)
final_noise += ((1.0/pow(persistance,i))*
((tex3D(Texture0, txr*pow(2,i))*2)-1));
// The wood is defined by a set of concentric rings in the XY
// plane. Those rings are pertubated by the computed noise.
final_noise = abs(final_noise);
float grain = cos(dot(noisetxr.xy,noisetxr.xy) + final_noise*4);//what
is this ??
return wood_color - pow(grain,8)/2; //raising the cosine to higher power
}
I know that raising the cosine function to higher power will create
sharper rings, but what does the dot product mean ? Why it can create a
circle value ?