Problem with circular wave

Hello,

I try to implement circular water from the GPU Gems chapter 1. (http://http.developer.nvidia.com/GPUGems/gpugems_ch01.html)
Here is reals formula:


Wave height:

with,

• Wavelength (L): the crest-to-crest distance between waves in world space. Wavelength L relates to frequency w as w = 2p/L
• Amplitude (A): the height from the water plane to the wave crest.
• Speed (S): the distance the crest moves forward per second. It is convenient to express speed as phase-constant , where = S x 2p/L.
• Direction (D ): the horizontal vector perpendicular to the wave front along which the crest travels.

Normal vector:

with,



Circular direction:




I implemented these formula in the tesselation evaluation shader.

Here is the source code:

#version 430 core

// In
layout (quads, equal_spacing, cw) in;

// Uni
uniform float   uni_Time;
uniform float   uni_Frequency;
uniform float   uni_Amplitude;
uniform float   uni_Fi;
uniform vec2    uni_Direction;

uniform sampler2D   uni_Texture;

// Out
out vec3    normal;

void main(void)
{
    // Compute new vertice pos
    vec4    p1 = mix(gl_in[0].gl_Position, gl_in[1].gl_Position, gl_TessCoord.x);
    vec4    p2 = mix(gl_in[2].gl_Position, gl_in[3].gl_Position, gl_TessCoord.x);
    vec4    p = mix(p1, p2, gl_TessCoord.y);

    // Compute direction
    vec2    center = vec2(0.5f, 0.5f);
    vec2    dir = normalize(gl_TessCoord.yx - center);

    // Compute wave height
    float   theta = dot(dir, gl_TessCoord.yx);
    p.y -= uni_Amplitude * sin(theta * uni_Frequency + uni_Time * uni_Fi);

    // Compute normal
    float   A = uni_Amplitude * dir.x * uni_Frequency;
    normal.x = - (A * cos(theta * uni_Frequency + uni_Time * uni_Fi));
    A = uni_Amplitude * dir.y * uni_Frequency;
    normal.y = - (A * cos(theta * uni_Frequency + uni_Time * uni_Fi));
    normal.z = 1.0f;
    normal = normalize(normal);

    gl_Position = p;
}

and the video:

[media]https:

The problem is,

In the case where i choose directional wave, it works fine (direction and normal vector.)
But, in the case where i choose circular wave, i get a wrong wave and normal ...

I think that, with circular wave, my direction is wrong ... but i dont understand why ...

Thanks for your help