Gerstner Wave

⚠ Attention, this is a part of the Shader , its just an algorithm, which means that you come to complement and adapt it to your project. Just add parameters and appendes with another wave, also concern Normal, just sort out all the norms on the output channel.

normal_reconstruct -> NORMAL // Final Normal Reconsctruct

wave_vertex_offset  -> VERTEX // Final vertex offset

Shader code

// === Gerstner Wave Node ===
vec3 input_wave_direction;       // Shader Parameter
float input_wave_length;         // Shader Parameter
float input_wave_height;         // Shader Parameter
float input_wave_peak_sharpness; // Shader Parameter

vec3 vertex_position = VERTEX;
float gravity = 9.807;
float time = TIME;
float tau = 6.28319;

// Calculate wave properties
float wave_number = tau / input_wave_length;
float wave_speed = sqrt(gravity * wave_number);
float wave_phase_time = time * wave_speed;

vec3 wave_direction_normalized = normalize(input_wave_direction);
vec3 wave_vector = wave_direction_normalized * wave_number;

float phase_offset = dot(vertex_position, wave_vector);
float wave_phase = phase_offset - wave_phase_time;

// Trigonometric wave response
float wave_cos = cos(wave_phase);
float wave_sin = sin(wave_phase);

// Vertical displacement
vec3 up_vector = vec3(0.0, 1.0, 0.0);
vec3 vertical_displacement = wave_cos * up_vector * input_wave_height;

// Horizontal displacement
float wave_height_scaled = input_wave_height * wave_number;
float steepness_ratio = input_wave_peak_sharpness / wave_height_scaled;
float horizontal_amplitude = steepness_ratio * input_wave_height;
float horizontal_displacement_magnitude = wave_sin * horizontal_amplitude;
vec3 horizontal_displacement = horizontal_displacement_magnitude * wave_direction_normalized;

// Final vertex offset
vec3 wave_vertex_offset = vertical_displacement - horizontal_displacement;

// Final Normal Reconsctruct
vec3 normal_reconstruct = GerstnerWave_CalculateNormal(
    wave_sin,
    wave_cos,
    wave_height_scaled,
    wave_direction_normalized,
    steepness_ratio);


///////////////// NORMAL RECONSTRUCT ALGORITHM ////////////////

vec3 GerstnerWave_CalculateNormal(
float input_wave_sin, 
float input_wave_cos, 
float input_wave_height_scaled,
vec3 input_wave_direction_normalized,
float input_steepness_ratio)
{
    
    // Normal calculation
    float sin_component = input_wave_sin * input_wave_height_scaled;
    float cos_component = input_wave_cos * input_wave_height_scaled;

    vec3 normal_lateral = input_wave_direction_normalized * sin_component;
    float normal_vertical = input_steepness_ratio * cos_component;

    vec3 wave_normal = vec3(normal_lateral.x, -normal_vertical , normal_lateral.z);
    return wave_normal;
}

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