add engine version

2 files changed, 414 insertions, 0 deletions

diff --git a/engine-ocean/Game/Ocean/ocean.cpp b/engine-ocean/Game/Ocean/ocean.cpp
new file mode 100644
index 0000000..e8b88a8
--- /dev/null
+++ b/engine-ocean/Game/Ocean/ocean.cpp
@@ -0,0 +1,325 @@
+#include "ocean.h"
+#include <iostream>
+#include <Eigen/Dense>
+
+ocean::ocean()
+{
+    // to be used for efficiency during fft
+    init_wave_index_constants();
+
+}
+
+// initializes static constants (aka they are not time dependent)
+void ocean::init_wave_index_constants(){
+
+    for (int i=0; i<N; i++){
+        Eigen::Vector2i m_n = index_1d_to_2d(i);
+        int n_prime = m_n[0];
+        int m_prime = m_n[1];
+
+        Eigen::Vector2d k = get_k_vector(n_prime, m_prime);
+        Eigen::Vector2d k_conj = get_k_vector(-n_prime, m_prime);
+
+
+        // store h0'(n,m) and w'(n,m) for every index, to be used for later
+        Eigen::Vector2d h0_prime = h_0_prime(k);
+
+        // conjugate of a+bi is a-bi
+        Eigen::Vector2d h0_prime_conj = h_0_prime(k_conj);
+        h0_prime_conj = Eigen::Vector2d(h0_prime_conj[0], -h0_prime_conj[1]);
+
+        double w_prime = omega_prime(k);
+
+        // populate map to be used for later
+        WaveIndexConstant wave_const;
+        wave_const.h0_prime = h0_prime;
+        wave_const.h0_prime_conj = h0_prime_conj;
+        wave_const.w_prime = w_prime;
+        wave_const.base_horiz_pos = get_horiz_pos(i);
+        wave_const.k_vector = k;
+
+        m_waveIndexConstants[i] = wave_const;
+
+        // initialize m_current_h to be h0 for now
+        m_current_h.push_back(h0_prime);
+        m_displacements.push_back(Eigen::Vector2d(0.0, 0.0));
+    }
+}
+
+std::vector<Eigen::Vector2d> ocean::fast_fft(std::vector<Eigen::Vector2d> h)
+{
+    int N = h.size();
+    std::vector<Eigen::Vector2d> H = std::vector<Eigen::Vector2d>(N);
+
+    if (N == 1)
+    {
+        H[0] = h[0];
+        return H;
+    }
+    else
+    {
+        std::vector<Eigen::Vector2d> even = std::vector<Eigen::Vector2d>(N / 2);
+        std::vector<Eigen::Vector2d> odd = std::vector<Eigen::Vector2d>(N / 2);
+
+        for (int i = 0; i < N / 2; i++)
+        {
+            even[i] = h[2 * i];
+            odd[i] = h[2 * i + 1];
+        }
+
+        std::vector<Eigen::Vector2d> even_fft = fast_fft(even);
+        std::vector<Eigen::Vector2d> odd_fft = fast_fft(odd);
+
+        for (int i = 0; i < N / 2; i++)
+        {
+
+            Eigen::Vector2d k = m_waveIndexConstants[i].k_vector;
+            Eigen::Vector2d x = m_waveIndexConstants[i].base_horiz_pos;
+
+
+            double k_dot_xz = k.dot(x);
+
+            Eigen::Vector2d omega = complex_exp(k_dot_xz);
+            Eigen::Vector2d omega_times_odd = Eigen::Vector2d(omega[0] * odd_fft[i][0] - omega[1] * odd_fft[i][1], omega[0] * odd_fft[i][1] + omega[1] * odd_fft[i][0]);
+
+            H[i] = Eigen::Vector2d(even_fft[i][0] + omega_times_odd[0], even_fft[i][1] + omega_times_odd[1]);
+            H[i + N / 2] = Eigen::Vector2d(even_fft[i][0] - omega_times_odd[0], even_fft[i][1] - omega_times_odd[1]);
+        }
+
+        return H;
+    }
+}
+
+// fast fourier transform at time t
+void ocean::fft_prime(double t){
+
+//    // NON FFT
+//    for (int i=0; i<N; i++){
+//        Eigen::Vector2d h_t_prime = h_prime_t(i, t); // vector(real, imag)
+
+//        m_current_h[i] = h_t_prime;
+//    }
+
+//    return;
+
+    // FFT
+    std::vector<Eigen::Vector2d> h_tildas = std::vector<Eigen::Vector2d>();
+
+    // find each h_tilda at each index, to be used for next for loop
+    for (int i=0; i<N; i++){
+        Eigen::Vector2d h_t_prime = h_prime_t(i, t); // vector(real, imag)
+
+        h_tildas.emplace_back(h_t_prime);
+    }
+
+    // for each position in grid, sum up amplitudes dependng on that position
+    for (int i=0; i<N; i++){
+        Eigen::Vector2d x_vector = m_waveIndexConstants[i].base_horiz_pos;
+        m_current_h[i] = Eigen::Vector2d(0.0, 0.0);
+        m_displacements[i] = Eigen::Vector2d(0.0, 0.0);
+
+
+        for (int j = 0; j < N; j++){
+            Eigen::Vector2d k_vector = m_waveIndexConstants[j].k_vector;
+            Eigen::Vector2d h_tilda_prime = h_tildas[j]; // vector(real, imag)
+
+
+            // add x vector and k vector as imaginary numbers
+            double imag_xk_sum = x_vector.dot(k_vector);
+            Eigen::Vector2d exp = complex_exp(imag_xk_sum); // vector(real, imag)
+
+            double real_comp = h_tilda_prime[0]*exp[0] - h_tilda_prime[1]*exp[1];
+            double imag_comp = h_tilda_prime[0]*exp[1] + h_tilda_prime[1]*exp[0];
+
+            m_current_h[i] += Eigen::Vector2d(real_comp, imag_comp);
+
+            Eigen::Vector2d k_normalized = k_vector.normalized();
+
+            m_displacements[i] += k_normalized*imag_comp;
+
+        }
+    }
+
+}
+
+// time dependent calculation of h'(n,m,t)
+Eigen::Vector2d ocean::h_prime_t(int i, double t){
+    Eigen::Vector2d h0_prime = m_waveIndexConstants[i].h0_prime; // vector(real, imag)
+    Eigen::Vector2d h0_prime_conj = m_waveIndexConstants[i].h0_prime_conj; // vector(real, imag)
+    double w_prime = m_waveIndexConstants[i].w_prime;
+
+    Eigen::Vector2d pos_complex_exp = complex_exp(w_prime*t); // vector(real, imag)
+    Eigen::Vector2d neg_complex_exp = complex_exp(-w_prime*t); // vector(real, imag)
+
+    // now multiply our four vector(real, imag) out
+
+    double real_comp =
+            h0_prime[0]*pos_complex_exp[0]
+            - h0_prime[1]*pos_complex_exp[1]
+            + h0_prime_conj[0]*neg_complex_exp[0]
+            + h0_prime_conj[1]*neg_complex_exp[1];
+
+    double imag_comp =
+            h0_prime[0]*pos_complex_exp[1]
+            + h0_prime[1]*pos_complex_exp[0]
+            + h0_prime_conj[0]*neg_complex_exp[1]
+            - h0_prime_conj[1]*neg_complex_exp[0];
+
+
+
+    return Eigen::Vector2d(real_comp, imag_comp);
+}
+
+double ocean::omega_prime(Eigen::Vector2d k){
+    // calculate omega^4 first to prevent sqrts
+    double w = sqrt(gravity*k.norm());
+
+    return w;
+}
+
+Eigen::Vector2d ocean::h_0_prime(Eigen::Vector2d k){
+    double Ph_prime = phillips_prime(k);
+    std::pair<double,double> randoms = sample_complex_gaussian();
+    double random_r = randoms.first;
+    double random_i = randoms.second;
+
+    // seperate real and imag products
+    double coeff = 0.707106781187 * sqrt(Ph_prime);
+    double real_comp = coeff*random_r;
+    double imag_comp = coeff*random_i;
+
+    return Eigen::Vector2d(real_comp, imag_comp);
+}
+
+
+double ocean::phillips_prime(Eigen::Vector2d k){
+    double k_mag = k.norm();
+
+    k.normalize();
+    double dot_prod = k.dot(omega_wind);
+
+    double output = 0.0;
+    // l = 1
+    if (k_mag < .0001) return 0.0;
+
+    if (k_mag > 1.0){
+
+       output =  A*exp(-(k_mag*k_mag))*dot_prod*dot_prod/(k_mag*k_mag*k_mag*k_mag);
+    } else {
+       output =  A*exp(-1.0/(k_mag*L*k_mag*L))*dot_prod*dot_prod/(k_mag*k_mag*k_mag*k_mag);
+
+    }
+
+
+
+    return output;
+}
+
+Eigen::Vector2d ocean::get_k_vector(int n_prime, int m_prime){
+    double n_ = (double)n_prime;
+    double m_ = (double)m_prime;
+    double N_ = (double)num_rows;
+    double M_ = (double)num_cols;
+
+    double k_x = (2.0*M_PI*n_ - M_PI*N_)/Lx;
+    double k_z = (2.0*M_PI*m_ - M_PI*M_)/Lz;
+
+    return Eigen::Vector2d(k_x, k_z);
+}
+
+Eigen::Vector2d ocean::get_horiz_pos(int i){
+    Eigen::Vector2i m_n = index_1d_to_2d(i);
+    double n_prime = (double)m_n[0];
+    double m_prime = (double)m_n[1];
+    double N_ = (double)num_rows;
+    double M_ = (double)num_cols;
+
+
+    double x = (n_prime-.5*N_)*Lx / N_;
+    double z = (m_prime-.5*M_)*Lz / M_;
+
+
+
+    return Eigen::Vector2d(x, z);
+}
+
+
+Eigen::Vector2i ocean::index_1d_to_2d(int i){
+    int row = i/num_rows; // n'
+    int col = i%num_rows; // m'
+
+    return Eigen::Vector2i(row, col);
+
+}
+
+std::pair<double,double> ocean::sample_complex_gaussian(){
+    double uniform_1 = (double)rand() / (RAND_MAX);
+    double uniform_2 = (double)rand() / (RAND_MAX);
+
+    // set a lower bound on zero to avoid undefined log(0)
+    if (uniform_1 == 0)
+    {
+        uniform_1 = 1e-10;
+    }
+    if (uniform_2 == 0)
+    {
+        uniform_2 = 1e-10;
+    }
+
+    // real and imaginary parts of the complex number
+    double real = sqrt(-2 * log(uniform_1)) * cos(2 * M_PI * uniform_2);
+    double imag = sqrt(-2 * log(uniform_1)) * sin(2 * M_PI * uniform_2);
+
+    return std::make_pair(real, imag);
+}
+
+Eigen::Vector2d ocean::complex_exp(double exponent){
+    double real = cos(exponent);
+    double imag = sin(exponent);
+
+    return Eigen::Vector2d(real, imag);
+}
+
+std::vector<Eigen::Vector3f> ocean::get_vertices()
+{
+    std::vector<Eigen::Vector3f> vertices = std::vector<Eigen::Vector3f>();
+    for (int i = 0; i < N; i++){
+        Eigen::Vector2d horiz_pos = spacing*m_waveIndexConstants[i].base_horiz_pos;
+        Eigen::Vector2d amplitude = m_current_h[i];
+
+
+        // calculate displacement
+        Eigen::Vector2d disp = lambda*m_displacements[i];
+
+
+        // for final vertex position, use the real number component of amplitude vector
+        vertices.push_back(Eigen::Vector3f(horiz_pos[0] + disp[0], amplitude[0], horiz_pos[1] + disp[1]));
+    }
+    return vertices;
+}
+
+std::vector<Eigen::Vector3i> ocean::get_faces()
+{
+    // connect the vertices into faces
+    std::vector<Eigen::Vector3i> faces = std::vector<Eigen::Vector3i>();
+    for (int i = 0; i < N; i++)
+    {
+        int x = i / num_rows;
+        int z = i % num_rows;
+
+        // connect the vertices into faces
+        if (x < num_rows - 1 && z < num_cols - 1)
+        {
+            int i1 = i;
+            int i2 = i + 1;
+            int i3 = i + num_rows;
+            int i4 = i + num_rows + 1;
+
+//            faces.emplace_back(i2, i1, i3);
+//            faces.emplace_back(i2, i3, i4);
+                        faces.emplace_back(i1, i2, i3);
+                        faces.emplace_back(i3, i2, i4);
+        }
+    }
+    return faces;
+}
diff --git a/engine-ocean/Game/Ocean/ocean.h b/engine-ocean/Game/Ocean/ocean.h
new file mode 100644
index 0000000..b2abe87
--- /dev/null
+++ b/engine-ocean/Game/Ocean/ocean.h
@@ -0,0 +1,89 @@
+#ifndef ocean_H
+#define ocean_H
+
+#include <map>
+#include <vector>
+#include <utility>
+#include <Eigen/Dense>
+
+// for every 1d index up to length*width
+struct WaveIndexConstant{
+    Eigen::Vector2d h0_prime = Eigen::Vector2d(0.f, 0.f);
+    Eigen::Vector2d h0_prime_conj = Eigen::Vector2d(0.f, 0.f);
+
+    double w_prime = 0.0;
+
+
+    Eigen::Vector2d base_horiz_pos = Eigen::Vector2d(0.f, 0.f); // static horiz pos with no displacement
+    Eigen::Vector2d k_vector = Eigen::Vector2d(0.f, 0.f); // static horiz pos with no displacement
+
+
+
+};
+
+class ocean
+{
+public:
+    ocean();
+    void updateVertexAmplitudes(double t);
+    std::vector<Eigen::Vector3f> get_vertices();
+    std::vector<Eigen::Vector3i> get_faces();
+    void fft_prime(double t);
+
+
+
+
+
+private:
+
+    Eigen::Vector2i index_1d_to_2d(int i);
+    Eigen::Vector2d get_k_vector(int n_prime, int m_prime);
+    double phillips_prime(Eigen::Vector2d k);
+    Eigen::Vector2d h_0_prime(Eigen::Vector2d k);
+    double omega_prime(Eigen::Vector2d k);
+    void init_wave_index_constants();
+    Eigen::Vector2d complex_exp(double exponent);
+    Eigen::Vector2d h_prime_t(int i, double t);
+    Eigen::Vector2d get_horiz_pos(int i);
+    std::pair<double, double> sample_complex_gaussian();
+    std::vector<Eigen::Vector2d> fast_fft(std::vector<Eigen::Vector2d> h);
+
+
+
+
+
+
+
+
+
+    std::map<int, WaveIndexConstant> m_waveIndexConstants; // stores constants that only need to be calculate once for each grid constant
+
+
+
+    const double Lx = 10.0;
+    const double Lz = 10.0;
+
+    const int num_rows = 8;
+    const int num_cols = 8;
+
+    const int N = num_rows*num_cols; // total number of grid points
+    const double lambda = .40; // how much displacement matters
+    const double spacing = 35.0; // spacing between grid points
+
+    const double A = 1.0; // numeric constant for the Phillips spectrum
+    const double V = 5.5; // wind speed
+    const double gravity = 9.81;
+    const double L = V*V/gravity;
+    const Eigen::Vector2d omega_wind = Eigen::Vector2d(1.0, 0.0); // wind direction, used in Phillips equation
+
+    std::vector<Eigen::Vector2d> m_current_h; // current height fields for each K
+    std::vector<Eigen::Vector2d> m_displacements; // current displacement vector for each K
+
+
+
+    const double D = 1.0; // Depth below mean water level (for dispersion relation)
+
+
+};
+
+#endif // ocean_H