first draft to generate waves

2 files changed, 330 insertions, 0 deletions

diff --git a/src/ocean/ocean.cpp b/src/ocean/ocean.cpp
new file mode 100644
index 0000000..f70a553
--- /dev/null
+++ b/src/ocean/ocean.cpp
@@ -0,0 +1,259 @@
+//
+// Created by Michael Foiani on 4/9/24.
+//
+
+#include <iostream>
+#include "ocean.h"
+
+// TODO: make these private instance variables
+
+ocean::ocean()
+{
+	initial_h = std::vector<std::pair<double, double>>();
+	// initialize the initial height fields
+	for (int i = 0; i < N; i++)
+	{
+		initial_h.push_back(amplitude_0(i));
+	}
+}
+
+/* Maps the 1D k-index into it's 2D waveform vector */
+std::pair<double, double> ocean::k_index_to_k_vector
+	(
+		int k_index
+	)
+{
+	// get the x and z indices
+	int x = k_index % length;
+	int z = k_index / length;
+
+	// calculate the k_x and k_z values, according to the length
+	double k_x = (2 * M_PI * x - N) / (double) length;
+	double k_z = (2 * M_PI * z - N) / (double) width;
+
+	return std::make_pair(k_x, k_z);
+}
+
+/*
+ * Randomly generates a complex number by
+ * 	importance sampling a Gaussian distribution
+ * 	with mean 0 and variance 1.
+ *
+ * Applies the Box-Muller transform to generate,
+ * 	citation: en.wikipedia.org/wiki/Box%E2%80%93Muller_transform
+ */
+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);
+}
+
+/*
+ * Generates the Phillips spectrum for a given k-index.
+ * See section 4.3 of the paper.
+ */
+double ocean::phillips_spectrum
+	(
+	int k_index
+	)
+{
+	// get the k_x, k_z values & amplitude of k
+	std::pair<double, double> k = k_index_to_k_vector(k_index);
+	double k_x = k.first;
+	double k_z = k.second;
+	double k_magnitude = sqrt(k_x * k_x + k_z * k_z);
+
+	// calculate L, the max wave size from wind speed V
+	double L = (V * V) / 9.81;
+	// get the strength of k onto the wind direction
+	double k_dot_omega = k_x * omega_wind.first + k_z * omega_wind.second;
+
+	// calculate certain parts of the Phillips formula
+	double k_dot_omega_squared = k_dot_omega * k_dot_omega;
+	double KL_squared = (k_magnitude * L) * (k_magnitude * L);
+	double k_fourth = k_magnitude * k_magnitude * k_magnitude * k_magnitude;
+
+	double phillips =
+		A // numeric constant
+		* exp(-1 / KL_squared)
+		/ (k_fourth)
+		* k_dot_omega_squared;
+
+	// TODO: consider the small length check as described in the paper
+	return phillips;
+}
+
+/*
+ * Generates the initial (i.e. t = 0) fourier amplitude.
+ * See section 4.4 of the paper.
+ */
+std::pair<double, double> ocean::amplitude_0
+	(
+		int k_index
+	)
+{
+	std::pair<double, double> xi = sample_complex_gaussian();
+
+	double xi_real = xi.first;
+	double xi_imag = xi.second;
+
+	double sqrt_phillips = sqrt(phillips_spectrum(k_index));
+
+	double real = (1 / sqrt(2)) * xi_real * sqrt_phillips;
+	double imag = (1 / sqrt(2)) * xi_imag * sqrt_phillips;
+
+	return std::make_pair(real, imag);
+}
+
+/*
+ * Maps the negative k-index from a given k-index,
+ * used for the complex conjugate in amplitude_t
+ */
+int ocean::k_index_to_negative_k_index
+	(
+		int k_index
+	)
+{
+	int x = k_index % length;
+	int z = k_index / length;
+
+	int x_neg = length - x;
+	int z_neg = width - z;
+
+	return z_neg * length + x_neg;
+}
+
+/*
+ * Calculates the dispersion relation for a given k-index.
+ * See section 4.2 of the paper.
+ */
+double ocean::omega_dispersion
+	(
+		double k_magnitude,
+		bool is_shallow
+	)
+{
+	if (is_shallow)
+	{
+		double tanh_kD = tanh(D * k_magnitude);
+		return sqrt(9.81 * k_magnitude * tanh_kD);
+	}
+	else
+	{
+		return sqrt(9.81 * k_magnitude);
+	}
+}
+
+std::pair<double, double> ocean::exp_complex
+	(
+		std::pair<double, double> z
+	)
+{
+	double real = exp(z.first) * cos(z.second);
+	double imag = exp(z.first) * sin(z.second);
+
+	return std::make_pair(real, imag);
+}
+
+/*
+ * Generates the fourier amplitude at time t.
+ * See section 4.4 of the paper.
+ */
+std::pair<double, double> ocean::amplitude_t
+	(
+		double t,
+		int k_index
+	)
+{
+	// get the initial height (and it's conjugate)
+	std::pair<double, double> h_0 = initial_h[k_index];
+	std::pair<double, double> h_0_conjugate = initial_h[k_index_to_negative_k_index(k_index)];
+	h_0_conjugate = std::make_pair(h_0_conjugate.first, -h_0_conjugate.second);
+
+	// get dispersion from k
+	std::pair<double, double> k = k_index_to_k_vector(k_index);
+	double k_magnitude = sqrt(k.first * k.first + k.second * k.second);
+	double omega = omega_dispersion(k_magnitude);
+
+	// calculate the complex exponential terms
+	double omega_t = omega * t;
+	std::pair<double, double> exp_positive = exp_complex(std::make_pair(0, omega_t));
+	std::pair<double, double> exp_negative = exp_complex(std::make_pair(0, -omega_t));
+
+	// add the real and imaginary part together from both h_0 and h_0_conjugate
+	double real =
+		// h+0 real
+		h_0.first * exp_positive.first
+		- h_0.second * exp_positive.second
+		// h_0_conjugate real
+		+ h_0_conjugate.first * exp_negative.first
+		- h_0_conjugate.second * exp_negative.second;
+	double imag =
+		// h_0 imaginary
+		h_0.first * exp_positive.second
+		+ h_0.second * exp_positive.first
+		// h_0_conjugate imaginary
+		+ h_0_conjugate.first * exp_negative.second
+		+ h_0_conjugate.second * exp_negative.first;
+
+	return std::make_pair(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++)
+	{
+		std::pair<double, double> k = k_index_to_k_vector(i);
+		double k_x = k.first;
+		double k_z = k.second;
+
+		double amplitude = initial_h[i].first;
+
+		std::cout << "k_x: " << k_x << " k_z: " << k_z << " amplitude: " << amplitude << std::endl;
+
+		vertices.emplace_back(k_x, amplitude, k_z);
+	}
+	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 % length;
+		int z = i / length;
+
+		// connect the vertices into faces
+		if (x < length - 1 && z < width - 1)
+		{
+			int i1 = i;
+			int i2 = i + 1;
+			int i3 = i + length;
+			int i4 = i + length + 1;
+
+			faces.emplace_back(i1, i2, i3);
+			faces.emplace_back(i2, i3, i4);
+		}
+	}
+	return faces;
+}
diff --git a/src/ocean/ocean.h b/src/ocean/ocean.h
new file mode 100644
index 0000000..7e436cf
--- /dev/null
+++ b/src/ocean/ocean.h
@@ -0,0 +1,71 @@
+//
+// Created by Michael Foiani on 4/9/24.
+//
+
+#ifndef OCEAN_H
+#define OCEAN_H
+
+#include <vector>
+#include <utility>
+#include <Eigen/Dense>
+
+
+class ocean
+{
+public:
+	ocean();
+
+	const int length = 16; // length of grid
+	const int width = 16; // width of grid
+	const int N = length * width; // total number of grid points
+
+	const double A = 100; // numeric constant for the Phillips spectrum
+	const double V = 5.0; // wind speed
+	const std::pair<double, double> omega_wind
+		= std::make_pair(1.0, 0.0); // wind direction
+
+	std::vector<std::pair<double, double>> initial_h; // initial height fields for each K
+
+	const double D = 1; // Depth below mean water level (for dispersion relation)
+
+	std::vector<Eigen::Vector3f> get_vertices
+	();
+	std::vector<Eigen::Vector3i> get_faces
+	();
+
+	std::pair<double, double> k_index_to_k_vector
+	(
+		int k_index
+	);
+	std::pair<double, double> sample_complex_gaussian
+		();
+	double phillips_spectrum
+	(
+		int k_index
+	);
+	std::pair<double, double> amplitude_0
+	(
+		int k_index
+	);
+	int k_index_to_negative_k_index
+	(
+		int k_index
+	);
+	double omega_dispersion
+	(
+		double k_magnitude,
+		bool is_shallow=false
+	);
+	std::pair<double, double> exp_complex
+	(
+		std::pair<double, double> z
+	);
+	std::pair<double, double> amplitude_t
+	(
+		double t,
+		int k_index
+	);
+};
+
+
+#endif //OCEAN_H