added energy overlay

shaders/fragment_quad.glsl

@@ -0,0 +1,11 @@
+#version 330 core
+
+out vec4 FragColor;
+
+in vec2 texCoord;
+
+uniform sampler2D quadTexture;
+
+void main() {
+    FragColor = texture(quadTexture, texCoord);
+}

shaders/shaders.qrc

@@ -1,6 +1,8 @@
 <RCC>
     <qresource prefix="/shaders/">
-        <file>vertex.glsl</file>
+        <file>vertex_pendula.glsl</file>
-        <file>fragment.glsl</file>
+        <file>fragment_pendula.glsl</file>
+        <file>vertex_quad.glsl</file>
+        <file>fragment_quad.glsl</file>
     </qresource>
 </RCC>

shaders/vertex_pendula.glsl

@@ -7,8 +7,8 @@ layout (location = 2) in float vMassRadius;
 uniform mat3 VP;
 
 uniform bool drawPoints;
-uniform float screenSizePixels;
+uniform int simulationSizePixels;
-uniform float screenSizeMeters;
+uniform float simulationSizeMeters;
 uniform float depthOffset;
 
 out vec3 color;
@@ -16,8 +16,11 @@ out vec3 color;
 void main() {
     gl_Position = vec4(VP * vPos, 1.0);
     if (drawPoints){
+        // Points always on top of neighbouring lines
         gl_Position.z -= depthOffset * 0.5;
-        gl_PointSize = vMassRadius / screenSizeMeters * screenSizePixels * 2;
+
+        // PointSize is diameter in Pixels
+        gl_PointSize = vMassRadius / simulationSizeMeters * simulationSizePixels * 2;
     } else {
         color = vColor;
     }

shaders/vertex_quad.glsl

@@ -0,0 +1,11 @@
+#version 330 core
+
+layout (location = 0) in vec2 vPos;
+layout (location = 1) in vec2 vTex;
+
+out vec2 texCoord;
+
+void main() {
+    gl_Position = vec4(vPos, 0, 1);
+    texCoord = vTex;
+}

src/GLWidget.cpp

@@ -6,24 +6,25 @@
 #include "Simulation.h"
 #include <QApplication>
 #include <QDialog>
-#include "FPS.h"
+#include "Overlay.h"
 #include <QOpenGLShaderProgram>
+#include "FPS.h"
 
 GLWidget::GLWidget(Simulation * simulation) : simulation(simulation) {
-	startTimer(1000 / 144);
+	startTimer(1000 / 60);
-	fps = new FPS;
+	overlay = new Overlay(simulation);
-	fps->setUpdateInterval(500);
 	connect(simulation, &Simulation::layoutChanged, this, &GLWidget::uploadStaticDataToGPU);
+	connect(simulation, &Simulation::layoutChanged, overlay, &Overlay::fetchEnergyLimit);
 	connect(simulation, &Simulation::positionChanged, this, &GLWidget::changePosition);
 }
 
 void GLWidget::initializeGL() {
 	initializeOpenGLFunctions();
 
-	program = new QOpenGLShaderProgram;
+	pendulaProgram = new QOpenGLShaderProgram;
-	program->addShaderFromSourceFile(QOpenGLShader::Vertex, ":/shaders/vertex.glsl");
+	pendulaProgram->addShaderFromSourceFile(QOpenGLShader::Vertex, ":/shaders/vertex_pendula.glsl");
-	program->addShaderFromSourceFile(QOpenGLShader::Fragment, ":/shaders/fragment.glsl");
+	pendulaProgram->addShaderFromSourceFile(QOpenGLShader::Fragment, ":/shaders/fragment_pendula.glsl");
-	program->link();
+	pendulaProgram->link();
 
 	glGenVertexArrays(1, &VAO);
 	glGenBuffers(1, &positionVBO);
@@ -35,57 +36,53 @@ void GLWidget::initializeGL() {
 	glEnable(GL_PROGRAM_POINT_SIZE);
 	glEnable(GL_PRIMITIVE_RESTART);
 	glEnable(GL_PRIMITIVE_RESTART_FIXED_INDEX);
-	glEnable(GL_DEPTH_TEST);
+	glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
 	glDepthFunc(GL_LESS);
 	glClearDepth(1);
 	glClearColor(.15, .15, .15, 1);
 
-	std::vector<Pendulum*> empty;
+	uploadStaticDataToGPU();
-	uploadStaticDataToGPU(&empty);
+
+	overlay->init();
 }
 
 void GLWidget::paintGL() {
-	// Native OpenGL
+	glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
-	{
-
-		glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
 
-		program->bind();
+	// Content
-		program->setUniformValue("VP", VP);
+	{
+		glViewport(0, 0, width(), height());
+		glEnable(GL_DEPTH_TEST);
+		glDisable(GL_BLEND);
+		pendulaProgram->bind();
+		pendulaProgram->setUniformValue("VP", VP);
 
 		glBindVertexArray(VAO);
 
 		// Lines
 		{
-			program->setUniformValue("drawPoints", false);
+			pendulaProgram->setUniformValue("drawPoints", false);
 			glDrawElements(GL_LINE_STRIP, indexCount, GL_UNSIGNED_INT, nullptr);
 		}
 
 		// Mass Circles
 		if (showMasses) {
-			program->setUniformValue("drawPoints", true);
+			pendulaProgram->setUniformValue("drawPoints", true);
-			program->setUniformValue("depthOffset", depthOffset);
+			pendulaProgram->setUniformValue("depthOffset", depthOffset);
-			program->setUniformValue("screenSizePixels", screenSizePixels * 0.9f);
+			pendulaProgram->setUniformValue("simulationSizePixels", simulationSizePixels);
-			program->setUniformValue("screenSizeMeters", float(simulation->sizeMeters));
+			pendulaProgram->setUniformValue("simulationSizeMeters", float(simulation->sizeMeters));
 			glDrawElements(GL_POINTS, indexCount, GL_UNSIGNED_INT, nullptr);
 		}
 
 		glBindVertexArray(0);
 	}
 
-	QPixmap img(size());
+	// Overlay
-	auto p = new QPainter(&img);
-	// FPS
 	{
-		p->setPen(Qt::white);
+		glDisable(GL_DEPTH_TEST);
-		auto font = p->font();
+		glEnable(GL_BLEND);
-		font.setPixelSize(20);
+		overlay->draw();
-		p->setFont(font);
-		fps->newFrame();
-		QString fpsString = "FPS: " + QString::fromStdString(std::to_string(fps->current));
-		p->drawText(0, 0, 100, 100, Qt::AlignTop | Qt::AlignLeft, fpsString);
 	}
-	p->end();
 }
 
 void GLWidget::timerEvent(QTimerEvent *e) {
@@ -101,7 +98,8 @@ bool GLWidget::AnyDialogOpen() {
 	return false;
 }
 
-void GLWidget::uploadStaticDataToGPU(const std::vector<Pendulum *> *pendula) {
+void GLWidget::uploadStaticDataToGPU() {
+	auto pendula = &simulation->pendula;
 
 	int pointCount = std::transform_reduce(pendula->begin(), pendula->end(), 0, [](int prev, int curr){
 		return prev + curr + 1;
@@ -185,11 +183,11 @@ void GLWidget::uploadStaticDataToGPU(const std::vector<Pendulum *> *pendula) {
 	simulation->pendulaMutex.unlock();
 }
 
-void GLWidget::changePosition(const std::vector<Pendulum *> *pendula) {
+void GLWidget::changePosition() {
 	glBindBuffer(GL_ARRAY_BUFFER, positionVBO);
 	auto positions = (GLfloat*) glMapBufferRange(GL_ARRAY_BUFFER, 0, GLsizeiptr(positionCount * sizeof(float)), GL_MAP_WRITE_BIT);
 	size_t index = 0;
-	for (const auto p : *pendula){
+	for (const auto p : simulation->pendula){
 		index += 3;
 		for (auto x : p->X){
 			positions[index++] = float(x.x);
@@ -202,16 +200,15 @@ void GLWidget::changePosition(const std::vector<Pendulum *> *pendula) {
 }
 
 void GLWidget::resizeGL(int w, int h) {
-	screenSizePixels = std::min(float(w), float(h));
+	simulationSizePixels = std::min(w, h) - 100;
-	float scale = screenSizePixels / float(simulation->sizeMeters) * 2 * 0.9f;
+	float scale = float(simulationSizePixels) / float(simulation->sizeMeters) * 2;
 
 	VP.setToIdentity();
-	VP(0, 0) = 1 / float(w);
+	VP(0, 0) = scale / float(w);
-	VP(1, 1) = -1 / float(h);
+	VP(1, 1) = scale / float(h);
-	VP *= scale;
-	VP(2, 2) = 1;
 
-	glViewport(0, 0, w, h);
+	int s = simulationSizePixels;
+	overlay->resize(QSize(w, h), QRect((w - s) / 2, (h - s) / 2, s, s));
 }
 
 void GLWidget::showMassesChanged(int state) {

src/GLWidget.h

@@ -6,8 +6,8 @@
 
 class Pendulum;
 class Simulation;
-class FPS;
 class QOpenGLShaderProgram;
+class Overlay;
 
 class GLWidget : public QOpenGLWidget, protected QOpenGLExtraFunctions {
 public:
@@ -20,10 +20,10 @@ protected:
 public slots:
 	void showMassesChanged(int state);
 private slots:
-	void uploadStaticDataToGPU(const std::vector<Pendulum *> *pendula);
+	void uploadStaticDataToGPU();
-	void changePosition(const std::vector<Pendulum *> *pendula);
+	void changePosition();
 private:
-	QOpenGLShaderProgram * program;
+	QOpenGLShaderProgram * pendulaProgram;
 	GLuint VAO;
 	GLuint positionVBO;
 	GLuint colorVBO;
@@ -32,11 +32,11 @@ private:
 	GLsizei indexCount = 0;
 	GLsizei positionCount = 0;
 	QMatrix3x3 VP;
-	float screenSizePixels;
+	int simulationSizePixels;
 	float depthOffset;
 	bool showMasses;
 
 	Simulation * simulation;
-	FPS * fps;
+	Overlay * overlay;
 	static bool AnyDialogOpen();
 };

src/MainWindow.cpp

@@ -30,6 +30,8 @@ MainWindow::MainWindow() {
 	resetLengths();
 
 	buildUI();
+
+	normalizeLengths();
 }
 
 void MainWindow::buildUI() {

src/Overlay.cpp

@@ -0,0 +1,177 @@
+#include "Overlay.h"
+#include "FPS.h"
+#include <QPainter>
+#include <QOpenGLShaderProgram>
+#include "Simulation.h"
+#include <iostream>
+#include <QOpenGLTexture>
+#include <sstream>
+#include <iomanip>
+
+Overlay::Overlay(Simulation * simulation) : simulation(simulation) {
+	fps = new FPS;
+	fps->setUpdateInterval(500);
+}
+
+void Overlay::init() {
+	initializeOpenGLFunctions();
+
+	program = new QOpenGLShaderProgram;
+	program->addShaderFromSourceFile(QOpenGLShader::Vertex, ":/shaders/vertex_quad.glsl");
+	program->addShaderFromSourceFile(QOpenGLShader::Fragment, ":/shaders/fragment_quad.glsl");
+	program->link();
+
+	float quadVertices[] = {
+			-1,  1, 0, 1, // top left
+			-1, -1, 0, 0, // bottom left
+			 1, -1, 1, 0, // bottom right
+			 1,  1, 1, 1  // top right
+	};
+
+	GLuint indices[] = {
+			0, 1, 2, 2, 3, 0
+	};
+
+	glGenVertexArrays(1, &VAO);
+	glBindVertexArray(VAO);
+
+	GLuint VBO;
+	glGenBuffers(1, &VBO);
+	glBindBuffer(GL_ARRAY_BUFFER, VBO);
+	glBufferData(GL_ARRAY_BUFFER, sizeof(quadVertices), quadVertices, GL_STATIC_DRAW);
+
+	GLuint EBO;
+	glGenBuffers(1, &EBO);
+	glBindBuffer(GL_ELEMENT_ARRAY_BUFFER, EBO);
+	glBufferData(GL_ELEMENT_ARRAY_BUFFER, sizeof(indices), indices, GL_STATIC_DRAW);
+
+	glVertexAttribPointer(0, 2, GL_FLOAT, GL_FALSE, 4 * sizeof(float), nullptr);
+	glVertexAttribPointer(1, 2, GL_FLOAT, GL_FALSE, 4 * sizeof(float), (GLvoid*) (2 * sizeof(float)));
+	glEnableVertexAttribArray(0);
+	glEnableVertexAttribArray(1);
+
+	glBindVertexArray(0);
+}
+
+void Overlay::draw() {
+	int w = viewportSize.width();
+	int h = (viewportSize.height() - simulationRect.height()) / 2;
+
+	// Top HUD with Energy Plot
+	{
+		glViewport(0, viewportSize.height() - h, w, h);
+
+		QImage hud(w, h, QImage::Format_RGBA8888);
+		hud.fill(Qt::transparent);
+
+		QPainter p(&hud);
+		p.setRenderHints(QPainter::Antialiasing);
+		p.setPen(Qt::white);
+		auto font = p.font();
+		font.setPixelSize(15);
+		p.setFont(font);
+
+		auto m = p.fontMetrics();
+
+		double pot = simulation->potentialEnergy;
+		double kin = simulation->kineticEnergy;
+		double total = pot + kin;
+
+		QColor empty(50, 50, 50);
+		QColor full(80, 80, 80);
+
+		// Total energy bar
+		{
+			double lossPercentage = (1 - total / energyLimit) * 100;
+
+			std::stringstream text;
+			text << std::fixed << std::setprecision(0) << "Total Energy: " << total << " J";
+			text << " --- ";
+			text << "Loss: " << std::setprecision(1) << lossPercentage << " %";
+			QString totalText = QString::fromStdString(text.str());
+
+			int x = int(total / energyLimit * w);
+
+			p.fillRect(0, 0, w, h / 2, empty);
+			p.fillRect(0, 0, x, h / 2, full);
+			p.drawLine(x, 0, x, h / 2);
+			p.drawText(0, 0, w, h / 2, Qt::AlignCenter | Qt::AlignVCenter, totalText);
+		}
+
+		// Split energy bar
+		{
+			int potX = total == 0 ? int(0.5 * w) : int(pot / total * w);
+			p.fillRect(0, h / 2, w, h / 2, empty);
+			p.fillRect(0, h / 2, potX, h / 2, full);
+
+			std::stringstream text;
+			text << std::fixed << std::setprecision(0) << "Potential: " << pot << " J";
+			QString potText = QString::fromStdString(text.str());
+
+			text = std::stringstream();
+			text << std::fixed << std::setprecision(0) << "Kinetic: " << kin << " J";
+			QString kinText = QString::fromStdString(text.str());
+
+			int textWidth1 = m.horizontalAdvance(potText);
+			int textWidth2 = m.horizontalAdvance(kinText);
+			int x1 = (w - textWidth1) / 4;
+			int x2 = (w - textWidth2) / 4 * 3;
+
+			p.drawLine(potX, h / 2, potX, h);
+			p.drawText(x1, h / 2, textWidth1, h / 2, Qt::AlignCenter | Qt::AlignVCenter, potText);
+			p.drawText(x2, h / 2, textWidth2, h / 2, Qt::AlignCenter | Qt::AlignVCenter, kinText);
+		}
+
+		p.drawLine(0, 0, w, 0);
+		p.drawLine(0, h / 2, w, h / 2);
+		p.drawLine(0, h, w, h);
+
+		drawTexture(&hud);
+	}
+
+	// Bottom HUD with FPS and UPS
+	{
+		glViewport(0, 0, w, h);
+
+		QImage hud(w, h, QImage::Format_RGBA8888);
+
+		// Background
+		hud.fill(Qt::transparent);
+
+		QPainter p(&hud);
+		p.setRenderHints(QPainter::Antialiasing);
+
+		// FPS
+		{
+			p.setPen(Qt::white);
+			auto font = p.font();
+			font.setPixelSize(15);
+			p.setFont(font);
+			fps->newFrame();
+			std::stringstream text;
+			text << "FPS: " << fps->current << "\n";
+			text << "UPS: " << simulation->ups->current;
+			p.drawText(0, 0, 100, h, Qt::AlignBottom | Qt::AlignLeft, QString::fromStdString(text.str()));
+		}
+		drawTexture(&hud);
+	}
+}
+
+void Overlay::resize(QSize newViewportSize, QRect newSimulationRect) {
+	viewportSize = newViewportSize;
+	simulationRect = newSimulationRect;
+}
+
+void Overlay::drawTexture(QImage *image) {
+	glBindVertexArray(VAO);
+	program->bind();
+
+	QOpenGLTexture texture(image->mirrored());
+	texture.bind();
+
+	glDrawElements(GL_TRIANGLES, 6, GL_UNSIGNED_INT, nullptr);
+}
+
+void Overlay::fetchEnergyLimit() {
+	energyLimit = simulation->kineticEnergy + simulation->potentialEnergy;
+}

src/Overlay.h

@@ -0,0 +1,29 @@
+#include <QRect>
+
+#include <QOpenGLExtraFunctions>
+
+class QOpenGLWidget;
+class FPS;
+class QOpenGLShaderProgram;
+class QOpenGLTexture;
+class Simulation;
+
+class Overlay : public QObject, protected QOpenGLExtraFunctions {
+	Q_OBJECT
+
+	FPS * fps;
+	QSize viewportSize;
+	QRect simulationRect;
+	QOpenGLShaderProgram * program;
+	GLuint VAO;
+	void drawTexture(QImage *image);
+	Simulation * simulation;
+	double energyLimit = 0;
+public slots:
+	void fetchEnergyLimit();
+public:
+	explicit Overlay(Simulation *);
+	void init();
+	void draw();
+	void resize(QSize newViewportSize, QRect newSimulationRect);
+};

src/Pendulum.cpp

@@ -7,9 +7,9 @@ Pendulum::Pendulum(const std::vector<double> &M,
 				   const std::vector<double> &L,
 				   QColor color, double startAngle) : M(M), L(L), color(color){
 
-	startAngle *= 3.141 / 180;
+	startAngle *= M_PI / 180;
 
-	Vector direction(-sin(startAngle), cos(startAngle));
+	Vector direction(-sin(startAngle), -cos(startAngle));
 	Vector currentPosition(0, 0);
 
 	for (int i = 0; i < M.size(); i++){
@@ -31,7 +31,7 @@ void Pendulum::update(double h, double g) {
 	for (int i = 0; i < X.size(); i++){
 
 		// explicit integration with gravity as external force
-		V[i] = V[i] + Vector(0, g * h);
+		V[i] = V[i] + Vector(0, -g * h);
 		Vector p2 = X[i] + V[i] * h;
 
 		// solve distance constraint
@@ -64,3 +64,20 @@ void Pendulum::update(double h, double g) {
 
 
 }
+
+double Pendulum::potentialEnergy(double gravity) const {
+	double total = 0;
+	double zeroLevel = 0;
+	for (int i = 0; i < X.size(); i++){
+		zeroLevel -= L[i];
+		total += M[i] * gravity * (X[i].y - zeroLevel);
+	}
+	return total;
+}
+
+double Pendulum::kineticEnergy() const {
+	double total = 0;
+	for (int i = 0; i < V.size(); i++)
+		total += M[i] * V[i].squaredLength();
+	return total / 2;
+}

src/Pendulum.h

@@ -12,6 +12,8 @@ public:
 					  const std::vector<double> &L,
 					  QColor color, double startAngle);
 	void update(double, double);
+	double potentialEnergy(double gravity) const;
+	double kineticEnergy() const;
 private:
 	friend class GLWidget;
 	std::vector<Vector> X, V;

src/Simulation.cpp

@@ -4,36 +4,47 @@
 #include <QThread>
 #include <omp.h>
 #include <iostream>
+#include "FPS.h"
 
 Simulation::Simulation() {
+	ups = new FPS;
+	ups->setUpdateInterval(100);
+
 	timer = new QTimer(this);
 	QTimer::connect(timer, &QTimer::timeout, this, &Simulation::update);
 	timer->setInterval(updateInterval);
 	timer->start();
-	lastUpdate = system_clock::now();
 };
 
 void Simulation::update() {
-	auto thisUpdate = system_clock::now();
-	auto ms = (int)duration_cast<milliseconds>(thisUpdate - lastUpdate).count();
-	lastUpdate = thisUpdate;
-
 	if (!isPlaying)
 		return;
 
-	double h = (timescale * updateInterval) / 1000;
+	ups->newFrame();
 
-	h /= substeps;
+	double h = (timescale * updateInterval) / 1000 / substeps;
 
 	pendulaMutex.lock();
 
+	double newPotentialEnergy = 0;
+	double newKineticEnergy = 0;
+
 	#pragma omp parallel for
 	for (int i = 0; i < pendula.size(); i++){ // NOLINT(*-loop-convert) // not ranged based for msvc
 		for (int k = 0; k < substeps; k++)
 			pendula[i]->update(h, gravity);
+		double localPotentialEnergy = pendula[i]->potentialEnergy(gravity);
+		double localKineticEnergy = pendula[i]->kineticEnergy();
+		#pragma omp atomic
+		newPotentialEnergy += localPotentialEnergy;
+		#pragma omp atomic
+		newKineticEnergy += localKineticEnergy;
 	}
 
-	emit positionChanged(&pendula);
+	potentialEnergy = newPotentialEnergy;
+	kineticEnergy = newKineticEnergy;
+
+	emit positionChanged();
 }
 
 void Simulation::clearPendula() {
@@ -47,7 +58,9 @@ void Simulation::clearPendula() {
 	pendula.clear();
 	pendula.shrink_to_fit();
 
-	emit layoutChanged(&pendula);
+	updateEnergy();
+
+	emit layoutChanged();
 }
 
 void Simulation::addPendula(const std::vector<Pendulum *> &add) {
@@ -56,6 +69,16 @@ void Simulation::addPendula(const std::vector<Pendulum *> &add) {
 	for (auto p : add)
 		pendula.push_back(p);
 
-	emit layoutChanged(&pendula);
+	updateEnergy();
+
+	emit layoutChanged();
+}
+
+void Simulation::updateEnergy() {
+	potentialEnergy = kineticEnergy = 0;
+	for (auto p : pendula){
+		potentialEnergy += p->potentialEnergy(gravity);
+		kineticEnergy += p->kineticEnergy();
+	}
 }
 

src/Simulation.h

@@ -8,6 +8,7 @@
 using namespace std::chrono;
 
 class QTimer;
+class FPS;
 
 class Simulation : public QObject {
 	Q_OBJECT
@@ -20,20 +21,24 @@ public:
 	double timescale {};
 	int substeps {};
 
+	double potentialEnergy = 0, kineticEnergy = 0;
+
 	bool isPlaying = false;
 
+	std::vector<Pendulum *> pendula;
+
 	std::mutex pendulaMutex;
+	FPS * ups;
 signals:
-	void layoutChanged(const std::vector<Pendulum *> *newPendula);
+	void layoutChanged();
-	void positionChanged(const std::vector<Pendulum *> *changedPendula);
+	void positionChanged();
 public slots:
 	void clearPendula();
 	void addPendula(const std::vector<Pendulum *> &add);
 private slots:
 	void update();
 private:
+	void updateEnergy();
 	QTimer * timer;
-	int updateInterval = 17;
+	int updateInterval = 16;
-	std::vector<Pendulum *> pendula;
-	time_point<system_clock> lastUpdate;
 };

src/Vector.cpp

@@ -29,3 +29,7 @@ Vector operator/(Vector v, double divisor){
 	return {v.x / divisor, v.y / divisor};
 }
 
+double Vector::squaredLength() const {
+	return x * x + y * y;
+}
+

src/Vector.h

@@ -3,6 +3,7 @@ struct Vector {
 	Vector(double x, double y);
 
 	double length() const;
+	double squaredLength() const;
 	void normalize();
 
 	friend Vector operator +(Vector lhs, Vector rhs);

src/main.cpp

@@ -11,6 +11,7 @@ int main(int argc, char* argv[]) {
 	QSurfaceFormat fmt;
 	fmt.setSamples(4);
 	fmt.setDepthBufferSize(32);
+	fmt.setSwapInterval(1);
 	fmt.setVersion(3, 3);
 	fmt.setProfile(QSurfaceFormat::CoreProfile);
 	QSurfaceFormat::setDefaultFormat(fmt);