feat: correct elliptical orbital motion

src/main.cpp

@@ -51,8 +51,8 @@ int main()
     GLuint litProgram = compileShaderProgram("./frag_lit.glsl");
     GLuint unlitProgram = compileShaderProgram("./frag_unlit.glsl");
 
-    Icosphere planet(0.3, 3, litProgram);
+    Icosphere planet(0.2, 3, litProgram);
-    Icosphere orbiter(0.1, 2, litProgram);
+    Icosphere orbiter(0.07, 2, litProgram);
     Orbit orbit(100);
 
     // Main loop
@@ -63,7 +63,7 @@ int main()
 
         float time = glfwGetTime();
 
-        glm::vec3 pos = orbit.getPosition(time * .3);
+        glm::vec3 pos = orbit.getPosition(time);
         orbiter.setPosition(pos);
 
         // Render lit objects

src/orbit.cpp

@@ -7,14 +7,14 @@ Orbit::Orbit(int vertexCount) :
     _keplerianElements(std::vector<float>(6))
 {
     _keplerianElements[astro::semiMajorAxisIndex] = .75;
-    _keplerianElements[astro::eccentricityIndex] = .3;
+    _keplerianElements[astro::eccentricityIndex] = .5;
     _keplerianElements[astro::inclinationIndex] = _pi / 2.0 + 1;
     _keplerianElements[astro::argumentOfPeriapsisIndex] = 2.0;
     _keplerianElements[astro::longitudeOfAscendingNodeIndex] = 0;
 
     for (int i = 0; i < vertexCount; i++)
     {
-        float t = (float)i / (float)vertexCount;
+        float t = (float)i / (float)vertexCount * 2.0 * _pi;
         glm::vec3 pos = getPosition(t);
 
         _vertices.push_back(pos.x);
@@ -40,12 +40,23 @@ Orbit::Orbit(int vertexCount) :
 
 // Interpolate a position around the orbit.
 // t is in range 0..1 and wraps.
-glm::vec3 Orbit::getPosition(float t)
+glm::vec3 Orbit::getPosition(const float meanAnomaly)
 {
-    float a = t * 2.0 * _pi;
+    // Get eccentric anomaly from elliptical mean anomaly
+    const float eccentricity = _keplerianElements[astro::eccentricityIndex];
+    float eccentricAnomaly = astro::convertEllipticalMeanAnomalyToEccentricAnomaly(
+        eccentricity,
+        meanAnomaly,
+        (float)10e-3,
+        100);
+
+    // Get true anomaly from eccentric anomaly
+    float trueAnomaly = astro::convertEccentricAnomalyToTrueAnomaly(
+        eccentricAnomaly,
+        eccentricity);
 
     std::vector<float> kepler(_keplerianElements);
-    kepler[astro::trueAnomalyIndex] = a;
+    kepler[astro::trueAnomalyIndex] = trueAnomaly;
 
     std::vector<float> cartesian = astro::convertKeplerianToCartesianElements(kepler, 1.0);
     return glm::vec3(

src/orbit.hpp

@@ -11,7 +11,7 @@ public:
     Orbit(int vertexCount);
     void render();
 
-    glm::vec3 getPosition(float t);
+    glm::vec3 getPosition(const float meanAnomaly);
 
     ~Orbit(); 
 private: