/* METHODS */
//we will plot the parameter along the horizontal axis and the orbit values along the vertical.
public static List <Vector3> GetOrbit(QuadraticFunction quadraticFunction, float muMin, float muMax, int steps, float orbitPoint, int minOrbits, int maxOrbits, float scale)
{
List <Vector3> coordinates = new List <Vector3>();
float dmu = (muMax - muMin) / steps;
//loop through mu's:
for (float mu = muMin; mu < muMax; mu += dmu)
{
float orbitValue = orbitPoint;
quadraticFunction.mu = mu;
//loop through number of orbits to graph:
for (int i = 0; i < maxOrbits; i++)
{
float currentOrbit = quadraticFunction.Image(orbitValue);
if (i > minOrbits)
{
coordinates.Add(new Vector3(scale * mu, scale * currentOrbit, quadraticFunction.position.Z));
}
orbitValue = currentOrbit;
}
}
return(coordinates);
}
private Environment[] GetScholarsDayEnvironments()
{
Environment[] scholarsDayEnvironments = new Environment[23];
//set environments:
Vector3 graphicalAnalysisPosition = new Vector3(0, 0, -10);
Vector3 lorenzPosition = new Vector3(0, -29, -55);
Vector3 white = new Vector3(1, 1, 1);
Vector3 black = new Vector3(0, 0, 0);
int numberOfNodes = 1000;
float nodeVelocity = 0.03f;
int pointSize = 0;
int functionPointSize = 1;
float scale = 5;
//first environment: demonstrate how graphical analysis is a great representation of iterating functions.
CosineFunction cosineFunction = new CosineFunction(-6f, 6f, 1000, scale, graphicalAnalysisPosition, white, functionPointSize, 1);
scholarsDayEnvironments[0] = LoadGraphicalAnalysis(cosineFunction, scale, 1000, nodeVelocity, false, pointSize);
//second through ninth environments: quadratic function. change the mu values around.
//QuadraticFunction quadraticFunction;
QuadraticFunction quadraticFunction;
QuadraticSquareFunction quadraticSquareFunction;
float startTime = 0;
float finalTime = 1;
int steps = 1000;
//change mu around:
scholarsDayEnvironments[1] = LoadGraphicalAnalysis(quadraticFunction = new QuadraticFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 1f), scale, numberOfNodes, nodeVelocity, false, pointSize);
scholarsDayEnvironments[2] = LoadGraphicalAnalysis(quadraticFunction = new QuadraticFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 1.5f), scale, numberOfNodes, nodeVelocity, false, pointSize);
scholarsDayEnvironments[3] = LoadGraphicalAnalysis(quadraticFunction = new QuadraticFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 2), scale, numberOfNodes, nodeVelocity, false, pointSize);
scholarsDayEnvironments[4] = LoadGraphicalAnalysis(quadraticFunction = new QuadraticFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 2.5f), scale, numberOfNodes, nodeVelocity, false, pointSize);
scholarsDayEnvironments[5] = LoadGraphicalAnalysis(quadraticFunction = new QuadraticFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 3), scale, numberOfNodes, nodeVelocity, false, pointSize);
scholarsDayEnvironments[6] = LoadGraphicalAnalysis(quadraticFunction = new QuadraticFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 3.2f), scale, numberOfNodes, nodeVelocity, false, pointSize);
scholarsDayEnvironments[7] = LoadGraphicalAnalysis(quadraticFunction = new QuadraticFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 3.5f), scale, numberOfNodes, nodeVelocity, false, pointSize);
scholarsDayEnvironments[8] = LoadGraphicalAnalysis(quadraticFunction = new QuadraticFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 3.839f), scale, numberOfNodes, nodeVelocity, false, pointSize);
scholarsDayEnvironments[9] = LoadGraphicalAnalysis(quadraticFunction = new QuadraticFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 4), scale, numberOfNodes, nodeVelocity, false, pointSize);
scholarsDayEnvironments[14] = LoadGraphicalAnalysis(quadraticSquareFunction = new QuadraticSquareFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 1), scale, numberOfNodes, nodeVelocity, false, pointSize);
scholarsDayEnvironments[15] = LoadGraphicalAnalysis(quadraticSquareFunction = new QuadraticSquareFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 1.5f), scale, numberOfNodes, nodeVelocity, false, pointSize);
scholarsDayEnvironments[16] = LoadGraphicalAnalysis(quadraticSquareFunction = new QuadraticSquareFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 2), scale, numberOfNodes, nodeVelocity, false, pointSize);
scholarsDayEnvironments[17] = LoadGraphicalAnalysis(quadraticSquareFunction = new QuadraticSquareFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 2.5f), scale, numberOfNodes, nodeVelocity, false, pointSize);
scholarsDayEnvironments[18] = LoadGraphicalAnalysis(quadraticSquareFunction = new QuadraticSquareFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 3), scale, numberOfNodes, nodeVelocity, false, pointSize);
scholarsDayEnvironments[19] = LoadGraphicalAnalysis(quadraticSquareFunction = new QuadraticSquareFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 3.2f), scale, numberOfNodes, nodeVelocity, false, pointSize);
scholarsDayEnvironments[20] = LoadGraphicalAnalysis(quadraticSquareFunction = new QuadraticSquareFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 3.5f), scale, numberOfNodes, nodeVelocity, false, pointSize);
scholarsDayEnvironments[21] = LoadGraphicalAnalysis(quadraticSquareFunction = new QuadraticSquareFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 3.839f), scale, numberOfNodes, nodeVelocity, false, pointSize);
scholarsDayEnvironments[22] = LoadGraphicalAnalysis(quadraticSquareFunction = new QuadraticSquareFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 4.5f), scale, numberOfNodes, nodeVelocity, false, pointSize);
//watch points escape without the chaos tracker:
scholarsDayEnvironments[10] = LoadGraphicalAnalysis(quadraticFunction = new QuadraticFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 5), scale, 1000, nodeVelocity, false, pointSize);
//watch points escape with the chaos tracker:
scholarsDayEnvironments[11] = LoadGraphicalAnalysis(quadraticFunction = new QuadraticFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 5), scale, 10000, nodeVelocity, true, pointSize);
//Mandelbrot set:
scholarsDayEnvironments[12] = LoadMandelbrotFractal();
//Lorenz:
//scholarsDayEnvironments[13] = LoadLorenzDataSet(lorenzPosition, 10, 10, 10, 0, 100, 30000, 10, 30, 8f / 3f);
//scholarsDayEnvironments[13] = LoadDoublePendulumDataSet(new Vector3(0, 0, -10), 0.5f, 0.5f, 2, 1, 0, 10, 1000, 1, 1, 2, 2);
//scholarsDayEnvironments[11] = LoadGraphicalAnalysis(quadraticFunction = new QuadraticFunction(startTime, finalTime, steps, scale, graphicalAnalysisPosition, white, functionPointSize, 4), scale, numberOfNodes, nodeVelocity, false, pointSize);
scholarsDayEnvironments[13] = LoadBifurcationDiagramDataSet(new Vector3(-3, 0, -1), new Vector3(0, 0, 0), new QuadraticFunction(0, 1, 1000, 5, new Vector3(-3, 0, -1), new Vector3(0, 0, 0), 1, 1), 1f, 4f, 10000, 0.75f, 400, 500, 1);
return(scholarsDayEnvironments);
}
private Environment LoadBifurcationDiagramDataSet(Vector3 position, Vector3 color, QuadraticFunction quadraticFunction, float muMin, float muMax, int steps, float orbitPoint, int minOrbits, int maxOrbits, float scale)
{
return(new DataSet(loader, position, color, PrimitiveType.Points, Mathematics.BifurcationDiagram.GetOrbit(quadraticFunction, muMin, muMax, steps, orbitPoint, minOrbits, maxOrbits, scale)));
}
