public ComputedFractalValues ReturnComputedFractalValues(RectangleInPlane fractalRectangleIn, int xMaxIn, int yMaxIn, IList <FractalColorValue> fractalColorValuesIn, System.Windows.Forms.ProgressBar fractalProgressIn)
{
if (fractalColorValuesIn.Count < NumberOfColorUsed)
{
throw new FractalObserverException("Fractal PythagorasTree needs more colors that are available in the input parameter fractalColorValuesIn!");
}
ComputedFractalValues aComputedFractalValuesValues = new ComputedFractalValues();
for (int aCurrentYPos = 0; aCurrentYPos < yMaxIn; aCurrentYPos++)
{
fractalProgressIn.Value = (int)(100.0 * ((double)aCurrentYPos / (double)yMaxIn));
for (int aCurrentXPos = 0; aCurrentXPos < xMaxIn; aCurrentXPos++)
{
int tempValue = 0;
ComplexNumber c = new ComplexNumber();
c.Re = fractalRectangleIn.StartX + Math.Abs(fractalRectangleIn.StartX - fractalRectangleIn.EndX) * ((double)aCurrentXPos / (double)xMaxIn);
c.Im = fractalRectangleIn.StartY + Math.Abs(fractalRectangleIn.StartY - fractalRectangleIn.EndY) * ((double)aCurrentYPos / (double)yMaxIn);
int n = 0;
myZValues[n].Re = 0.0;
myZValues[n].Im = 0.0;
// computation of value for function z2+c, if it converges (if it is bounded) the point is part of mandelbrot set
do
{
n++;
myZValues[n] = ComplexOperations.Add(Equation.ComplexFunctionValue(myZValues[n - 1]), c);
} while (((Math.Abs(myZValues[n].Re) < myMaximumValueForConvergation) && (Math.Abs(myZValues[n].Im) < myMaximumValueForConvergation)) && (n < (MaximumNumberOfIterations - 1)));
tempValue = n;
ComputedFractalValue aCFValue = new ComputedFractalValue();
FractalColorValue aFractalColorValue = ReturnColor(tempValue, fractalColorValuesIn);
aCFValue.ColorValue = aFractalColorValue;
aCFValue.AddComputedPoint(new System.Drawing.Point(aCurrentXPos, aCurrentYPos));
aCFValue.TypeOfShape = TypesOfShape.Point;
aCFValue.UsedTypeOfCoordinateSystem = TypesOfCoordinateSystem.Screen;
aComputedFractalValuesValues.AddComputedFractalValue(aCFValue);
}
}
return(aComputedFractalValuesValues);
}
// recursive method - this method computes the points of snowflake
private void CreateNewCurveAndAddItToCFV(PointInPlane startPointIn, PointInPlane endPointIn, IList <FractalColorValue> fractalColorValuesIn, ref ComputedFractalValue cfvIn, int currentIterationIn)
{
if (currentIterationIn < (MaximumNumberOfIterations - 1))
{
const double aAngle = Math.PI / 3.0; // angle of 60 degrees - equilateral triangle
PointInPlane aOneThirdPoint = new PointInPlane(startPointIn.x + (endPointIn.x - startPointIn.x) / 3.0, startPointIn.y + (endPointIn.y - startPointIn.y) / 3.0);
PointInPlane aTwoThirdPoint = new PointInPlane(startPointIn.x + (endPointIn.x - startPointIn.x) / 1.5, startPointIn.y + (endPointIn.y - startPointIn.y) / 1.5);
PointInPlane aRotatedLinePoint = RotateLine(aOneThirdPoint, aTwoThirdPoint, aAngle);
CreateNewCurveAndAddItToCFV(startPointIn, aOneThirdPoint, fractalColorValuesIn, ref cfvIn, currentIterationIn + 1);
CreateNewCurveAndAddItToCFV(aOneThirdPoint, aRotatedLinePoint, fractalColorValuesIn, ref cfvIn, currentIterationIn + 1);
CreateNewCurveAndAddItToCFV(aRotatedLinePoint, aTwoThirdPoint, fractalColorValuesIn, ref cfvIn, currentIterationIn + 1);
CreateNewCurveAndAddItToCFV(aTwoThirdPoint, endPointIn, fractalColorValuesIn, ref cfvIn, currentIterationIn + 1);
}
else
{
cfvIn.AddComputedPoint(startPointIn);
cfvIn.AddComputedPoint(endPointIn);
}
}
// recursive method - here are computed the squares of pythagoras tree
private void CreateSquare(PointInPlane[] rectanglePointsIn, IList <FractalColorValue> fractalColorValuesIn /*, SquareOrientation squareOrientationIn*/, ref ComputedFractalValues cfvIn, int currentIterationIn)
{
if (rectanglePointsIn.Length < 4)
{
throw new FractalObserverException("The input parameter rectanglePointsIn in Methode CreateSquare must have at least four values (for each vertex one) !");
}
ComputedFractalValue aCFValue = new ComputedFractalValue();
FractalColorValue aFractalColorValue = ReturnColor(currentIterationIn, fractalColorValuesIn);
aCFValue.ColorValue = aFractalColorValue;
aCFValue.TypeOfShape = TypesOfShape.Rectangle;
aCFValue.UsedTypeOfCoordinateSystem = TypesOfCoordinateSystem.Plane;
aCFValue.AddComputedPoint(rectanglePointsIn[0]);
aCFValue.AddComputedPoint(rectanglePointsIn[1]);
aCFValue.AddComputedPoint(rectanglePointsIn[2]);
aCFValue.AddComputedPoint(rectanglePointsIn[3]);
cfvIn.AddComputedFractalValue(aCFValue);
if (currentIterationIn < MaximumNumberOfIterations)
{
double aScalingCoefficient = 1.0 / Math.Sqrt(2.0);
double aRotationAngle = Math.PI / 4.0;
{ // right rectangle values computed
PointInPlane[] aNewRightRectangle = new PointInPlane[4];
PointInPlane aMovingVector = rectanglePointsIn[2] - rectanglePointsIn[1];
// scale to new rectangle
aNewRightRectangle[1] = rectanglePointsIn[1];
aNewRightRectangle[0] = PointInPlane.ScalePoint(rectanglePointsIn[1], rectanglePointsIn[0], aScalingCoefficient);
aNewRightRectangle[2] = PointInPlane.ScalePoint(rectanglePointsIn[1], rectanglePointsIn[2], aScalingCoefficient);
aNewRightRectangle[3] = PointInPlane.ScalePoint(rectanglePointsIn[1], rectanglePointsIn[3], aScalingCoefficient);
// rotate to new rectangle
aNewRightRectangle[0] = PointInPlane.RotatePoint(aNewRightRectangle[0], aNewRightRectangle[1], aRotationAngle);
aNewRightRectangle[1] = PointInPlane.RotatePoint(aNewRightRectangle[1], aNewRightRectangle[1], aRotationAngle);
aNewRightRectangle[2] = PointInPlane.RotatePoint(aNewRightRectangle[2], aNewRightRectangle[1], aRotationAngle);
aNewRightRectangle[3] = PointInPlane.RotatePoint(aNewRightRectangle[3], aNewRightRectangle[1], aRotationAngle);
// move to new rectangle position
aNewRightRectangle[0] = PointInPlane.MovePoint(aNewRightRectangle[0], aMovingVector);
aNewRightRectangle[1] = PointInPlane.MovePoint(aNewRightRectangle[1], aMovingVector);
aNewRightRectangle[2] = PointInPlane.MovePoint(aNewRightRectangle[2], aMovingVector);
aNewRightRectangle[3] = PointInPlane.MovePoint(aNewRightRectangle[3], aMovingVector);
CreateSquare(aNewRightRectangle, fractalColorValuesIn, ref cfvIn, currentIterationIn + 1);
}
{ // left rectangle values computed
aRotationAngle = -Math.PI / 4.0;
PointInPlane[] aNewLeftRectangle = new PointInPlane[4];
PointInPlane aMovingVector = rectanglePointsIn[3] - rectanglePointsIn[0];
// scale to new rectangle
aNewLeftRectangle[0] = rectanglePointsIn[0];
aNewLeftRectangle[1] = PointInPlane.ScalePoint(rectanglePointsIn[0], rectanglePointsIn[1], aScalingCoefficient);
aNewLeftRectangle[2] = PointInPlane.ScalePoint(rectanglePointsIn[0], rectanglePointsIn[2], aScalingCoefficient);
aNewLeftRectangle[3] = PointInPlane.ScalePoint(rectanglePointsIn[0], rectanglePointsIn[3], aScalingCoefficient);
// rotate to new rectangle
aNewLeftRectangle[0] = PointInPlane.RotatePoint(aNewLeftRectangle[0], aNewLeftRectangle[0], aRotationAngle);
aNewLeftRectangle[1] = PointInPlane.RotatePoint(aNewLeftRectangle[1], aNewLeftRectangle[0], aRotationAngle);
aNewLeftRectangle[2] = PointInPlane.RotatePoint(aNewLeftRectangle[2], aNewLeftRectangle[0], aRotationAngle);
aNewLeftRectangle[3] = PointInPlane.RotatePoint(aNewLeftRectangle[3], aNewLeftRectangle[0], aRotationAngle);
// move to new rectangle position
aNewLeftRectangle[0] = PointInPlane.MovePoint(aNewLeftRectangle[0], aMovingVector);
aNewLeftRectangle[1] = PointInPlane.MovePoint(aNewLeftRectangle[1], aMovingVector);
aNewLeftRectangle[2] = PointInPlane.MovePoint(aNewLeftRectangle[2], aMovingVector);
aNewLeftRectangle[3] = PointInPlane.MovePoint(aNewLeftRectangle[3], aMovingVector);
CreateSquare(aNewLeftRectangle, fractalColorValuesIn, ref cfvIn, currentIterationIn + 1);
}
}
}
public ComputedFractalValues ReturnComputedFractalValues(RectangleInPlane fractalRectangleIn, int xMaxIn, int yMaxIn, IList <FractalColorValue> fractalColorValuesIn, System.Windows.Forms.ProgressBar fractalProgressIn)
{
if (fractalColorValuesIn.Count < NumberOfColorUsed)
{
throw new FractalObserverException("Fractal PythagorasTree needs more colors that are available in the input parameter fractalColorValuesIn!");
}
ComputedFractalValues aComputedFractalValues = new ComputedFractalValues();
myZRoots.Clear();
for (int aCurrentYPos = 0; aCurrentYPos < yMaxIn; aCurrentYPos++)
{
fractalProgressIn.Value = (int)(100.0 * ((double)aCurrentYPos / (double)yMaxIn));
for (int aCurrentXPos = 0; aCurrentXPos < xMaxIn; aCurrentXPos++)
{
int tempRoot = 0;
int tempValue = 0;
int n = 0;
// initial values
myZValues[n].Re = fractalRectangleIn.StartX + Math.Abs(fractalRectangleIn.StartX - fractalRectangleIn.EndX) * ((double)aCurrentXPos / (double)xMaxIn);
myZValues[n].Im = fractalRectangleIn.StartY + Math.Abs(fractalRectangleIn.StartY - fractalRectangleIn.EndY) * ((double)aCurrentYPos / (double)yMaxIn);
// computation of next values until the maximum iteration count or until the conditions are met
do
{
n++;
myZValues[n] = ComplexOperations.Substract(myZValues[n - 1], ComplexOperations.Divide(Equation.ComplexFunctionValue(myZValues[n - 1]), Equation.ComplexFunctionDerivativeValue(myZValues[n - 1])));
} while (((Math.Abs(myZValues[n].Re - myZValues[n - 1].Re) > myTreshold) || (Math.Abs(myZValues[n].Im - myZValues[n - 1].Im) > myTreshold)) && (n < (MaximumNumberOfIterations - 1)));
ComputedFractalValue aCFValue = null;
FractalColorValue aFractalColorValue;
// if the solution did not converge to root, then return zero values
if (n >= (MaximumNumberOfIterations - 1) || double.IsNaN(myZValues[n].Re) || double.IsNaN(myZValues[n].Im))
{
aCFValue = new ComputedFractalValue();
aFractalColorValue = ReturnColor(tempRoot, tempValue, fractalColorValuesIn);
aCFValue.ColorValue = aFractalColorValue;
aCFValue.AddComputedPoint(new System.Drawing.Point(aCurrentXPos, aCurrentYPos));
aCFValue.TypeOfShape = TypesOfShape.Point;
aCFValue.UsedTypeOfCoordinateSystem = TypesOfCoordinateSystem.Screen;
aComputedFractalValues.AddComputedFractalValue(aCFValue);
continue;
}
bool aNewRoot = true;
int aRootNumber = 0;
// find out if the root is new until now, or if the current root was found already
for (int i = 0; i < myZRoots.Count; i++)
{
if ((Math.Abs(myZRoots[i].Re - myZValues[n].Re) < myTreshold) && (Math.Abs(myZRoots[i].Im - myZValues[n].Im) < myTreshold))
{
aNewRoot = false;
aRootNumber = i;
break;
}
}
// if this root is new until now, add new item to myZRoots List
if (aNewRoot)
{
ComplexNumber aComplexRoot = new ComplexNumber();
aComplexRoot.Re = myZValues[n].Re;
aComplexRoot.Im = myZValues[n].Im;
myZRoots.Add(aComplexRoot);
aRootNumber = myZRoots.Count - 1;
}
// sets the computed values for this pixel to return structure and return it
tempValue = n;
if (aRootNumber == 0)
{
tempRoot = 1;
}
else if (aRootNumber == 1)
{
tempRoot = 2;
}
else if (aRootNumber == 2)
{
tempRoot = 3;
}
else
{
throw new FractalObserverException("Error occured during computation of fractal, wrong number of roots was found!");
}
// storing of output of computation
aCFValue = new ComputedFractalValue();
aFractalColorValue = ReturnColor(tempRoot, tempValue, fractalColorValuesIn);
aCFValue.ColorValue = aFractalColorValue;
aCFValue.AddComputedPoint(new System.Drawing.Point(aCurrentXPos, aCurrentYPos));
aCFValue.TypeOfShape = TypesOfShape.Point;
aCFValue.UsedTypeOfCoordinateSystem = TypesOfCoordinateSystem.Screen;
aComputedFractalValues.AddComputedFractalValue(aCFValue);
}
}
return(aComputedFractalValues);
}