/**************************************************************************
*
***************************************************************************/
private void Zoom(Rectangle window)
{
// don't bother zooming if the size is too small.
if (window.Height < 10 || window.Width < 10)
{
return;
}
// stretch zoom
using (Bitmap bitmap = new Bitmap(myPictureBox.Width, myPictureBox.Height, PixelFormat.Format32bppPArgb))
using (Graphics g = Graphics.FromImage((Image)bitmap))
{
g.DrawImage(_canvas, myPictureBox.ClientRectangle, window, GraphicsUnit.Pixel);
}
myPictureBox.Invalidate(true);
// HORRIBLE !!
// Need to use async/await
Application.DoEvents();
// calculate new window and render
aComplexNumber tlPoint = new aComplexNumber();
aComplexNumber brPoint = new aComplexNumber();
TransformCoord(window.X, window.Y, ref tlPoint);
TransformCoord(window.Right, window.Bottom, ref brPoint);
_complexWindow.MinX = tlPoint.Real;
_complexWindow.MaxX = brPoint.Real;
_complexWindow.MinY = brPoint.Imaginary;
_complexWindow.MaxY = tlPoint.Imaginary;
Render();
}
/**************************************************************************
* Test the given coordinate to see if it is inside the Mandelbrot set
*
* Returns 0 if it is part of the set.
* If not, returns the number of tries reached.
*
***************************************************************************/
private int TestForMandelbrotSetAsync(int x, int y)
{
int iterationsTaken = 0;
aComplexNumber Z = new aComplexNumber();
aComplexNumber C = new aComplexNumber();
// Set initial value of Zn to 0+0i
Z.Real = 0;
Z.Imaginary = 0;
// get the imaginary coordinate that is represented by our current position
TransformCoord(x, y, ref C);
// To test for divergence, we perform an iterative loop of the form:
// Zn+1 = Zn^2 + C
//
// If the magnitude of Z goes above 2, then it is within the Mandelbrot set.
double ZrSq = Z.Real * Z.Real;
double ZiSq = Z.Imaginary * Z.Imaginary;
for (iterationsTaken = 0; iterationsTaken < _complexWindow.MaxThreshold; iterationsTaken++)
{
/***********************************
* aComplexNumber Zn = Z.Squared() + C;
* if (Zn.IsDivergent())
* break;
* Z = Zn;
***********************************/
// optimisation of above code
// Test for divergence
// No need to do the square root for a little perf. increase.
if (ZrSq + ZiSq > 4.0)
{
break;
}
Z.Imaginary = Z.Real * Z.Imaginary;
Z.Imaginary += Z.Imaginary;
Z.Imaginary += C.Imaginary;
Z.Real = ZrSq - ZiSq + C.Real;
ZrSq = Z.Real * Z.Real;
ZiSq = Z.Imaginary * Z.Imaginary;
}
if (iterationsTaken >= _complexWindow.MaxThreshold)
{
return(0);
}
// Not inside the Mandelbrot set
return(iterationsTaken);
}
/**************************************************************************
* Handler for the mouse button up event
*
* Use this event to update our image if we have been zooming or panning.
***************************************************************************/
private void PictureBox_MouseUp(object sender, MouseEventArgs e)
{
if (e.Button == MouseButtons.Left)
{
if (_isZooming)
{
_isZooming = false;
Point endZoomPoint = new Point(e.X, e.Y);
// Call zoom function
Rectangle window = new Rectangle(
Math.Min(_startPoint.X, endZoomPoint.X),
Math.Min(_startPoint.Y, endZoomPoint.Y),
Math.Abs(_startPoint.X - endZoomPoint.X),
Math.Abs(_startPoint.Y - endZoomPoint.Y));
Zoom(window);
}
else if (_isPanning)
{
_isPanning = false;
Point endPoint = new Point(e.X, e.Y);
_panninggrapics?.Dispose();
_panninggrapics = null;
// calculate distance moved on each axis.
aComplexNumber start = new aComplexNumber();
aComplexNumber end = new aComplexNumber();
TransformCoord(_startPoint.X, _startPoint.Y, ref start);
TransformCoord(endPoint.X, endPoint.Y, ref end);
double deltaX = end.Real - start.Real;
double deltaY = end.Imaginary - start.Imaginary;
_complexWindow.MinX -= deltaX;
_complexWindow.MaxX -= deltaX;
_complexWindow.MinY -= deltaY;
_complexWindow.MaxY -= deltaY;
using (Bitmap tempbitmap = (Bitmap)_canvas.Clone())
using (Graphics g = Graphics.FromImage(_canvas))
{
GraphicsUnit gu = GraphicsUnit.Pixel;
g.FillRectangle(new SolidBrush(Color.SeaGreen), _canvas.GetBounds(ref gu));
g.DrawImage(tempbitmap, (endPoint.X - _startPoint.X), (endPoint.Y - _startPoint.Y));
}
Render();
}
}
}
/**************************************************************************
* Handles the mouse movement event
*
* This handler has a few tasks.
* . Handles image movement, if we are panning
* . Updates zoom coordinates, if we are zooming in.
*
***************************************************************************/
private void PictureBox_MouseMove(object sender, MouseEventArgs e)
{
// If we are still rendering our image, then do no continue
if (_isRendering)
{
return;
}
if (_isZooming)
{
Point endZoomPoint = new Point(e.X, e.Y);
_ZoomWindow = new Rectangle(
Math.Min(_startPoint.X, endZoomPoint.X),
Math.Min(_startPoint.Y, endZoomPoint.Y),
Math.Abs(_startPoint.X - endZoomPoint.X),
Math.Abs(_startPoint.Y - endZoomPoint.Y));
myPictureBox.Invalidate();
return;
}
// we are panning our image, so move to the new position
if (_isPanning)
{
Point endPoint = new Point(e.X, e.Y);
_panninggrapics.FillRectangle(new SolidBrush(Color.DimGray), myPictureBox.ClientRectangle);
_panninggrapics.DrawImage(_canvas, (endPoint.X - _startPoint.X), (endPoint.Y - _startPoint.Y));
return;
}
aComplexNumber C = new aComplexNumber();
TransformCoord(e.X, e.Y, ref C);
// output the coordinates to the screen
statusLabel.Text = $"x: {C.Real:0.####} y:{C.Imaginary:0.####}";
}
public aComplexNumber(aComplexNumber c)
{
_real = c._real;
_imaginary = c._imaginary;
}
/**************************************************************************
* Maps the given screen position to the complex plane being rendered
***************************************************************************/
private void TransformCoord(int x, int y, ref aComplexNumber complexPoint)
{
complexPoint.Real = ((x * (_complexWindow.MaxX - _complexWindow.MinX)) / myPictureBox.Width) + _complexWindow.MinX;
complexPoint.Imaginary = (((myPictureBox.Height - y) * (_complexWindow.MaxY - _complexWindow.MinY)) / myPictureBox.Height) + _complexWindow.MinY;
}
/**************************************************************************
* Transform the given screen coordinate to the represented complex number
***************************************************************************/
private void TransformCoord(Point screenPoint, ref aComplexNumber complexPoint)
{
TransformCoord(screenPoint.X, screenPoint.Y, ref complexPoint);
}
