/// <summary>
/// Draws a line from (-1, 1) to (1, 1) (transformed according to transform) as the base unit.
/// </summary>
/// <param name="transform">Coordinate transform to apply</param>
/// <param name="image">Image upon which to render the line</param>
/// <param name="color">Color to use</param>
/// <param name="secondaryColor">Color to render onto auxilliary image (not used)</param>
public static void renderLine(Matrix <double> transform, DirectBitmap image, int color, int secondaryColor)
{
Vector <double> pointA = DenseVector.OfArray(new double[] { -1.0, 1.0, 1.0 });
Vector <double> pointB = DenseVector.OfArray(new double[] { 1.0, 1.0, 1.0 });
Vector <double> pointAT = transform * pointA;
Vector <double> pointBT = transform * pointB;
ImProc.DrawLine(pointAT[0] / pointAT[2], pointAT[1] / pointAT[2], pointBT[0] / pointBT[2], pointBT[1] / pointBT[2], color, image);
}
/// <summary>
/// Renders the primary spirals of the fractal (transformed according to transform) as the base unit.
/// NOTE: This will only render the spirals correctly if the transform is a product of
/// rotations, translations and scalings (must scale both coordinates uniformly)
/// </summary>
/// <param name="transform">Coordinate transform to apply</param>
/// <param name="image">Image upon which to render the spirals</param>
/// <param name="color">Color to use</param>
/// <param name="secondaryColor">Color to render onto auxilliary image (not used)</param>
public static void renderPrimarySpirals(Matrix <double> transform, DirectBitmap image, int color, int secondaryColor)
{
Vector <double> pointA = DenseVector.OfArray(new double[] { -1.0, 1.0, 1.0 });
Vector <double> pointB = DenseVector.OfArray(new double[] { 1.0, 1.0, 1.0 });
Vector <double> pointAT = transform * pointA;
Vector <double> pointBT = transform * pointB;
double scaleFactor = Math.Sqrt(transform.SubMatrix(0, 2, 0, 2).Determinant());
Vector <double> xBasis = DenseVector.OfArray(new double[] { 1.0, 0.0, 0.0 }); // make 3rd coordinate zero so translation is ignored
Vector <double> xBasisT = transform * xBasis;
double theta = Math.Atan2(xBasisT[1], xBasisT[0]);
ImProc.DrawSpiral(pointAT[0] / pointAT[2], pointAT[1] / pointAT[2], theta + Math.PI / 2, scaleFactor * 1.0 / 3.0, 6 * Math.PI, Math.PI / 2, Math.PI / 512, 1.0 / 16.0, color, image);
ImProc.DrawSpiral(pointBT[0] / pointBT[2], pointBT[1] / pointBT[2], theta - Math.PI / 2, scaleFactor * 2.0 / 3.0, 6 * Math.PI, Math.PI / 2, Math.PI / 512, 1.0 / 16.0, color, image);
}
/// <summary>
/// Renders the secondary spirals of the fractal in blue (transformed according to transform) as the base unit.
/// NOTE: This will only render the spirals correctly if the transform is a product of
/// rotations, translations and scalings (must scale both coordinates uniformly)
/// </summary>
/// <param name="transform">Coordinate transform to apply</param>
/// <param name="image">Image upon which to render the spirals</param>
/// <param name="color">Color to use</param>
/// <param name="color">Color to use</param>
/// <param name="secondaryColor">Color to render onto auxilliary image</param>
public void renderSecondarySpirals(Matrix <double> transform, DirectBitmap image, int color, int secondaryColor)
{
Vector <double> origin = DenseVector.OfArray(new double[] { 0.0, 0.0, 1.0 });
Vector <double> originT = transform * origin;
// NOTE: Second spiral originating at pointB is not strictly necessary
// (it will be constructed as a copy in another iteration). We only include
// it so we can extend the theta bounds farther than they would otherwise go).
Vector <double> pointB = DenseVector.OfArray(new double[] { -0.5, 0.5, 1.0 });
Vector <double> pointBT = transform * pointB;
double scaleFactor = Math.Sqrt(transform.SubMatrix(0, 2, 0, 2).Determinant());
Vector <double> xBasis = DenseVector.OfArray(new double[] { 1.0, 0.0, 0.0 }); // make 3rd coordinate zero so translation is ignored
Vector <double> xBasisT = transform * xBasis;
double theta = Math.Atan2(xBasisT[1], xBasisT[0]);
// Suppress rendering if the origin is not a boundary pixel of the dragon fractal
bool render = true;
if (null != ReferenceImage)
{
int x = (int)(originT[0] / originT[2] + 0.5);
int y = (int)(originT[1] / originT[2] + 0.5);
if (x >= 0 && x < ReferenceImage.Width && y >= 0 && y < ReferenceImage.Height)
{
if ((ReferenceImage.Bits[ReferenceImage.Width * y + x] & 0x00ffffff) == 0)
{
render = false;
}
}
}
if (render)
{
double thetaPlusSpan, thetaMinusSpan;
ImProc.DrawSpiral(originT[0] / originT[2], originT[1] / originT[2], theta + Math.PI, scaleFactor * 1.0 / 4.0, Math.PI / 512, 1.0 / 16.0, color, image, out thetaPlusSpan, out thetaMinusSpan);
if (null != AuxImage && (thetaMinusSpan > 0 || thetaPlusSpan > 0))
{
ImProc.DrawThickSpiral(originT[0] / originT[2], originT[1] / originT[2], theta + Math.PI, scaleFactor * 1.0 / 4.0, thetaPlusSpan, thetaMinusSpan, Math.PI / 512, 1.0 / 16.0, 0.1, secondaryColor, AuxImage);
}
}
}
static void Main(string[] args)
{
string OUTPUT_DIRECTORY = @"C:\Users\Dianna2\data\DragonFractal";
Directory.CreateDirectory(OUTPUT_DIRECTORY);
double base_size = (512.0 / 45.0); // base size is approximately 11.378 inches, fractal will be approximately 3 * base_size by 2 * base_size.
double subImageWidth = 9.0; // width of sub-images in inches
double subImageHeight = 6.5; // height of sub-images in inches
int previewSF = 16; // Scale factor to use between the initial low-res preview and the final rull-res result. Must be a power of 2.
double[] toolRadii = new double[] { 1 / 32.0, 1 / 16.0, 1 / 8.0, 1 / 4.0 }; // radii of the tools we have available in inches, ordered from smallest to largest
const int N_ITER_PREVIEW = 18;
const int N_ITER_FINAL = 26;
const int N_ITER_SECONDARY_PREVIEW = 10;
const int N_ITER_SECONDARY_FINAL = 14;
// Iterated function system defining the dragon fractal
Fractal fractal = new Fractal();
fractal.IFS = new List <Matrix <double> >();
var Translate = DenseMatrix.OfArray(new double[, ] {
{ 1, 0, 1 }, { 0, 1, -1 }, { 0, 0, 1 }
});
var Scale = DenseMatrix.OfArray(new double[, ] {
{ Math.Sqrt(0.5), 0, 0 }, { 0, Math.Sqrt(0.5), 0 }, { 0, 0, 1 }
});
var Rot45 = DenseMatrix.OfArray(new double[, ] {
{ Math.Cos(Math.PI / 4), -Math.Sin(Math.PI / 4), 0 }, { Math.Sin(Math.PI / 4), Math.Cos(Math.PI / 4), 0 }, { 0, 0, 1 }
});
var Rot135 = DenseMatrix.OfArray(new double[, ] {
{ Math.Cos(3 * Math.PI / 4), -Math.Sin(3 * Math.PI / 4), 0 }, { Math.Sin(3 * Math.PI / 4), Math.Cos(3 * Math.PI / 4), 0 }, { 0, 0, 1 }
});
fractal.IFS.Add(Rot45 * Scale * Translate);
fractal.IFS.Add(Rot135 * Scale * Translate);
// x and y coordinates of the coffee table boundary polygon
double[] xCoords = null, yCoords = null;
// x and y coordinates of the (estimated) resin boundary polygon
double[] xCoordsResin = null, yCoordsResin = null;
for (int bigIter = 0; bigIter < 2; ++bigIter)
{
int sf = (0 == bigIter ? 1 : previewSF) * 256; // note: needs to be a power of 2
int DPI = (int)Math.Round(sf / base_size); // dots (pixels) per inch
int pad = (0 == bigIter ? 1 : previewSF) * 140;
int w = 3 * sf + pad;
int h = 2 * sf + pad;
var finalTransform = DenseMatrix.OfArray(new double[, ] {
{ sf, 0, 4 * sf / 3 + pad / 2 }, { 0, sf, sf / 3 + pad / 2 }, { 0, 0, 1 }
});
using (DirectBitmap image = new DirectBitmap(w, h),
borderImage = new DirectBitmap(w, h),
thickImage = new DirectBitmap(w, h))
{
int white = unchecked ((int)0xffffffff); // white
int black = unchecked ((int)0xff000000); // black
int red = unchecked ((int)0xffff0000); // red
int blue = unchecked ((int)0xff0000ff); // blue
//int green = unchecked((int)0xff00ff00); // green
// Initialize the image with white
for (int y = 0; y < h; ++y)
{
for (int x = 0; x < w; ++x)
{
image.Bits[w * y + x] = white;
thickImage.Bits[w * y + x] = white;
}
}
// Render fractal to N_ITER_PREVIEW/N_ITER_FINAL iterations, using a simple line segment as the base unit
fractal.RenderFractal(image, 0 == bigIter ? N_ITER_PREVIEW : N_ITER_FINAL, Fractal.renderLine, finalTransform, black, black);
ImProc.BWBoundary(image, borderImage, black); // compute boundary
fractal.ReferenceImage = borderImage;
fractal.AuxImage = thickImage;
// Render the primary spirals of the fractal onto both image and thickImage
fractal.RenderFractal(image, 0, Fractal.renderPrimarySpirals, finalTransform, blue, black);
fractal.RenderFractal(thickImage, 0, Fractal.renderPrimarySpirals, finalTransform, black, black);
// Draw special thick spirals directly onto the thickImage
Vector <double> pointA = DenseVector.OfArray(new double[] { -1.0, 1.0, 1.0 });
Vector <double> pointB = DenseVector.OfArray(new double[] { 1.0, 1.0, 1.0 });
Vector <double> pointAT = finalTransform * pointA;
Vector <double> pointBT = finalTransform * pointB;
double scaleFactor = Math.Sqrt(finalTransform.SubMatrix(0, 2, 0, 2).Determinant());
Vector <double> xBasis = DenseVector.OfArray(new double[] { 1.0, 0.0, 0.0 }); // make 3rd coordinate zero so translation is ignored
Vector <double> xBasisT = finalTransform * xBasis;
double theta = Math.Atan2(xBasisT[1], xBasisT[0]);
for (int i = 0; i < 12; ++i)
{
ImProc.DrawTaperedSpiral(pointAT[0] / pointAT[2], pointAT[1] / pointAT[2], theta + Math.PI / 4 + i * Math.PI / 4, scaleFactor * Math.Sqrt(2.0) * Math.Pow(0.5, 0.5 * i) / 3.0, 0, Math.PI / 4, Math.PI / 1000, 1.0 / 16.0, 0.02, 1.0, black, thickImage);
ImProc.DrawTaperedSpiral(pointBT[0] / pointBT[2], pointBT[1] / pointBT[2], theta - 3 * Math.PI / 4 + i * Math.PI / 4, scaleFactor * Math.Sqrt(2.0) * Math.Pow(0.5, 0.5 * i) * 2.0 / 3.0, 0, Math.PI / 4, Math.PI / 1000, 1.0 / 16.0, 0.02, 1.0, black, thickImage);
}
int nIterSS = 0 == bigIter ? N_ITER_SECONDARY_PREVIEW : N_ITER_SECONDARY_FINAL; // number of iterations of the secondary spirals to compute
// Render iterations of the secondary spirals onto the fractal
for (int i = 0; i < nIterSS; ++i)
{
fractal.RenderFractal(image, i, fractal.renderSecondarySpirals, finalTransform, blue, black);
}
// Clean up the white diagonal lines
ImProc.BWFilter(thickImage, ImProc.CleanWhiteDiagonalsLUT);
IO.SaveImage(image, Path.Combine(OUTPUT_DIRECTORY, "thinfractal" + bigIter.ToString() + ".bmp"));
IO.SaveImage(borderImage, Path.Combine(OUTPUT_DIRECTORY, "fractalborder" + bigIter.ToString() + ".bmp"));
if (0 == bigIter)
{
// Dilate fractal with a circular filter of radius 60
byte[,] maskImage = ImProc.ToBWByteNeq(image, white); // mask indicates where original image is non-white
bool[,] kernel = ImProc.GenerateDiscKernel(60);
int kernelRadius = (kernel.GetLength(0) - 1) / 2;
maskImage = ImProc.BWDilate(maskImage, kernel, kernelRadius, kernelRadius);
byte[,] maskImage2 = new byte[h, w];
ImProc.BWBoundary4(maskImage, maskImage2, 255);
maskImage = null;
// Detect the contour
ImProc.FindClosedContour(maskImage2, out xCoords, out yCoords);
// Smooth the contour
double sigma = 5.0;
int halfWidth = (int)Math.Ceiling(3.0 * sigma);
double[] gaussKernel = ImProc.ConstructGaussianKernel(sigma, halfWidth, true);
double[] xCoordsSmooth = ImProc.Convolve1D(xCoords, gaussKernel, 1, -1, 1);
double[] yCoordsSmooth = ImProc.Convolve1D(yCoords, gaussKernel, 1, -1, 1);
// Decimate smoothed curves so curvature based smoothing will work faster
int N = xCoords.Length;
int N2 = N / 10;
xCoords = new double[N2];
yCoords = new double[N2];
for (int i = 0; i < N2; ++i)
{
xCoords[i] = xCoordsSmooth[(int)(i * N / (double)N2 + 0.5)];
yCoords[i] = yCoordsSmooth[(int)(i * N / (double)N2 + 0.5)];
}
// Apply further curvature-based smoothing
ImProc.CurvatureSmoothContour(xCoords, yCoords, 2000.0, 1.0, 10.0, true);
// Estimate resin boundary
maskImage = ImProc.ToBWByteNeq(image, white); // mask indicates where original image is non-white
kernel = ImProc.GenerateDiscKernel((DPI * 3) / 8); // Filter radius = 3/8 inch
kernelRadius = (kernel.GetLength(0) - 1) / 2;
maskImage = ImProc.BWDilate(maskImage, kernel, kernelRadius, kernelRadius);
//maskImage2 = new byte[h, w];
List <Tuple <int, int> > seeds = new List <Tuple <int, int> >();
seeds.Add(Tuple.Create(0, 0));
List <Tuple <int, int> > contour;
ImProc.BWSelect(maskImage, out maskImage2, seeds, 0, 255, 0, out contour);
maskImage = new byte[h, w];
ImProc.BWBoundary4(maskImage2, maskImage, 255);
maskImage2 = null;
// Detect the contour
ImProc.FindClosedContour(maskImage, out xCoordsResin, out yCoordsResin);
// Smooth the contour
sigma = 5.0;
halfWidth = (int)Math.Ceiling(3.0 * sigma);
gaussKernel = ImProc.ConstructGaussianKernel(sigma, halfWidth, true);
xCoordsSmooth = ImProc.Convolve1D(xCoordsResin, gaussKernel, 1, -1, 1);
yCoordsSmooth = ImProc.Convolve1D(yCoordsResin, gaussKernel, 1, -1, 1);
// Decimate smoothed curves so curvature based smoothing will work faster
N = xCoordsResin.Length;
N2 = N / 10;
xCoordsResin = new double[N2];
yCoordsResin = new double[N2];
for (int i = 0; i < N2; ++i)
{
xCoordsResin[i] = xCoordsSmooth[(int)(i * N / (double)N2 + 0.5)];
yCoordsResin[i] = yCoordsSmooth[(int)(i * N / (double)N2 + 0.5)];
}
}
else
{
// Scale contour by a factor of previewSF
int N = xCoords.Length;
for (int i = 0; i < N; ++i)
{
xCoords[i] = xCoords[i] * previewSF;
yCoords[i] = yCoords[i] * previewSF;
}
N = xCoordsResin.Length;
for (int i = 0; i < N; ++i)
{
xCoordsResin[i] = xCoordsResin[i] * previewSF;
yCoordsResin[i] = yCoordsResin[i] * previewSF;
}
}
// Clear borderImage for more drawing operations
ImProc.SetColor(borderImage, black); // Comment out this line to include the fractal boundary in the final image
// Add the boundaries of the region(s) reachable by each tool
for (int t = 0; t < toolRadii.Length; ++t)
{
// Open the fractal with a disc shaped kernel of radius toolRadii[t],
// adding this boundary to the original boundary. This will show
// us how far a tool of radius toolRadii[t] can make it into the spirals.
byte[,] tempMask = ImProc.ToBWByteEq(thickImage, black);
bool[,] kernel = ImProc.GenerateDiscKernel(DPI * toolRadii[t]);
int kernelRadius = (kernel.GetLength(0) - 1) / 2;
tempMask = ImProc.BWOpen(tempMask, kernel, kernelRadius, kernelRadius);
ImProc.BWBoundary(tempMask, borderImage, 255);
GC.Collect(); // free up memory we temporarily allocated
}
// Dilate the blue region in the first image with a disc shaped kernel of radius of toolRadii[0]
// Then draw these pixels in black onto the thickImage. This will make the spirals of the thick image
// never get thinner than our smallest tool.
{
byte[,] tempMask = ImProc.ToBWByteEq(image, blue);
bool[,] kernel = ImProc.GenerateDiscKernel(DPI * toolRadii[0]);
int kernelRadius = (kernel.GetLength(0) - 1) / 2;
tempMask = ImProc.BWDilate(tempMask, kernel, kernelRadius, kernelRadius);
ImProc.DrawColor(thickImage, tempMask, black);
}
GC.Collect(); // free up memory we temporarily allocated
// Clean up the white diagonal lines
ImProc.BWFilter(thickImage, ImProc.CleanWhiteDiagonalsLUT);
IO.SaveImage(thickImage, Path.Combine(OUTPUT_DIRECTORY, "fractal" + bigIter.ToString() + ".bmp"));
// Extract and add boundary of thick fractal
ImProc.BWBoundary(thickImage, borderImage, black);
// Invert the image
ImProc.BWInvert(borderImage);
// Draw contour onto borderImage
ImProc.DrawClosedContour(xCoords, yCoords, black, borderImage);
// Draw resin contour onto borderImage, and save info (area enclosed by curve)
if (0 == bigIter)
{
ImProc.DrawClosedContour(xCoordsResin, yCoordsResin, red, borderImage);
}
string fractalInfoFilename = Path.Combine(OUTPUT_DIRECTORY, "fractalinfo" + bigIter.ToString() + ".txt");
using (StreamWriter sw = new StreamWriter(fractalInfoFilename))
{
double areaPixels = ImProc.MeasureArea(xCoords, yCoords);
sw.WriteLine("Total area enclosed by boundary = " + (areaPixels / (144.0 * DPI * DPI)).ToString() + " square feet");
areaPixels = ImProc.MeasureArea(xCoordsResin, yCoordsResin);
sw.WriteLine("Resin area = " + (areaPixels / (144.0 * DPI * DPI)).ToString() + " square feet");
}
IO.SaveImage(borderImage, Path.Combine(OUTPUT_DIRECTORY, "fractalwithboundary" + bigIter.ToString() + ".bmp"));
// Divide the image into sub-images and save them
if (1 == bigIter)
{
DirectBitmap[] subImages = ImProc.partitionImage(borderImage, (int)Math.Round(subImageWidth * DPI), (int)Math.Round(subImageHeight * DPI), black);
int nImages = subImages.Length;
for (int i = 0; i < nImages; ++i)
{
// See if we can find any non-white pixels in the interior of this image
bool done = false;
for (int y = 1; y < subImages[i].Height - 1; ++y)
{
for (int x = 1; x < subImages[i].Width - 1; ++x)
{
if ((subImages[i].Bits[subImages[i].Width * y + x] & 0x00ffffff) != (white & 0x00ffffff))
{
done = true;
break;
}
}
if (done)
{
break;
}
}
if (!done)
{
continue; // skip saving this image if we couldn't find any non-white pixels
}
using (Graphics graphics = Graphics.FromImage(subImages[i].Bitmap))
{
using (Font arialFont = new Font("Arial", 36))
{
string text = i.ToString();
// Measure string.
SizeF stringSize = new SizeF();
stringSize = graphics.MeasureString(text, arialFont);
int hw = (int)Math.Ceiling(0.5 * (stringSize.Width + DPI / 2.0));
int hh = (int)Math.Ceiling(0.5 * (stringSize.Height + DPI / 2.0));
// Find a suitable location to put the text
byte[,] tempMask = ImProc.ToBWByteEq(subImages[i], white);
bool[,] kernel = ImProc.GenerateRectKernel(2 * hw + 1, 1);
tempMask = ImProc.BWErode(tempMask, kernel, 1, hw);
kernel = ImProc.GenerateRectKernel(1, 2 * hh + 1);
tempMask = ImProc.BWErode(tempMask, kernel, hh, 1);
// Find a pixel of tempMask near the center that is white
int wi = tempMask.GetLength(1);
int hi = tempMask.GetLength(0);
int best_x = wi / 2;
int best_y = hi / 2;
done = false;
for (int y = hi / 4; y < 3 * hi / 4; ++y)
{
for (int x = wi / 4; x < 3 * wi / 4; ++x)
{
if (tempMask[y, x] == 255)
{
best_x = x;
best_y = y;
done = true;
break;
}
}
if (done)
{
break;
}
}
// Draw the text onto the image
graphics.DrawString(text, arialFont, Brushes.Black, best_x - 0.5f * stringSize.Width, best_y - 0.5f * stringSize.Height);
}
}
IO.SaveImage(subImages[i], Path.Combine(OUTPUT_DIRECTORY, "subimage" + i.ToString() + ".bmp"), DPI, DPI);
}
}
}
}
}