/// <summary>
/// Returns the maximal absolute distance between the components of
/// the two matrices.
/// </summary>
public static __ftype__ DistanceMax(__nmtype__ a, __nmtype__ b)
{
return(Fun.Max( /*# n.ForEach(i => { */
Fun.Max( /*# m.ForEach(j => { */
Fun.Abs(b.M__i____j__ - a.M__i____j__) /*#
* }, comma); */) /*# }, comma); */));
}
/// <summary>
/// Uses the 2 random series (seriesIndex, seriesIndex+1)
/// </summary>
public static V3d Spherical(
IRandomSeries rnds, int seriesIndex)
{
double phi = Constant.PiTimesTwo * rnds.UniformDouble(seriesIndex);
double z = 1.0 - 2.0 * rnds.UniformDouble(seriesIndex + 1);
double r = Fun.Max(1.0 - z * z, 0.0).Sqrt();
return(new V3d(r * phi.Cos(), r * phi.Sin(), z));
}
/// <summary>
/// Stitches the images provided in the 2D array into one large image according to the position in the array.
/// The array is treated as column-major. Therefore, the array
/// {{1, 2, 3}}
/// {{4, 5, 6}}
/// produces the image
/// 1 2 3
/// 4 6 7
/// Null-items are allowed an result in black spot at the corresponding position.
/// The color format of all images must be equal and have byte format.
/// </summary>
/// <param name="images">The 2D image array that should be stitched.</param>
/// <returns>Stitched image</returns>
public static PixImage <T> Stitch <T>(this PixImage <T>[][] images)
{
if (images.IsEmptyOrNull())
{
return(null);
}
// Find largest extensions
var numRows = images.Length;
var numColumns = images.Max(img => img.Length);
// Find largest X Y
var sizesX = new int[numColumns].SetByIndex(c => images.Max(ic => (ic[c] == null) ? 0 : ic[c].Size.X));
var sizesY = images.Map(img => img.Max(img2 => (img2 == null) ? 0 : img2.Size.Y));
var width = sizesX.Sum();
var height = sizesY.Sum();
// The first image in the array, used to determine the color format
var fst = images.First(img => img.Length > 0).First(img => img != null);
if (fst == null)
{
Report.Line("Empty image array!");
return(null);
}
// Assure that the color format fits
if (images.TrueForAny(imgs => imgs.Where(i => i != null).TrueForAny(img => img.Format != fst.Format)))
{
Report.Line("Color format not matching!");
return(null);
}
// Allocate new image
var target = new PixImage <T>(fst.Format, new V2i(width, height));
for (int r = 0, y = 0; r < numRows; r++)
{
for (int c = 0, x = 0; c < Fun.Max(numColumns, images[r].Length); c++)
{
var source = images[r][c];
if (source != null)
{
target.Set(x, y, source);
}
x += sizesX[c];
}
y += sizesY[r];
}
return(target);
}
/// <summary>
/// UnDistortion of pixel coordinates.
/// </summary>
public V2d UndistortPixel(V2d p2, V2i imageSize)
{
var maxSize = Fun.Max(imageSize.X, imageSize.Y);
var y = (p2.Y - PrincipalPoint.Y * imageSize.Y) / (FocalLength.Y * maxSize);
var x = (p2.X - PrincipalPoint.X * imageSize.X - Skew * maxSize * y) / (FocalLength.X * maxSize);
ComputeUndistortionParamsForCameraPoint(x, y, out double rd, out double tx, out double ty);
double xd = x * rd + tx;
double yd = y * rd + ty;
return(new V2d(
FocalLength.X * maxSize * xd + Skew * maxSize * yd + PrincipalPoint.X * imageSize.X,
FocalLength.Y * maxSize * yd + PrincipalPoint.Y * imageSize.Y));
}
/// <summary>
/// Supplied normal MUST be normalized, uses the 2 random series
/// (seriesIndex, seriesIndex+1).
/// </summary>
public static V3d Lambertian(
V3d normal, IRandomSeries rnds, int seriesIndex)
{
V3d vec;
double squareLen;
do
{
double phi = Constant.PiTimesTwo * rnds.UniformDouble(seriesIndex);
double z = 1.0 - 2.0 * rnds.UniformDouble(seriesIndex + 1);
double r = Fun.Max(1.0 - z * z, 0.0).Sqrt();
vec = new V3d(r * phi.Cos(), r * phi.Sin(), z) + normal;
squareLen = vec.LengthSquared;
}while (squareLen < 0.000001);
vec *= 1.0 / squareLen.Sqrt();
return(vec);
}
/// <summary>
/// Project a point from camera space into image space according to the intrinsic camera parameters.
/// This documents the camera model.
/// </summary>
public V2d ProjectToImage(V3d p, V2d imageSize)
{
// projection
double x = p.X / p.Z;
double y = p.Y / p.Z;
// undo distortion here
ComputeUndistortionParamsForCameraPoint(x, y, out double rd, out double tx, out double ty);
// undistorted point:
double xd = x * rd + tx;
double yd = y * rd + ty;
double maxSize = Fun.Max(imageSize.X, imageSize.Y);
// point in image:
return(new V2d(
FocalLength.X * maxSize * xd + Skew * maxSize * yd + PrincipalPoint.X * imageSize.X,
FocalLength.Y * maxSize * yd + PrincipalPoint.Y * imageSize.Y));
}
/// <summary>
/// Compute the Delaunay triangluation of the supplied points. Note that
/// the supplied point array must be by 3 larger than the actual number of
/// points.
/// </summary>
private static void Triangulate2d(V2d[] pa,
out Triangle1i[] ta, out int triangleCount)
{
int vc = pa.Length - 4;
int tcMax = 2 * vc + 2; // sharp upper bound with no degenerates
int ecMax = 6 * vc - 3; // sharp bound: last step replaces all tris
ta = new Triangle1i[tcMax];
var ra = new double[tcMax];
var ca = new V2d[tcMax];
var ea = new Line1i[ecMax];
// -------------------------------------- set up the supertriangle
ta[0] = new Triangle1i(vc, vc + 2, vc + 1);
ra[0] = -1.0;
ta[1] = new Triangle1i(vc, vc + 3, vc + 2);
ra[1] = -1.0;
int tc = 2, cc = 0; // triangle count, complete count
// ------------- superquad vertices at the end of vertex array
var box = new Box2d(pa.Take(vc)).EnlargedBy(0.1);
V2d center = box.Center, size = box.Size;
pa[vc + 0] = box.Min;
pa[vc + 1] = new V2d(box.Min.X, box.Max.Y);
pa[vc + 2] = box.Max;
pa[vc + 3] = new V2d(box.Max.X, box.Min.Y);
// ------------------------------ include the points one at a time
for (int i = 0; i < vc; i++)
{
V2d p = pa[i];
int ec = 0;
/*
* if the point lies inside the circumcircle then the triangle
* is removed and its edges are added to the edge array
*/
for (int ti = cc; ti < tc; ti++)
{
var tr = ta[ti];
double r2 = ra[ti];
if (r2 < 0.0)
{
Triangle2d.ComputeCircumCircleSquared(
pa[tr.I0], pa[tr.I1], pa[tr.I2],
out center, out r2);
ra[ti] = r2; ca[ti] = center;
}
else
{
center = ca[ti];
}
// ---------------- include this if points are sorted by X
if (center.X < p.X && (p.X - center.X).Square() > r2)
{
Fun.Swap(ref ta[ti], ref ta[cc]);
ra[ti] = ra[cc]; ca[ti] = ca[cc];
++cc; continue;
}
if (Vec.DistanceSquared(p, center) <= r2)
{
int nec = ec + 3;
if (nec >= ecMax)
{
ecMax = Fun.Max(nec, (int)(1.1 * (double)ecMax));
Array.Resize(ref ea, ecMax);
}
ea[ec] = tr.Line01; ea[ec + 1] = tr.Line12; ea[ec + 2] = tr.Line20;
--tc; ec = nec;
ta[ti] = ta[tc]; ra[ti] = ra[tc]; ca[ti] = ca[tc];
--ti;
}
}
// ---------------------------------------- tag multiple edges
for (int ei = 0; ei < ec - 1; ei++)
{
for (int ej = ei + 1; ej < ec; ej++)
{
if (ea[ei].I0 == ea[ej].I1 && ea[ei].I1 == ea[ej].I0)
{
ea[ei] = Line1i.Invalid; ea[ej] = Line1i.Invalid;
}
}
}
// ------------------ form new triangles for the current point
for (int ei = 0; ei < ec; ei++)
{
var e = ea[ei];
if (e.I0 < 0 || e.I1 < 0)
{
continue; // skip tagged edges
}
if (tc >= tcMax) // necessary for degenerate cases
{
tcMax = Fun.Max(tcMax + 1, (int)(1.1 * (double)tcMax));
Array.Resize(ref ta, tcMax);
Array.Resize(ref ra, tcMax);
Array.Resize(ref ca, tcMax);
}
ta[tc] = new Triangle1i(e.I0, e.I1, i);
ra[tc++] = -1.0;
}
}
// ------------------ remove triangles with supertriangle vertices
for (int ti = 0; ti < tc; ti++)
{
if (ta[ti].I0 >= vc || ta[ti].I1 >= vc || ta[ti].I2 >= vc)
{
ta[ti--] = ta[--tc];
}
}
triangleCount = tc;
}