void tracetoList(List <List <Curve> > ListOfPathes)
{
if (ListOfPathes == null)
{
return;
}
for (int i = 0; i < pathlist.Count; i++)
{
Path P = pathlist[i];
List <Curve> CurveList = new List <Curve>();
ListOfPathes.Add(CurveList);
dPoint L = P.curve.c[(P.curve.n - 1) * 3 + 2];
for (int j = 0; j < P.curve.n; j++)
{
dPoint A = P.curve.c[j * 3 + 1];
dPoint B = P.curve.c[j * 3 + 2];
if (P.curve.tag[j] == POTRACE_CORNER)
{
CurveList.Add(new Curve(CurveKind.Line, L, L, A, A));
CurveList.Add(new Curve(CurveKind.Line, A, A, B, B));
}
else
{
dPoint CP = P.curve.c[j * 3];
CurveList.Add(new Curve(CurveKind.Bezier, L, CP, A, B));
}
L = B;
}
}
}
/* range over the straight line segment [a,b] when lambda ranges over [0,1] */
static dPoint interval(double lambda, dPoint a, dPoint b)
{
dPoint res = new dPoint();
res.X = a.X + lambda * (b.X - a.X);
res.Y = a.Y + lambda * (b.Y - a.Y);
return(res);
}
/// <summary>
/// Creates a curve
/// </summary>
/// <param name="Kind"></param>
/// <param name="A">Startpoint</param>
/// <param name="ControlPointA">Controlpoint</param>
/// <param name="ControlPointB">Controlpoint</param>
/// <param name="B">Endpoint</param>
public Curve(CurveKind Kind, dPoint A, dPoint ControlPointA, dPoint ControlPointB, dPoint B)
{
this.Kind = Kind;
this.A = A;
this.B = B;
this.ControlPointA = ControlPointA;
this.ControlPointB = ControlPointB;
}
/* return a direction that is 90 degrees counterclockwise from p2-p0,
* but then restricted to one of the major wind directions (n, nw, w, etc) */
static dPoint dorth_infty(dPoint p0, dPoint p2)
{
dPoint r = new dPoint();
r.Y = sign(p2.X - p0.X);
r.X = -sign(p2.Y - p0.Y);
return(r);
}
/* calculate (p1-p0)*(p3-p2) */
static double iprod1(dPoint p0, dPoint p1, dPoint p2, dPoint p3)
{
double x1, y1, x2, y2;
x1 = p1.X - p0.X;
y1 = p1.Y - p0.Y;
x2 = p3.X - p2.X;
y2 = p3.Y - p2.Y;
return(x1 * x2 + y1 * y2);
}
/* calculate (p1-p0)x(p3-p2) */
static double cprod(dPoint p0, dPoint p1, dPoint p2, dPoint p3)
{
double x1, y1, x2, y2;
x1 = p1.X - p0.X;
y1 = p1.Y - p0.Y;
x2 = p3.X - p2.X;
y2 = p3.Y - p2.Y;
return(x1 * y2 - x2 * y1);
}
/* return (p1-p0)x(p2-p0), the area of the parallelogram */
static double dpara(dPoint p0, dPoint p1, dPoint p2)
{
double x1, y1, x2, y2;
x1 = p1.X - p0.X;
y1 = p1.Y - p0.Y;
x2 = p2.X - p0.X;
y2 = p2.Y - p0.Y;
return(x1 * y2 - x2 * y1);
}
/* calculate point of a bezier curve */
static dPoint bezier(double t, dPoint p0, dPoint p1, dPoint p2, dPoint p3)
{
double s = 1 - t; dPoint res = new dPoint();
/* Note: a good optimizing compiler (such as gcc-3) reduces the
* following to 16 multiplications, using common subexpression
* elimination. */
res.X = s * s * s * p0.X + 3 * (s * s * t) * p1.X + 3 * (t * t * s) * p2.X + t * t * t * p3.X;
res.Y = s * s * s * p0.Y + 3 * (s * s * t) * p1.Y + 3 * (t * t * s) * p2.Y + t * t * t * p3.Y;
return(res);
}
internal static List <List <Curve> > BuildFilling(List <List <Curve> > plist, double spacing, double w, double h, LaserGRBL.RasterConverter.ImageProcessor.Direction dir)
{
if (dir == LaserGRBL.RasterConverter.ImageProcessor.Direction.NewInsetFilling)
{
return(BuildInsetFilling(plist, spacing));
}
List <List <Curve> > flist = new List <List <Curve> >();
Clipper c = new Clipper();
AddGridSubject(c, spacing, w, h, dir);
AddGridClip(plist, c);
long t1 = Tools.HiResTimer.TotalMilliseconds;
PolyTree solution = new PolyTree();
bool succeeded = c.Execute(ClipType.ctIntersection, solution, PolyFillType.pftEvenOdd, PolyFillType.pftEvenOdd);
long t2 = Tools.HiResTimer.TotalMilliseconds;
System.Diagnostics.Debug.WriteLine($"ClipperExecute: {t2 - t1}ms");
//GraphicsPath result = new GraphicsPath();
List <List <IntPoint> > ll = Clipper.OpenPathsFromPolyTree(solution);
foreach (List <IntPoint> pg in ll)
{
PointF[] pts = PolygonToPointFArray(pg, resolution);
if (pts.Count() > 2)
{
; // result.AddPolygon(pts);
}
else
{
dPoint a = new dPoint(pts[0].X, pts[0].Y);
dPoint b = new dPoint(pts[1].X, pts[1].Y);
flist.Add(new List <Curve>()
{
new Curve(CurveKind.Line, a, a, b, b)
});
}
//result.AddLine(pts[0], pts[1]);
}
flist.Reverse();
return(flist);
}
/* Apply quadratic form Q to vector w = (w.x,w.y) */
static double quadform(Quad Q, dPoint w)
{
double sum = 0;
double[] v = new double[3];
v[0] = w.X;
v[1] = w.Y;
v[2] = 1;
sum = 0.0;
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 3; j++)
{
sum += v[i] * Q.at(i, j) * v[j];
}
}
return(sum);
}
/* calculate the point t in [0..1] on the (convex) bezier curve
* (p0,p1,p2,p3) which is tangent to q1-q0. Return -1.0 if there is no
* solution in [0..1]. */
static double tangent(dPoint p0, dPoint p1, dPoint p2, dPoint p3, dPoint q0, dPoint q1)
{
double A, B, C; /* (1-t)^2 A + 2(1-t)t B + t^2 C = 0 */
double a, b, c; /* a t^2 + b t + c = 0 */
double d, s, r1, r2;
A = cprod(p0, p1, q0, q1);
B = cprod(p1, p2, q0, q1);
C = cprod(p2, p3, q0, q1);
a = A - 2 * B + C;
b = -2 * A + 2 * B;
c = A;
d = b * b - 4 * a * c;
if (a == 0 || d < 0)
{
return(-1.0);
}
s = Math.Sqrt(d);
r1 = (-b + s) / (2 * a);
r2 = (-b - s) / (2 * a);
if (r1 >= 0 && r1 <= 1)
{
return(r1);
}
else if (r2 >= 0 && r2 <= 1)
{
return(r2);
}
else
{
return(-1.0);
}
}
private static List <List <Curve> > ToPotraceList(List <List <IntPoint> > ll, bool close)
{
List <List <Curve> > flist = new List <List <Curve> >();
foreach (List <IntPoint> pg in ll)
{
if (pg.Count == 2)
{
dPoint a = new dPoint(pg[0].X / resolution, pg[0].Y / resolution);
dPoint b = new dPoint(pg[1].X / resolution, pg[1].Y / resolution);
flist.Add(new List <Curve>()
{
new Curve(CurveKind.Line, a, a, b, b)
});
}
else
{
List <Curve> potcurve = new List <Curve>();
for (int i = 0; i < pg.Count - 1; i++)
{
dPoint a = new dPoint(pg[i].X / resolution, pg[i].Y / resolution);
dPoint b = new dPoint(pg[i + 1].X / resolution, pg[i + 1].Y / resolution);
potcurve.Add(new Curve(CurveKind.Line, a, a, b, b));
}
if (close)
{
dPoint a = new dPoint(pg[pg.Count - 1].X / resolution, pg[pg.Count - 1].Y / resolution);
dPoint b = new dPoint(pg[0].X / resolution, pg[0].Y / resolution);
potcurve.Add(new Curve(CurveKind.Line, a, a, b, b));
}
flist.Add(potcurve);
}
}
//flist.Reverse();
return(flist);
}
/* ddenom/dpara have the property that the square of radius 1 centered
* at p1 intersects the line p0p2 iff |dpara(p0,p1,p2)| <= ddenom(p0,p2) */
static double ddenom(dPoint p0, dPoint p2)
{
dPoint r = dorth_infty(p0, p2);
return(r.Y * (p2.X - p0.X) - r.X * (p2.Y - p0.Y));
}
public static Rg.Point3d ToRhPoint(this Pt.dPoint input, double height)
{
return(new Rg.Point3d(input.x, height - input.y, 0));
}
/* Stage 3: vertex adjustment (Sec. 2.3.1). */
/* Adjust vertices of optimal polygon: calculate the intersection of
* the two "optimal" line segments, then move it into the unit square
* if it lies outside. Return 1 with errno set on error; 0 on
* success. */
/* calculate "optimal" point-slope representation for each line segment */
static void adjustVertices(Path path)
{
int m = path.m;
int[] po = path.po;
int n = path.len;
List <Point> pt = path.pt;
double x0 = path.x0;
double y0 = path.y0;
dPoint[] ctr = new dPoint[m];
dPoint[] dir = new dPoint[m];
Quad[] q = new Quad[m];
int i, j, k, l;
double[] v = new double[3];
dPoint s = new dPoint();
double d;
path.curve = new privcurve(m);
/* calculate "optimal" point-slope representation for each line
* segment */
for (i = 0; i < m; i++)
{
j = po[mod(i + 1, m)];
j = mod(j - po[i], n) + po[i];
ctr[i] = new dPoint();
dir[i] = new dPoint();
pointslope(path, po[i], j, ctr[i], dir[i]);
}
/* represent each line segment as a singular quadratic form; the
* distance of a point (x,y) from the line segment will be
* (x,y,1)Q(x,y,1)^t, where Q=q[i]. */
for (i = 0; i < m; i++)
{
q[i] = new Quad();
d = dir[i].X * dir[i].X + dir[i].Y * dir[i].Y;
if (d == 0.0)
{
for (j = 0; j < 3; j++)
{
for (k = 0; k < 3; k++)
{
q[i].data[j * 3 + k] = 0;
}
}
}
else
{
v[0] = dir[i].Y;
v[1] = -dir[i].X;
v[2] = -v[1] * ctr[i].Y - v[0] * ctr[i].X;
for (l = 0; l < 3; l++)
{
for (k = 0; k < 3; k++)
{
q[i].data[l * 3 + k] = v[l] * v[k] / d;
}
}
}
}
double dx, dy, det;
int z;
double xmin, ymin; /* coordinates of minimum */
double min, cand; /* minimum and candidate for minimum of quad. form */
/* now calculate the "intersections" of consecutive segments.
* Instead of using the actual intersection, we find the point
* within a given unit square which minimizes the square distance to
* the two lines. */
for (i = 0; i < m; i++)
{
Quad Q = new Quad();
dPoint w = new dPoint();
/* let s be the vertex, in coordinates relative to x0/y0 */
s.X = pt[po[i]].X - x0;
s.Y = pt[po[i]].Y - y0;
/* intersect segments i-1 and i */
j = mod(i - 1, m);
/* add quadratic forms */
for (l = 0; l < 3; l++)
{
for (k = 0; k < 3; k++)
{
Q.data[l * 3 + k] = q[j].at(l, k) + q[i].at(l, k);
}
}
while (true)
{
/* minimize the quadratic form Q on the unit square */
/* find intersection */
det = Q.at(0, 0) * Q.at(1, 1) - Q.at(0, 1) * Q.at(1, 0);
if (det != 0.0)
{
w.X = (-Q.at(0, 2) * Q.at(1, 1) + Q.at(1, 2) * Q.at(0, 1)) / det;
w.Y = (Q.at(0, 2) * Q.at(1, 0) - Q.at(1, 2) * Q.at(0, 0)) / det;
break;
}
/* matrix is singular - lines are parallel. Add another,
* orthogonal axis, through the center of the unit square */
if (Q.at(0, 0) > Q.at(1, 1))
{
v[0] = -Q.at(0, 1);
v[1] = Q.at(0, 0);
}
else if (Q.at(1, 1) != 0.0)
{
v[0] = -Q.at(1, 1);
v[1] = Q.at(1, 0);
}
else
{
v[0] = 1;
v[1] = 0;
}
d = v[0] * v[0] + v[1] * v[1];
v[2] = -v[1] * s.Y - v[0] * s.X;
for (l = 0; l < 3; l++)
{
for (k = 0; k < 3; k++)
{
Q.data[l * 3 + k] += v[l] * v[k] / d;
}
}
}
dx = Math.Abs(w.X - s.X);
dy = Math.Abs(w.Y - s.Y);
if (dx <= 0.5 && dy <= 0.5)
{
path.curve.vertex[i] = new dPoint(w.X + x0, w.Y + y0);
continue;
}
/* the minimum was not in the unit square; now minimize quadratic
* on boundary of square */
min = quadform(Q, s);
xmin = s.X;
ymin = s.Y;
if (Q.at(0, 0) != 0.0)
{
for (z = 0; z < 2; z++)
{
/* value of the y-coordinate */
w.Y = s.Y - 0.5 + z;
w.X = -(Q.at(0, 1) * w.Y + Q.at(0, 2)) / Q.at(0, 0);
dx = Math.Abs(w.X - s.X);
cand = quadform(Q, w);
if (dx <= 0.5 && cand < min)
{
min = cand;
xmin = w.X;
ymin = w.Y;
}
}
}
if (Q.at(1, 1) != 0.0)
{
for (z = 0; z < 2; z++)
{
/* value of the x-coordinate */
w.X = s.X - 0.5 + z;
w.Y = -(Q.at(1, 0) * w.X + Q.at(1, 2)) / Q.at(1, 1);
dy = Math.Abs(w.Y - s.Y);
cand = quadform(Q, w);
if (dy <= 0.5 && cand < min)
{
min = cand;
xmin = w.X;
ymin = w.Y;
}
}
}
/* check four corners */
for (l = 0; l < 2; l++)
{
for (k = 0; k < 2; k++)
{
w.X = s.X - 0.5 + l;
w.Y = s.Y - 0.5 + k;
cand = quadform(Q, w);
if (cand < min)
{
min = cand;
xmin = w.X;
ymin = w.Y;
}
}
}
path.curve.vertex[i] = new dPoint(xmin + x0, ymin + y0);
}
}
/* calculate p1 x p2 */
static double xprod(dPoint p1, dPoint p2)
{
return(p1.X * p2.Y - p1.Y * p2.X);
}
/* calculate distance between two points */
static double ddist(dPoint p, dPoint q)
{
return(Math.Sqrt((p.X - q.X) * (p.X - q.X) + (p.Y - q.Y) * (p.Y - q.Y)));
}
/* determine the center and slope of the line i..j. Assume i<j. Needs
* "sum" components of p to be set. */
static void pointslope(Path path, int i, int j, dPoint ctr, dPoint dir)
{
int n = path.len;
List <Sum> sums = path.sums;
double x, y, x2, xy, y2;
double a, b, c, lambda2, l;
int k = 0;
/* assume i<j */
int r = 0; /* rotations from i to j */
while (j >= n)
{
j -= n;
r += 1;
}
while (i >= n)
{
i -= n;
r -= 1;
}
while (j < 0)
{
j += n;
r -= 1;
}
while (i < 0)
{
i += n;
r += 1;
}
x = sums[j + 1].x - sums[i].x + r * sums[n].x;
y = sums[j + 1].y - sums[i].y + r * sums[n].y;
x2 = sums[j + 1].x2 - sums[i].x2 + r * sums[n].x2;
xy = sums[j + 1].xy - sums[i].xy + r * sums[n].xy;
y2 = sums[j + 1].y2 - sums[i].y2 + r * sums[n].y2;
k = j + 1 - i + r * n;
ctr.X = x / k;
ctr.Y = y / k;
a = (x2 - x * x / k) / k;
b = (xy - x * y / k) / k;
c = (y2 - y * y / k) / k;
lambda2 = (a + c + Math.Sqrt((a - c) * (a - c) + 4 * b * b)) / 2; /* larger e.value */
a -= lambda2;
c -= lambda2;
if (Math.Abs(a) >= Math.Abs(c))
{
l = Math.Sqrt(a * a + b * b);
if (l != 0)
{
dir.X = -b / l;
dir.Y = a / l;
}
}
else
{
l = Math.Sqrt(c * c + b * b);
if (l != 0)
{
dir.X = -c / l;
dir.Y = b / l;
}
}
if (l == 0)
{
dir.X = dir.Y = 0; /* sometimes this can happen when k=4:
* the two eigenvalues coincide */
}
}
private static List <List <Curve> > BuildInsetFilling(List <List <Curve> > plist, double spacing)
{
int loop = 1;
bool empty = false;
List <List <Curve> > flist = new List <List <Curve> >();
ClipperOffset c = new ClipperOffset();
foreach (List <Curve> LC in plist)
{
GraphicsPath Current = new GraphicsPath();
for (int j = 0; j < LC.Count; j++)
{
Curve C = LC[j];
if (C.Kind == CurveKind.Line)
{
Current.AddLine(new PointF((float)C.A.X, (float)C.A.Y), new PointF((float)C.B.X, (float)C.B.Y));
}
else
{
PointF A = new PointF((float)C.A.X, (float)C.A.Y);
Current.AddBezier(new PointF((float)C.A.X, (float)C.A.Y), new PointF((float)C.ControlPointA.X, (float)C.ControlPointA.Y), new PointF((float)C.ControlPointB.X, (float)C.ControlPointB.Y), new PointF((float)C.B.X, (float)C.B.Y));
}
}
AddClip(c, Current);
}
while (!empty)
{
long t1 = Tools.HiResTimer.TotalMilliseconds;
List <List <IntPoint> > solution = new List <List <IntPoint> >();
c.Execute(ref solution, -spacing * loop * resolution);
loop++;
long t2 = Tools.HiResTimer.TotalMilliseconds;
System.Diagnostics.Debug.WriteLine($"ClipperExecute: {t2 - t1}ms");
//GraphicsPath result = new GraphicsPath();
if (solution.Count == 0)
{
empty = true;
}
foreach (List <IntPoint> pg in solution)
{
PointF[] pts = PolygonToPointFArray(pg, resolution);
if (pts.Count() > 2)
{
List <Curve> curve = new List <Curve>();
for (int i = 0; i < pts.Length - 1; i++)
{
dPoint a = new dPoint(pts[i].X, pts[i].Y);
dPoint b = new dPoint(pts[i + 1].X, pts[i + 1].Y);
curve.Add(new Curve(CurveKind.Line, a, a, b, b));
}
//chiudi la figura
dPoint a1 = new dPoint(pts[pts.Length - 1].X, pts[pts.Length - 1].Y);
dPoint b1 = new dPoint(pts[0].X, pts[0].Y);
curve.Add(new Curve(CurveKind.Line, a1, a1, b1, b1));
flist.Add(curve);
}
else
{
dPoint a = new dPoint(pts[0].X, pts[0].Y);
dPoint b = new dPoint(pts[1].X, pts[1].Y);
flist.Add(new List <Curve>()
{
new Curve(CurveKind.Line, a, a, b, b)
});
}
//result.AddLine(pts[0], pts[1]);
}
}
return(flist);
}
public static Sw.Point ToPoint(this Pt.dPoint input)
{
return(new Sw.Point(input.x, input.y));
}