protected virtual double getlength()
{
double length = 0;
for (int i = 0; i < 10000; i++)
length += new LineD(GetCoordinate((i + 1)/10000.0), GetCoordinate(i/10000.0)).Length;
return length;
}
public override Bezier GetTranslatedBezier(bool reverse, double translation)
{
PointD q0;
PointD q1;
PointD q2;
if (reverse)
{
q0 = p2 + GetDirection(1).GetLeftHandNormal()*translation;
q2 = p0 + GetDirection(0).GetLeftHandNormal()*translation;
q1 = new LineD(q0, GetVelocity(1)).GetCrossingPoint(new LineD(q2, GetVelocity(0)));
}
else
{
q0 = p0 + GetDirection(0).GetRightHandNormal()*translation;
q2 = p2 + GetDirection(1).GetRightHandNormal()*translation;
q1 = new LineD(q0, GetVelocity(0)).GetCrossingPoint(new LineD(q2, GetVelocity(1)));
}
return new QuadraticBezier(q0, q1, q2);
}
public override Bezier GetTranslatedBezier(bool reverse, double translation)
{
var distancehashset = new HashSet<double>();
PointD q0;
PointD q1;
PointD q2;
PointD q3;
PointD c25;
PointD c50;
PointD c75;
VectorD direction0;
VectorD direction1;
double distance = 0;
// Determine the controlpoints of the new Bézier curve and points of the current curve with which
// you want to calibrate.
if (reverse)
{
q0 = p3 + GetDirection(1).GetLeftHandNormal()*translation;
q1 = p2 + GetDirection(1).GetLeftHandNormal()*translation;
q2 = p1 + GetDirection(0).GetLeftHandNormal()*translation;
q3 = p0 + GetDirection(0).GetLeftHandNormal()*translation;
c25 = GetCoordinate(0.75) + translation*GetDirection(0.75).GetLeftHandNormal();
c50 = GetCoordinate(0.50) + translation*GetDirection(0.50).GetLeftHandNormal();
c75 = GetCoordinate(0.25) + translation*GetDirection(0.25).GetLeftHandNormal();
direction0 = GetDirection(1);
direction1 = GetDirection(0);
}
else
{
q0 = p0 + GetDirection(0).GetRightHandNormal()*translation;
q1 = p1 + GetDirection(0).GetRightHandNormal()*translation;
q2 = p2 + GetDirection(1).GetRightHandNormal()*translation;
q3 = p3 + GetDirection(1).GetRightHandNormal()*translation;
c25 = GetCoordinate(0.25) + translation*GetDirection(0.25).GetRightHandNormal();
c50 = GetCoordinate(0.50) + translation*GetDirection(0.50).GetRightHandNormal();
c75 = GetCoordinate(0.75) + translation*GetDirection(0.75).GetRightHandNormal();
direction0 = GetDirection(0).GetInvertedVector();
direction1 = GetDirection(1).GetInvertedVector();
}
// Determine the distance between the calibrationpoint for the new Bézier curve.
distance += new LineD(getcoordinate(0.25, q0, q1, q2, q3), c25).Length;
distance += new LineD(getcoordinate(0.50, q0, q1, q2, q3), c50).Length;
distance += new LineD(getcoordinate(0.75, q0, q1, q2, q3), c75).Length;
distancehashset.Add(distance);
for (int i = 0; i < 1000; i++)
// Try to improve the control points 1000 times as described in the Bézier curve pdf
{
PointD q1backup = q1;
PointD q2backup = q2;
var distancesnew = new List<double>(new double[4]);
q1 = q1backup - 0.01*direction0;
distancesnew[0] += new LineD(getcoordinate(0.25, q0, q1, q2, q3), c25).Length;
distancesnew[0] += new LineD(getcoordinate(0.50, q0, q1, q2, q3), c50).Length;
distancesnew[0] += new LineD(getcoordinate(0.75, q0, q1, q2, q3), c75).Length;
q1 = q1backup + 0.01*direction0;
distancesnew[1] += new LineD(getcoordinate(0.25, q0, q1, q2, q3), c25).Length;
distancesnew[1] += new LineD(getcoordinate(0.50, q0, q1, q2, q3), c50).Length;
distancesnew[1] += new LineD(getcoordinate(0.75, q0, q1, q2, q3), c75).Length;
q2 = q2backup - 0.01*direction1;
distancesnew[2] += new LineD(getcoordinate(0.25, q0, q1, q2, q3), c25).Length;
distancesnew[2] += new LineD(getcoordinate(0.50, q0, q1, q2, q3), c50).Length;
distancesnew[2] += new LineD(getcoordinate(0.75, q0, q1, q2, q3), c75).Length;
q2 = q2backup + 0.01*direction1;
distancesnew[3] += new LineD(getcoordinate(0.25, q0, q1, q2, q3), c25).Length;
distancesnew[3] += new LineD(getcoordinate(0.50, q0, q1, q2, q3), c50).Length;
distancesnew[3] += new LineD(getcoordinate(0.75, q0, q1, q2, q3), c75).Length;
int minindex = distancesnew.IndexOf(distancesnew.Min());
switch (minindex)
{
case 0:
q1 = q1backup - 0.01*direction0;
break;
case 1:
q1 = q1backup + 0.01*direction0;
break;
case 2:
q2 = q2backup - 0.01*direction1;
break;
case 3:
q2 = q2backup + 0.01*direction1;
break;
}
distance = distancesnew[minindex];
if (distancehashset.Contains(distance))
break;
distancehashset.Add(distance);
}
return new CubicBezier(q0, q1, q2, q3);
}
public PointD GetCrossingPoint(LineD line)
{
return GetCrossingPoint(this, line);
}
// http://mathworld.wolfram.com/Line-LineIntersection.html
private static PointD GetCrossingPoint(LineD line1, LineD line2)
{
double x1 = line1.Point1.X;
double x2 = line1.Point2.X;
double x3 = line2.Point1.X;
double x4 = line2.Point2.X;
double y1 = line1.Point1.Y;
double y2 = line1.Point2.Y;
double y3 = line2.Point1.Y;
double y4 = line2.Point2.Y;
double x = ((x1*y2 - y1*x2)*(x3 - x4) - (x1 - x2)*(x3*y4 - y3*x4))/
((x1 - x2)*(y3 - y4) - (x3 - x4)*(y1 - y2));
double y = ((x1*y2 - y1*x2)*(y3 - y4) - (y1 - y2)*(x3*y4 - y3*x4))/
((x1 - x2)*(y3 - y4) - (x3 - x4)*(y1 - y2));
return new PointD(x, y);
}
public bool IsCoLinearWith(LineD line)
{
return new VectorD(Point1, Point2).IsCoLinearWith(new VectorD(line.Point1, line.Point2)) &&
GetDistance(line.Point1) < 0.001;
}
private void MakeCrossingGraphicsPath()
{
int length = cornerpoints.Length;
graphicspath = new GraphicsPath();
for (int i = 0; i < cornerpoints.Length; i++)
{
if (i%2 == 0)
graphicspath.AddLine(cornerpoints[i], cornerpoints[i + 1]);
else
{
VectorD vector1 =
new VectorD(cornerpoints[(i - 1)%length], cornerpoints[(i)%length]).GetRightHandNormal();
VectorD vector2 =
new VectorD(cornerpoints[(i + 1)%length], cornerpoints[(i + 2)%length]).GetRightHandNormal();
if (vector1.IsCoLinearWith(vector2))
graphicspath.AddLine(cornerpoints[(i)%length], cornerpoints[(i + 1)%length]);
else
{
var line1 = new LineD(cornerpoints[(i)%length], vector1);
var line2 = new LineD(cornerpoints[(i + 1)%length], vector2);
Bezier bezier = new QuadraticBezier(cornerpoints[(i)%length], line1.GetCrossingPoint(line2),
cornerpoints[(i + 1)%length]);
PointF[] points = bezier.GetDrawPoints();
graphicspath.AddBezier(points[0], points[1], points[2], points[3]);
}
}
}
}