// outputs (p) cp cp p cp cp p cp cp p..
public static void SplinePoints(IList <Point> ret, int count, Func <int, double> x, Func <int, double> y)
{
// flatten at resolution
var ea = new Point(x(1) - x(0), y(1) - y(0));
double eam = MathTool.Hypot(ea.X, ea.Y);
ret.Add(new Point(x(0), y(0))); // output point[0]
ret.Add(new Point(x(0), y(0))); // output a bogus control point
for (int i = 2; i < count; ++i)
{
var eb = new Point(x(i) - x(i - 1), y(i) - y(i - 1));
double ebm = MathTool.Hypot(eb.X, eb.Y);
double dot = (ea.X * eb.X + ea.Y * eb.Y) / (eam * ebm);
//double tension = 0.35*Math.Exp(0.5 * (dot + 1.0))/(Math.resolution-1);
double tension = 0.5 * (dot + 1.0);
tension = 1.0 + tension * (Math.E - 1.0);
tension = 0.5 * Math.Log(tension);
var d = new Point(x(i) - x(i - 2), y(i) - y(i - 2));
double dm = MathTool.Hypot(d.X, d.Y);
if (dm == 0)
{
dm = double.PositiveInfinity;
}
ret.Add(new Point(x(i - 1) - eam * tension * d.X / dm, y(i - 1) - eam * tension * d.Y / dm));
ret.Add(new Point(x(i - 1), y(i - 1)));
ret.Add(new Point(x(i - 1) + ebm * tension * d.X / dm, y(i - 1) + ebm * tension * d.Y / dm));
ea = eb;
eam = ebm;
}
ret.Add(new Point(x(count - 1), y(count - 1))); // output a bogus control point
ret.Add(new Point(x(count - 1), y(count - 1))); // output point[0]
}
public static IList <int> StripCoincident(int count, Func <int, double> x, Func <int, double> y, double resolution)
{
IList <int> ret = new List <int>();
for (int i = 0; i < count;)
{
double cx = x(i);
double cy = y(i);
int j = i;
ret.Add(j);
for (++i; i < count && MathTool.Hypot(x(j) - cx, y(j) - cy) < resolution; ++i)
{
cx = (cx * (double)(i - j) + x(i)) / (double)(i - j + 1);
cy = (cy * (double)(i - j) + y(i)) / (double)(i - j + 1);
}
}
return(ret);
}
/// <summary>
/// Smooth a line into a PathFigure of quadratic and cubic bezier splines.
/// </summary>
/// <param name="count">Number of equator in line.</param>
/// <param name="x">x coordinate of ith point.</param>
/// <param name="y">y coordinate of ith point.</param>
/// <returns>Smooth line.</returns>
public static PathFigure Smooth(int count, Func <int, double> x, Func <int, double> y)
{
var pathFigure = new PathFigure()
{
StartPoint = new Point(x(0), y(0))
};
int n = count - 1;
Point pa;
Point pb = new Point(x(0), y(0));
Point pc = new Point(x(0 + 1), y(0 + 1));
Point pd = new Point(x(0 + 2), y(0 + 2));
Point eab;
double mab;
Point ebc = new Point(pc.X - pb.X, pc.Y - pb.Y);
double mbc = MathTool.Hypot(ebc.X, ebc.Y);
Point ecd = new Point(pd.X - pc.X, pd.Y - pc.Y);
double mcd = MathTool.Hypot(ecd.X, ecd.Y);
Point tc;
double sc;
double alpha = 0.15;
double beta = 0.45;
{
// first quadratic patch
tc = new Point(pd.X - pb.X, pd.Y - pb.Y); { double m = MathTool.Hypot(tc.X, tc.Y); tc.X /= m; tc.Y /= m; }
sc = 0.5 + (ebc.X * ecd.X + ebc.Y * ecd.Y) / (2.0 * mbc * mcd);
QuadraticBezierSegment segment = new QuadraticBezierSegment()
{
Point1 = new Point(pc.X - tc.X * (alpha + beta * sc) * mbc, pc.Y - tc.Y * (alpha + beta * sc) * mbc),
Point2 = pc
};
if (double.IsNaN(segment.Point1.X) || double.IsNaN(segment.Point1.Y))
{
}
if (double.IsNaN(segment.Point2.X) || double.IsNaN(segment.Point2.Y))
{
}
pathFigure.Segments.Add(segment);
}
for (int i = 1; i < n - 1; ++i)
{
// intermediate cubic patches
pa = pb;
pb = pc;
pc = pd;
pd = new Point(x(i + 2), y(i + 2));
eab = ebc;
mab = mbc;
ebc = ecd;
mbc = mcd;
ecd = new Point(pd.X - pc.X, pd.Y - pc.Y);
mcd = MathTool.Hypot(ecd.X, ecd.Y);
Point tb = tc;
double sb = sc;
tc = new Point(pd.X - pb.X, pd.Y - pb.Y); { double m = MathTool.Hypot(tc.X, tc.Y); tc.X /= m; tc.Y /= m; }
sc = 0.5 + (ebc.X * ecd.X + ebc.Y * ecd.Y) / (2.0 * mbc * mcd);
BezierSegment segment = new BezierSegment()
{
Point1 = new Point(pb.X + tb.X * (alpha + beta * sb) * mbc, pb.Y + tb.Y * (alpha + beta * sb) * mbc),
Point2 = new Point(pc.X - tc.X * (alpha + beta * sc) * mbc, pc.Y - tc.Y * (alpha + beta * sc) * mbc),
Point3 = pc
};
pathFigure.Segments.Add(segment);
if (double.IsNaN(segment.Point1.X) || double.IsNaN(segment.Point1.Y))
{
}
if (double.IsNaN(segment.Point2.X) || double.IsNaN(segment.Point2.Y))
{
}
if (double.IsNaN(segment.Point3.X) || double.IsNaN(segment.Point3.Y))
{
}
}
{
// last quadratic patch
pa = pb;
pb = pc;
pc = pd;
// pd
eab = ebc;
mab = mbc;
ebc = ecd;
mbc = mcd;
Point tb = tc;
double sb = sc;
QuadraticBezierSegment segment = new QuadraticBezierSegment()
{
Point1 = new Point(pb.X + tb.X * (alpha + beta * sb) * mbc, pb.Y + tb.Y * (alpha + beta * sb) * mbc),
Point2 = pc
};
pathFigure.Segments.Add(segment);
if (double.IsNaN(segment.Point1.X) || double.IsNaN(segment.Point1.Y))
{
}
if (double.IsNaN(segment.Point2.X) || double.IsNaN(segment.Point2.Y))
{
}
}
return(pathFigure);
}