private LineSeries WindowCrossings(OneForm xOneForm, int length)
{
var allCrossings = new List <Tuple <double, double> >();
var windowEnteringCrossings = new List <Tuple <double, double> >();
foreach (var constraint in Constraints)
{
allCrossings.Add(Intersection(xOneForm, length, constraint));
}
foreach (var pt in allCrossings)
{
if (Constraints.Any(c => c.Violate(pt)))
{
continue;
}
windowEnteringCrossings.Add(pt);
}
var lineSeries = new LineSeries()
{
LineStyle = (length == 0 ? LineStyle.Solid : LineStyle.Dash),
Color = (length == 0 ? OxyColors.Black : OxyColors.Gray),
StrokeThickness = (length == 0 ? 2 : 0.5)
};
windowEnteringCrossings.ForEach(c => lineSeries.Points.Add(new DataPoint(c.Item1, c.Item2)));
return(lineSeries);
}
private Tuple <double, double> Intersection(OneForm o, int z, Constraint c)
{
// intersection betwen the line normal to a vector from the origin to point and the constraint
var y = o.X * c.Length * c.Length - c.X * z;
y /= (o.X * c.Y - c.X * o.Y);
var x = (z - o.Y * y) / o.X;
return(new Tuple <double, double>(x, y));
}
/// <summary>
/// Returns lines associated with the supplied 1-form
/// </summary>
/// <param name="oneForm"></param>
/// <returns></returns>
public IEnumerable <LineSeries> Lines(OneForm oneForm)
{
yield return(WindowCrossings(oneForm, 0));
var length = 1;
while (EntersWindow(oneForm, length))
{
yield return(WindowCrossings(oneForm, length++));
}
length = -1;
while (EntersWindow(oneForm, length))
{
yield return(WindowCrossings(oneForm, length--));
}
}
private bool EntersWindow(OneForm xOneForm, int length)
{
var entersWindow = false;
foreach (var constraint in Constraints)
{
var intersection = Intersection(xOneForm, length, constraint);
bool outside = false;
foreach (var c in Constraints)
{
if (c.Violate(intersection))
{
outside = true;
}
}
if (outside == false)
{
entersWindow = true;
}
}
return(entersWindow);
}
private LineSeries WindowCrossings(OneForm xOneForm, int length)
{
var allCrossings = new List<Tuple<double, double>>();
var windowEnteringCrossings = new List<Tuple<double, double>>();
foreach (var constraint in Constraints)
{
allCrossings.Add(Intersection(xOneForm, length, constraint));
}
foreach(var pt in allCrossings)
{
if (Constraints.Any(c => c.Violate(pt))) continue;
windowEnteringCrossings.Add(pt);
}
var lineSeries = new LineSeries()
{
LineStyle = (length == 0 ? LineStyle.Solid : LineStyle.Dash),
Color = (length == 0 ? OxyColors.Black : OxyColors.Gray),
StrokeThickness = (length == 0 ? 2 : 0.5)
};
windowEnteringCrossings.ForEach(c => lineSeries.Points.Add(new DataPoint(c.Item1, c.Item2)));
return lineSeries;
}
private Tuple<double, double> Intersection(OneForm o, int z, Constraint c)
{
// intersection betwen the line normal to a vector from the origin to point and the constraint
var y = o.X * c.Length * c.Length - c.X * z;
y /= (o.X * c.Y - c.X * o.Y);
var x = (z - o.Y * y ) / o.X;
return new Tuple<double, double>(x, y);
}
private Tuple<double, double> Increment(OneForm xOneForm, Tuple<double, double> point)
{
return new Tuple<double, double>(point.Item1 + xOneForm.UnitVector[0], point.Item2 + xOneForm.UnitVector[1]);
}
private bool EntersWindow(OneForm xOneForm, int length)
{
var entersWindow = false;
foreach (var constraint in Constraints)
{
var intersection = Intersection(xOneForm, length, constraint);
bool outside = false;
foreach(var c in Constraints)
{
if (c.Violate(intersection))
outside = true;
}
if (outside == false) entersWindow = true;
}
return entersWindow;
}
/// <summary>
/// Returns lines associated with the supplied 1-form
/// </summary>
/// <param name="oneForm"></param>
/// <returns></returns>
public IEnumerable<LineSeries> Lines(OneForm oneForm)
{
yield return WindowCrossings(oneForm, 0);
var length = 1;
while(EntersWindow(oneForm, length))
{
yield return WindowCrossings(oneForm, length++);
}
length = -1;
while (EntersWindow(oneForm, length))
{
yield return WindowCrossings(oneForm, length--);
}
}
private Tuple <double, double> Increment(OneForm xOneForm, Tuple <double, double> point)
{
return(new Tuple <double, double>(point.Item1 + xOneForm.UnitVector[0], point.Item2 + xOneForm.UnitVector[1]));
}