private static IEnumerable <SolutionSpec> EnumerateInitialSolutions(Polygon convexPolygon)
{
var rationalEdges = convexPolygon.Segments.Where(x => Arithmetic.IsSquare(x.QuadratOfLength)).OrderByDescending(x => x.QuadratOfLength);
foreach (var rationalEdge in rationalEdges)
{
yield return(GetInitialSolutionAtTheMiddleOfRationalEdge(convexPolygon, rationalEdge));
}
}
private static SolutionSpec GetInitialSolutionByLongestRationalEdge(Polygon problemPolygon)
{
var longestRationalEdge = problemPolygon.Segments.Where(x => Arithmetic.IsSquare(x.QuadratOfLength)).OrderBy(x => x.QuadratOfLength).LastOrDefault();
if (longestRationalEdge == null)
{
return(null);
}
return(GetInitialSolutionAtTheMiddleOfRationalEdge(problemPolygon, longestRationalEdge));
}
private void PaintSegments(Graphics g, Segment[] segments)
{
foreach (var segment in segments)
{
var color = Arithmetic.IsSquare(segment.QuadratOfLength) ? Color.Cyan : Color.Black;
PaintSegment(g, color, segment);
//PaintNode(g, color, segment.Start);
//PaintNode(g, color, segment.End);
}
}
public static KeyValuePair <Rational, double>[] ParallelGist(PointProjectionSolver solver, out double hasParallelFactor)
{
var result = new Dictionary <Rational, double>();
var segments = GetSegments(solver);
var hasParallelCount = 0;
foreach (var s1 in segments)
{
bool hasParallel = false;
foreach (var s2 in segments)
{
var sd = Arithmetic.InDistance2(s1.Start, s2);
var ed = Arithmetic.InDistance2(s1.End, s2);
if (sd.HasValue && ed.HasValue)
{
if (sd.Value == ed.Value)
{
var d = sd.Value;
if (d == 0 || d == 1)
{
continue;
}
if (!Arithmetic.IsSquare(d))
{
continue;
}
d = Arithmetic.Sqrt(d);
d = d.Reduce();
if (!result.ContainsKey(d))
{
result[d] = 0;
}
result[d]++;
if (!hasParallel)
{
hasParallelCount++;
hasParallel = true;
}
}
}
}
}
hasParallelFactor = ((double)hasParallelCount) / segments.Length;
return(result.OrderByDescending(p => p.Value).Take(3).ToArray());
}
public static SolutionSpec GetInitialSolutionAlongRationalEdge(Segment rationalEdge)
{
var initialSolution = SolutionSpec.CreateTrivial(x => x + rationalEdge.Start);
var edgeLen = new Rational(Arithmetic.Sqrt(rationalEdge.QuadratOfLength.Numerator), Arithmetic.Sqrt(rationalEdge.QuadratOfLength.Denomerator));
var a = rationalEdge.ToVector() / edgeLen;
var b = Vector.Parse("1,0");
if (b.VectorProdLength(a) == 0)
{
if (b.ScalarProd(a) > 0)
{
return(initialSolution);
}
return(initialSolution.Reflect(rationalEdge));
}
var bisect = new Segment(rationalEdge.Start, a + b + rationalEdge.Start);
return(initialSolution.Reflect(bisect).Reflect(rationalEdge));
}
public Rational Distance2To(Vector p)
{
return(Arithmetic.Distance2(p, this));
}