private static ulong GetMinHsf(Vector3D v)
{
var hsfAll = Numerics.GetHighestSquareFactorOfAll(
new[] { (ulong)Math.Abs(Math.Round(v.X)), (ulong)Math.Abs(Math.Round(v.Y)), (ulong)Math.Abs(Math.Round(v.Z)) }
.Where(h => h > 0).ToArray());
return(hsfAll);
}
public static ulong GetSurfacePoints(Cube c)
{
var s = (ulong)c.A.Length;
var s3 = s * s * s;
var hsf = Numerics.GetHighestSquareFactor(s);
var surfacePoints = s3 - (hsf + 2) * s + hsf + 1;
return(surfacePoints);
}
private bool CalcIsPrimitive()
{
var nonZeroSides = Sides.Where(s => s != 0).ToArray();
for (int f = 2; f <= (int)Math.Ceiling((double)Sides.Max()); f++)
{
if (nonZeroSides.All(s => Numerics.IsIntegral((double)s / f)))
{
return(false);
}
}
return(true);
}
public static bool IsIntegral(Vector3D v)
{
var isIntegral = Numerics.IsIntegral(v.X) && Numerics.IsIntegral(v.Y) && Numerics.IsIntegral(v.Z);
return(isIntegral);
}
public void FindTwins()
{
using (var cmd = new SqlCommand("delete primitivetripletwins", sqlConnection))
{
cmd.ExecuteNonQuery();
}
double count = 0, tot = 853831;
var twinFields = new string[] { "ux", "uy", "uz", "vx", "vy", "vz", "nx", "ny", "nz" };
var twinFieldParamNames = twinFields.Select(s => "@" + s).ToArray();
using (var cmd = new SqlCommand("select A,B,C,[Square] from primitivetriples", sqlConnection))
using (var cmdAlt = new SqlCommand(
"select a,b,c " +
"from primitivetriplepermutations " +
"where [square] = @square", sqlConnection))
using (var cmdIns = new SqlCommand($"insert primitivetripletwins({twinFields.ToCsvString()}) values({twinFieldParamNames.ToCsvString()})", sqlConnection))
{
var altSqParam = cmdAlt.Parameters.Add("@square", SqlDbType.Int);
var twin = twinFieldParamNames.ToDictionary(s => s, s => cmdIns.Parameters.Add(s, SqlDbType.Int));
using (var rs = cmd.ExecuteReader())
while (rs.Read())
{
Console.Write($"\r{count++/tot:0.00%} ");
var a = Convert.ToInt32(rs["A"]);
var b = Convert.ToInt32(rs["B"]);
var c = Convert.ToInt32(rs["C"]);
var square = Convert.ToInt32(rs["square"]);
var v1 = new Vector3D(a, b, c);
altSqParam.Value = square;
bool found = false;
using (var rsAlt = cmdAlt.ExecuteReader())
while (!found && rsAlt.Read())
{
var altA = Convert.ToInt32(rsAlt["A"]);
var altB = Convert.ToInt32(rsAlt["B"]);
var altC = Convert.ToInt32(rsAlt["C"]);
var v2 = new Vector3D(altA, altB, altC);
if (v1.IsAtRightAnglesTo(v2))
{
var cp = Vector3D.CrossProduct(v1, v2);
cp *= (v1.Length / cp.Length);
if (Numerics.IsIntegral(cp.X) && Numerics.IsIntegral(cp.Y) && Numerics.IsIntegral(cp.Z))
{
//found
twin["@ux"].Value = a;
twin["@uy"].Value = b;
twin["@uz"].Value = c;
twin["@vx"].Value = altA;
twin["@vy"].Value = altB;
twin["@vz"].Value = altC;
twin["@nx"].Value = (int)Math.Round(cp.X);
twin["@ny"].Value = (int)Math.Round(cp.Y);
twin["@nz"].Value = (int)Math.Round(cp.Z);
cmdIns.ExecuteNonQuery();
found = true;
}
}
}
if (!found)
{
throw new InvalidOperationException($"No twin vector found for {v1}");
}
}
}
}
