private static NurbsPoint RotateY(NurbsPoint P0, double theta)
{
var radians = theta * Math.PI / 180;
var x = (P0.X * Math.Cos(radians)) - (P0.Z * Math.Sin(radians));
var z = (P0.X * Math.Sin(radians)) + (P0.Z * Math.Cos(radians));
return(new NurbsPoint(x, P0.Y, z, P0.Weight));
}
private static NurbsPoint MiddlePoint(NurbsPoint P0, double theta)
{
var radians = theta * Math.PI / 180;
var beta = Math.Atan2(P0.Z, P0.X);
var x = (P0.X * Math.Cos(-beta)) - (P0.Z * Math.Sin(-beta));
var z = x * Math.Tan(radians / 2);
var x1 = (x * Math.Cos(beta)) - (z * Math.Sin(beta));
var z1 = (x * Math.Sin(beta)) + (z * Math.Cos(beta));
var w1 = P0.Weight * Math.Cos(radians / 2);
return(new NurbsPoint(x1, P0.Y, z1, w1));
}
public static List <NurbsPoint> Arc(NurbsPoint P0, int phi, out decimal[] knotVector)
{
var arcs = 0;
knotVector = new decimal[] { };
if (phi <= 90)
{
arcs = 1;
knotVector = new[] { 0M, 0, 0, 1, 1, 1 };
}
else if (phi <= 180)
{
arcs = 2;
knotVector = new[] { 0, 0, 0, 1M / 2, 1M / 2, 1, 1, 1 };
}
else if (phi <= 270)
{
arcs = 3;
knotVector = new[] { 0, 0, 0, 1M / 3, 1M / 3, 2M / 3, 2M / 3, 1, 1, 1 };
}
else if (phi <= 360)
{
arcs = 4;
knotVector = new[] { 0, 0, 0, 1M / 4, 1M / 4, 2M / 4, 2M / 4, 3M / 4, 3M / 4, 1, 1, 1 };
}
var theta = phi / (double)arcs;
var pointsList = new List <NurbsPoint> {
P0
};
if (arcs >= 1)
{
var P1 = SpaceLogic.MiddlePoint(pointsList.LastOrDefault(), theta);
var P2 = SpaceLogic.RotateY(pointsList.LastOrDefault(), theta);
pointsList.Add(P1);
pointsList.Add(P2);
}
if (arcs >= 2)
{
var P3 = SpaceLogic.MiddlePoint(pointsList.LastOrDefault(), theta);
var P4 = SpaceLogic.RotateY(pointsList.LastOrDefault(), theta);
pointsList.Add(P3);
pointsList.Add(P4);
}
if (arcs >= 3)
{
var P5 = SpaceLogic.MiddlePoint(pointsList.LastOrDefault(), theta);
var P6 = SpaceLogic.RotateY(pointsList.LastOrDefault(), theta);
pointsList.Add(P5);
pointsList.Add(P6);
}
if (arcs >= 4)
{
var P7 = SpaceLogic.MiddlePoint(pointsList.LastOrDefault(), theta);
var P8 = SpaceLogic.RotateY(pointsList.LastOrDefault(), theta);
pointsList.Add(P7);
pointsList.Add(P8);
}
return(pointsList);
}
public static NurbsPoint DeBoorSurface(
List <List <NurbsPoint> > controlNet,
decimal u,
decimal[] knotU,
decimal v,
decimal[] knotV)
{
var cPointsU = controlNet.First();
var cPointsV = controlNet.Transpose().First();
var p = knotU.Length - cPointsU.Count - 1;
var q = knotV.Length - cPointsV.Count - 1;
u = Math.Round(u, 21);
v = Math.Round(v, 21);
var magic = 0;
switch (u)
{
case 0:
magic += 1;
break;
case 1:
magic += 3;
break;
default:
magic += 2;
break;
}
switch (v)
{
case 0:
magic += 0;
break;
case 1:
magic += 6;
break;
default:
magic += 3;
break;
}
switch (magic)
{
case 1:
return(controlNet.First().First());
case 2:
return(NurbsLogic.DeBoor(p, controlNet.First(), u, knotU));
case 3:
return(controlNet.First().Last());
case 4:
return(NurbsLogic.DeBoor(q, controlNet.Transpose().First(), v, knotV));
case 5:
break;
case 6:
return(NurbsLogic.DeBoor(q, controlNet.Transpose().Last(), v, knotV));
case 7:
return(controlNet.Last().First());
case 8:
return(NurbsLogic.DeBoor(p, controlNet.Last(), u, knotU));
case 9:
return(controlNet.Last().Last());
default:
break;
}
var c = NurbsLogic.FindSpan(u, knotU);
var d = NurbsLogic.FindSpan(v, knotV);
var s = NurbsLogic.CheckMultiplicity(knotU, u);
var t = NurbsLogic.CheckMultiplicity(knotV, v);
NurbsPoint point;
if (u.GreaterThanOrEqualTo(knotU[c]) && u.LessThan(knotU[c + 1]) && v.GreaterThanOrEqualTo(knotV[d]) && v.LessThan(knotV[d + 1]))
{
var P = new NurbsPoint[c - s + 1, d - t + 1];
var Q = new NurbsPoint[c - s + 1];
for (var i = 0; i < P.GetLength(0); i++)
{
for (var j = 0; j < P.GetLength(1); j++)
{
P[i, j] = controlNet[j][i];
}
}
for (var i = 0; i < P.GetLength(0); i++)
{
var Pi = new List <NurbsPoint>();
for (var j = 0; j < P.GetLength(1); j++)
{
Pi.Add(P[i, j]);
}
Q[i] = NurbsLogic.DeBoor(q, Pi, v, knotV);
}
point = NurbsLogic.DeBoor(p, Q.ToList(), u, knotU);
}
else
{
// ReSharper disable once UnthrowableException
throw new IndexOutOfRangeException("u not in [u_c, u_c+1) or v not in [u_d, u_d+1)");
}
return(point);
}
