/// <summary>
/// The points index example is as following.
/// The reason for this setting is to look at the coordinate like points[x][y].
/// As a result, The number of U count is 3 and that of V count is 5.
///
/// 3*---7*--11*
/// | | |
/// 2*---6*--10*
/// | | |
/// 1*---5*---9*
/// | | |
/// 0*---4*---8*
///
/// </summary>
/// <param name="_pointsGrid"></param>
public NURBSSurface(IEnumerable <IEnumerable <IEnumerable <double> > > _pointsGrid, KnotSet uKnotVector, KnotSet vKnotVector, int uDegree, int vDegree, IEnumerable <IEnumerable <double> > _weights)
{
List <List <Point3d> > ptss = new List <List <Point3d> >();
List <List <double> > wss = new List <List <double> >();
for (int i = 0; i < _pointsGrid.Count(); i++)
{
wss.Add(new List <double>());
var ws = _weights.ElementAt(i);
ptss.Add(new List <Point3d>());
var pts = _pointsGrid.ElementAt(i);
for (int j = 0; j < pts.Count(); j++)
{
double w = ws.ElementAt(j);
wss.Last().Add(w);
IEnumerable <double> pt = pts.ElementAt(j);
Point3d target = new Point3d(pt);
ptss.Last().Add(target);
}
}
this.pointsGrid = ptss.Select(n => n.ToArray()).ToArray();
this.weights = wss.Select(n => n.ToArray()).ToArray();
this.uKnotVector = (KnotSet)uKnotVector.Clone();
this.vKnotVector = (KnotSet)vKnotVector.Clone();
this.uDegree = uDegree;
this.vDegree = vDegree;
}
public void CreateToUniform()
{
KnotSet knotSet = null;
int degree = int.MinValue;
int numControlPoints = int.MinValue;
double[] r = null;
double[] a = null;
numControlPoints = 3;
degree = 2;
knotSet = KnotSet.CreateToUniform(degree, numControlPoints);
r = knotSet.GetKnotArray();
a = new double[] { 0, 0, 0, 1, 1, 1 };
Assert.IsTrue(r.SequenceEqual(a));
numControlPoints = 4;
degree = 2;
knotSet = KnotSet.CreateToUniform(degree, numControlPoints);
r = knotSet.GetKnotArray();
a = new double[] { 0, 0, 0, 0.5, 1, 1, 1 };
Assert.IsTrue(r.SequenceEqual(a));
numControlPoints = 8;
degree = 3;
knotSet = KnotSet.CreateToUniform(degree, numControlPoints);
r = knotSet.GetKnotArray();
a = new double[] { 0, 0, 0, 0, 0.2, 0.4, 0.6, 0.8, 1, 1, 1, 1 };
Assert.IsTrue(r.SequenceEqual(a));
}
public void IsValid()
{
double[] knots = null;
KnotSet knotSet = null;
bool r;
bool a;
knots = new double[] { 1, 0, 3, 4 };
knotSet = new KnotSet(knots);
r = false;
a = knotSet.IsValid();
Assert.IsTrue(r == a);
knots = new double[] { 1, 2, 3, 2 };
knotSet = new KnotSet(knots);
r = false;
a = knotSet.IsValid();
Assert.IsTrue(r == a);
knots = new double[] { 1, 1, 3, 3 };
knotSet = new KnotSet(knots);
r = true;
a = knotSet.IsValid();
Assert.IsTrue(r == a);
}
public void GetIndexOf()
{
double[] knots = null;
KnotSet knotSet = null;
double r;
double a;
knots = new double[] { 1, 2, 3, 4 };
knotSet = new KnotSet(knots);
r = knotSet.GetIndexOf(1);
a = 2;
Assert.IsTrue(r == a);
knots = new double[] { 1, 2, 3, 4 };
knotSet = new KnotSet(knots);
Assert.ThrowsException <ArgumentOutOfRangeException>(() => knotSet.GetIndexOf(-1));
knots = new double[] { 1, 2, 3, 4 };
knotSet = new KnotSet(knots);
Assert.ThrowsException <ArgumentOutOfRangeException>(() => knotSet.GetIndexOf(5));
knots = new double[] { 1, 2, 3, 4 };
knotSet = new KnotSet(knots, false);
r = knotSet.GetIndexOf(-1);
a = 1;
Assert.IsTrue(r == a);
knots = new double[] { 1, 2, 3, 4 };
knotSet = new KnotSet(knots, false);
r = knotSet.GetIndexOf(7);
a = 4;
Assert.IsTrue(r == a);
}
/// <summary>
/// Cox-de Boor recursion formula implementation.
/// </summary>
protected Func <double, double> GetBasis(int i, int j, KnotSet knots)
{
Func <double, double> func = (t) =>
{
double t_i = knots.GetIndexOf(i);
double t_iplus1 = knots.GetIndexOf(i + 1);
if (j == 0)
{
if (t_i <= t && t < t_iplus1)
{
return(1);
}
else
{
return(0);
}
}
double coef1 = GetCoef(i, j, t, knots);
double coef2 = 1 - GetCoef(i + 1, j, t, knots);
Func <double, double> firstTerm = GetBasis(i, j - 1, knots);
Func <double, double> secondTerm = GetBasis(i + 1, j - 1, knots);
double first = firstTerm(t);
double second = secondTerm(t);
return(coef1 * first + coef2 * second);
};
return(func);
}
/// <summary>
/// Cox-de Boor recursion formula implementation.
/// </summary>
protected double GetCoef(int i, int j, double t, KnotSet knots)
{
if (knots.GetIndexOf(i + j) == knots.GetIndexOf(i))
{
return(0);
}
return((double)(t - knots.GetIndexOf(i)) / (double)(knots.GetIndexOf(i + j) - knots.GetIndexOf(i)));
}
protected override Func <double, double> GetBasisFunction(BasisInfo _info)
{
BSplineBasisInfo info = (BSplineBasisInfo)_info;
int i = info.I;
int j = info.J;
KnotSet knots = info.Knots;
Func <double, double> basis = GetBasis(i, j, knots);
return(basis);
}
public void GetMaxKnot()
{
KnotSet knots;
double[] vec;
double r, a;
vec = new double[] { 0, 1, 2, 3, 4 };
knots = new KnotSet(vec);
r = knots.GetMaxKnot();
a = 4;
Assert.IsTrue(r == a);
}
public BSplineCurve(IEnumerable <IEnumerable <double> > pts, KnotSet knots, int degree)
{
var pointList = new List <Point3d>();
foreach (var pt in pts)
{
Point3d pt3d = new Point3d(pt.ToArray());
pointList.Add(pt3d);
}
this.points = pointList.ToArray();
this.knotVector = (KnotSet)knots.Clone();
this.degree = degree;
}
public void GetKnotArray()
{
double[] knots = null;
KnotSet knotSet = null;
double[] r;
double[] a;
knots = new double[] { 1, 2, 3, 2 };
knotSet = new KnotSet(knots);
r = knotSet.GetKnotArray();
a = new double[] { 1, 2, 3, 2 };
Assert.IsTrue(r.SequenceEqual(a));
}
public void BSplineCurve()
{
double[][] pts = null;
KnotSet knotset = null;
int degree = int.MinValue;
BSplineCurve bSpline = null;
pts = new double[][]
{
new double[] { 0, 0, 0 },
new double[] { 2, 4, 0 },
new double[] { 4, 0, 0 },
new double[] { 6, 4, 0 },
};
knotset = new KnotSet(new double[] { 0, 0, 0, 0, 1, 1, 1, 1 });
degree = 3;
bSpline = new BSplineCurve(pts, knotset, degree);
}
public void NURBSCurve()
{
double[][] pts = null;
KnotSet knotset = null;
int degree = int.MinValue;
NURBSCurve bSpline = null;
double[] weights = null;
pts = new double[][]
{
new double[] { 0, 0, 0 },
new double[] { 2, 4, 0 },
new double[] { 4, 0, 0 },
new double[] { 6, 4, 0 },
};
knotset = new KnotSet(new double[] { 0, 0, 0, 0, 1, 1, 1, 1 });
weights = new double[] { 1, 1, 1, 1 };
degree = 3;
bSpline = new NURBSCurve(pts, knotset, weights, degree);
}
public void ParameterAt()
{
double[][][] ptGrid = null;
double[] r, a;
double u, v, e;
BSplineSurface surface = null;
int uDegree, vDegree;
KnotSet uKnot, vKnot;
uDegree = 2;
vDegree = 3;
uKnot = KnotSet.CreateToUniform(uDegree, 3);
vKnot = KnotSet.CreateToUniform(vDegree, 5);
ptGrid = new double[][][]
{
new double[][] {
new double[] { 0.0, 0.0, 1.0 },
new double[] { 0.0, 1.0, 2.0 },
new double[] { 0.0, 2.0, 0.0 },
new double[] { 0.0, 3.0, 1.0 },
new double[] { 0.0, 4.0, 1.0 },
},
new double[][] {
new double[] { 1.0, 0.0, 2.0 },
new double[] { 1.0, 1.0, 2.0 },
new double[] { 1.0, 2.0, 1.0 },
new double[] { 1.0, 3.0, 1.0 },
new double[] { 1.0, 4.0, 1.0 },
},
new double[][] {
new double[] { 2.0, 0.0, 2.0 },
new double[] { 2.0, 1.0, 1.0 },
new double[] { 2.0, 2.0, 1.0 },
new double[] { 2.0, 3.0, 1.0 },
new double[] { 2.0, 4.0, 2.0 },
},
};
u = 0.3;
v = 0.4;
e = 0.0001;
surface = new BSplineSurface(ptGrid, uKnot, vKnot, uDegree, vDegree);
r = surface.ParameterAt(u, v);
a = new double[] { 0.6, 1.696, 1.16312 };
Assert.IsTrue(r.SequenceEqual(a, e));
uDegree = 2;
vDegree = 3;
uKnot = KnotSet.CreateToUniform(uDegree, 3);
vKnot = KnotSet.CreateToUniform(vDegree, 5);
ptGrid = new double[][][]
{
new double[][] {
new double[] { 0.0, 0.0, 1.0 },
new double[] { 0.0, 1.0, 2.0 },
new double[] { 0.0, 2.0, 0.0 },
new double[] { 0.0, 3.0, 1.0 },
new double[] { 0.0, 4.0, 1.0 },
},
new double[][] {
new double[] { 1.0, 0.0, 2.0 },
new double[] { 1.0, 1.0, 2.0 },
new double[] { 1.0, 2.0, 1.0 },
new double[] { 1.0, 3.0, 1.0 },
new double[] { 1.0, 4.0, 1.0 },
},
new double[][] {
new double[] { 2.0, 0.0, 2.0 },
new double[] { 2.0, 1.0, 1.0 },
new double[] { 2.0, 2.0, 1.0 },
new double[] { 2.0, 3.0, 1.0 },
new double[] { 2.0, 4.0, 2.0 },
},
};
u = 1;
v = 0;
e = 0.0001;
surface = new BSplineSurface(ptGrid, uKnot, vKnot, uDegree, vDegree);
r = surface.ParameterAt(u, v);
a = new double[] { 2, 0, 2 };
Assert.IsTrue(r.SequenceEqual(a, e));
uDegree = 2;
vDegree = 3;
uKnot = KnotSet.CreateToUniform(uDegree, 3);
vKnot = KnotSet.CreateToUniform(vDegree, 5);
ptGrid = new double[][][]
{
new double[][] {
new double[] { 0.0, 0.0, 1.0 },
new double[] { 0.0, 1.0, 2.0 },
new double[] { 0.0, 2.0, 0.0 },
new double[] { 0.0, 3.0, 1.0 },
new double[] { 0.0, 4.0, 1.0 },
},
new double[][] {
new double[] { 1.0, 0.0, 2.0 },
new double[] { 1.0, 1.0, 2.0 },
new double[] { 1.0, 2.0, 1.0 },
new double[] { 1.0, 3.0, 1.0 },
new double[] { 1.0, 4.0, 1.0 },
},
new double[][] {
new double[] { 2.0, 0.0, 2.0 },
new double[] { 2.0, 1.0, 1.0 },
new double[] { 2.0, 2.0, 1.0 },
new double[] { 2.0, 3.0, 1.0 },
new double[] { 2.0, 4.0, 2.0 },
},
};
u = 1;
v = 1;
e = 0.0001;
surface = new BSplineSurface(ptGrid, uKnot, vKnot, uDegree, vDegree);
r = surface.ParameterAt(u, v);
a = new double[] { 2, 4, 2 };
Assert.IsTrue(r.SequenceEqual(a, e));
}
public void ParameterAt()
{
double[][] pts = null;
KnotSet knotset = null;
int degree = int.MinValue;
BSplineCurve bSpline = null;
double[] r, a;
double t;
double e;
pts = new double[][]
{
new double[] { 0, 0, 0 },
new double[] { 2, 4, 0 },
new double[] { 4, 0, 0 },
new double[] { 6, 4, 0 },
};
knotset = new KnotSet(new double[] { 0, 0, 0, 0, 1, 1, 1, 1 });
degree = 3;
bSpline = new BSplineCurve(pts, knotset, degree);
t = 0.5;
a = new double[] { 3, 2, 0 };
r = bSpline.ParameterAt(t);
Assert.IsTrue(a.SequenceEqual(r));
pts = new double[][]
{
new double[] { 0, 0, 0 },
new double[] { 2, 4, 0 },
new double[] { 4, 0, 0 },
new double[] { 6, 4, 0 },
};
knotset = new KnotSet(new double[] { 0, 0, 0, 0, 1, 1, 1, 1 });
degree = 3;
bSpline = new BSplineCurve(pts, knotset, degree);
t = 0.384;
a = new double[] { 2.3040000000000003, 1.9750256640000001, 0 };
r = bSpline.ParameterAt(t);
e = 0.0001;
Assert.IsTrue(a.SequenceEqual(r, e));
pts = new double[][]
{
new double[] { 0, 0, 0 },
new double[] { 2, 4, 0 },
new double[] { 4, 0, 0 },
new double[] { 6, 4, 0 },
};
knotset = new KnotSet(new double[] { 0, 0, 0, 0, 1, 1, 1, 1 });
degree = 3;
bSpline = new BSplineCurve(pts, knotset, degree);
t = 0.884;
a = new double[] { 5.304, 2.905969664, 0 };
r = bSpline.ParameterAt(t);
e = 0.0001;
Assert.IsTrue(a.SequenceEqual(r, e));
pts = new double[][]
{
new double[] { 1, 0, 0 },
new double[] { 2, 4, 0 },
new double[] { 4, 0, 0 },
new double[] { 6, 4, 0 },
};
knotset = new KnotSet(new double[] { 0, 0, 0, 0, 1, 1, 1, 1 });
degree = 3;
bSpline = new BSplineCurve(pts, knotset, degree);
t = 0;
a = new double[] { 1, 0, 0 };
r = bSpline.ParameterAt(t);
e = 0.0001;
Assert.IsTrue(a.SequenceEqual(r, e));
pts = new double[][]
{
new double[] { 1, 0, 0 },
new double[] { 2, 4, 0 },
new double[] { 6, 4, 0 },
};
knotset = new KnotSet(new double[] { 0, 0, 0, 1, 1, 1 });
degree = 2;
bSpline = new BSplineCurve(pts, knotset, degree);
t = 0;
a = new double[] { 1, 0, 0 };
r = bSpline.ParameterAt(t);
e = 0.0001;
Assert.IsTrue(a.SequenceEqual(r, e));
pts = new double[][]
{
new double[] { 0, 0, 0 },
new double[] { 2, 4, 0 },
new double[] { 6, 4, 0 },
};
knotset = new KnotSet(new double[] { 0, 0, 0, 1, 1, 1 });
degree = 2;
bSpline = new BSplineCurve(pts, knotset, degree);
t = 1;
a = new double[] { 6, 4, 0 };
r = bSpline.ParameterAt(t);
e = 0.0001;
Assert.IsTrue(a.SequenceEqual(r, e));
}
public void ParameterAt()
{
double[][] pts = null;
double[] weights = null;
KnotSet knotset = null;
int degree = int.MinValue;
NURBSCurve nurbs = null;
double[] r, a;
double t, e;
pts = new double[][]
{
new double[] { 0, 0, 0 },
new double[] { 2, 4, 0 },
new double[] { 4, 0, 0 },
};
weights = new double[] { 1, 3, 1 };
knotset = new KnotSet(new double[] { 0, 0, 0, 1, 1, 1 });
degree = 2;
nurbs = new NURBSCurve(pts, knotset, weights, degree);
t = 0.5;
a = new double[] { 2, 3, 0 };
r = nurbs.ParameterAt(t);
Assert.IsTrue(a.SequenceEqual(r));
pts = new double[][]
{
new double[] { 0, 0, 0 },
new double[] { 2, 4, 0 },
new double[] { 4, 0, 0 },
};
weights = new double[] { 1, 3, 1 };
knotset = new KnotSet(new double[] { 0, 0, 0, 1, 1, 1 });
degree = 2;
nurbs = new NURBSCurve(pts, knotset, weights, degree);
t = 1;
a = new double[] { 4, 0, 0 };
r = nurbs.ParameterAt(t);
e = 0.0001;
Assert.IsTrue(a.SequenceEqual(r, e));
pts = new double[][]
{
new double[] { 0, 0, 0 },
new double[] { 2, 4, 0 },
new double[] { 6, 4, 0 },
};
weights = new double[] { 1, 1, 1 };
knotset = new KnotSet(new double[] { 0, 0, 0, 1, 1, 1 });
degree = 2;
nurbs = new NURBSCurve(pts, knotset, weights, degree);
t = 1;
a = new double[] { 6, 4, 0 };
r = nurbs.ParameterAt(t);
e = 0.0001;
Assert.IsTrue(a.SequenceEqual(r, e));
pts = new double[][]
{
new double[] { 0.0, 0.0, 0.0 },
new double[] { 4.0, 5.0, 0.0 },
new double[] { 6.0, 1.0, 0.0 },
new double[] { 9.0, 5.0, 0.0 },
new double[] { 11.0, 3.0, 0.0 },
new double[] { 16.0, 4.0, 0.0 },
};
weights = new double[] { 1, 3, 1, 3, 1, 2 };
knotset = new KnotSet(new double[] { 0, 0, 0, 0, 1d / 3d, 2d / 3d, 1, 1, 1, 1 });
degree = 3;
nurbs = new NURBSCurve(pts, knotset, weights, degree);
t = 0.3;
a = new double[] { 5.52901, 3.849042, 0.0 };
r = nurbs.ParameterAt(t);
e = 0.0001;
Assert.IsTrue(Math.Abs(a[0] - r[0]) < e);
Assert.IsTrue(Math.Abs(a[1] - r[1]) < e);
Assert.IsTrue(Math.Abs(a[2] - r[2]) < e);
pts = new double[][]
{
new double[] { 0.0, 0.0, 0.0 },
new double[] { 4.0, 5.0, 0.0 },
new double[] { 6.0, 1.0, 0.0 },
new double[] { 9.0, 5.0, 0.0 },
new double[] { 11.0, 3.0, 0.0 },
new double[] { 16.0, 4.0, 0.0 },
};
weights = new double[] { 1, 3, 1, 3, 1, 2 };
knotset = new KnotSet(new double[] { 0, 0, 0, 0, 1d / 3d, 2d / 3d, 1, 1, 1, 1 });
degree = 3;
nurbs = new NURBSCurve(pts, knotset, weights, degree);
t = 0.3948;
a = new double[] { 6.9053986159719711, 3.6972003072706183, 0.0 };
r = nurbs.ParameterAt(t);
e = 0.0001;
Assert.IsTrue(r.SequenceEqual(a, e));
pts = new double[][]
{
new double[] { 0.0, 0.0, 0.0 },
new double[] { 4.0, 5.0, 0.0 },
new double[] { 6.0, 1.0, 0.0 },
new double[] { 9.0, 5.0, 0.0 },
new double[] { 11.0, 3.0, 0.0 },
new double[] { 16.0, 4.0, 0.0 },
};
weights = new double[] { 1, 3, 1, 3, 1, 2 };
knotset = new KnotSet(new double[] { 0, 0, 0, 0, 1d / 3d, 2d / 3d, 1, 1, 1, 1 });
degree = 3;
nurbs = new NURBSCurve(pts, knotset, weights, degree);
t = 1;
a = new double[] { 16, 4, 0 };
r = nurbs.ParameterAt(t);
e = 0.0001;
Assert.IsTrue(r.SequenceEqual(a, e));
}
public BSplineBasisInfo(int i, int j, KnotSet knots)
{
this.I = i;
this.J = j;
this.Knots = (KnotSet)knots.Clone();
}