public static List <NurbsCurve> CurveSplit(NurbsCurve curve, double u)
{
int degree = curve.Degree;
List <Vector> controlPoints = curve.ControlPoints;
KnotArray knots = curve.Knots;
List <double> knots_to_insert = new List <double>();
for (int i = 0; i <= degree; i++)
{
knots_to_insert.Add(u);
}
NurbsCurve refinedCurve = Modify.CurveKnotRefine(curve, knots_to_insert);
int s = Eval.KnotSpan(degree, u, knots);
KnotArray knots0 = (KnotArray)refinedCurve.Knots.ToList().GetRange(0, s + degree + 2);
KnotArray knots1 = (KnotArray)refinedCurve.Knots.ToList().GetRange(0, s + 1);
List <Vector> cpts0 = refinedCurve.ControlPoints.GetRange(0, s + 1);
List <Vector> cpts1 = refinedCurve.ControlPoints.GetRange(0, s + 1);
return(new List <NurbsCurve>()
{
new NurbsCurve(degree, knots0, cpts0), new NurbsCurve(degree, knots1, cpts1)
});
}
/// <summary>
/// Check whether a given list is a valid NURBS knot vector. This also checks the validity of the end points.
/// More specifically, this method checks if the knot vector is of the following structure:
/// The knot vector must be non-decreasing and of length (degree + 1) * 2 or greater
/// [ (degree + 1 copies of the first knot), internal non-decreasing knots, (degree + 1 copies of the last knot) ]
/// </summary>
/// <param name="vector">The knot vector to test</param>
/// <param name="degree">The degree</param>
/// <returns>Whether the array is a valid knot vector or knot</returns>
public static bool IsValidKnotVector(KnotArray vector, int degree)
{
if (vector.Count == 0)
{
return(false);
}
if (vector.Count < (degree + 1) * 2)
{
return(false);
}
var rep = vector.First();
for (int i = 0; i <= degree + 1; i++)
{
if (Math.Abs(vector[i] - rep) > Constants.EPSILON)
{
return(false);
}
}
rep = vector.Last();
for (int i = vector.Count - degree - 1; i <= vector.Count; i++)
{
if (Math.Abs(vector[i] - rep) > Constants.EPSILON)
{
return(false);
}
}
return(IsNonDecreasing(vector));
}
/// <summary>
/// find the span on the knot list of the given parameter, (corresponds to algorithm 2.1 from the NURBS book, piegl & Tiller 2nd edition)
///
/// </summary>
/// <param name="n">integer number of basis functions - 1 = knots.length - degree - 2</param>
/// <param name="degree">integer degree of function</param>
/// <param name="u">parameter</param>
/// <param name="knots">array of nondecreasing knot values</param>
/// <returns>the index of the knot span</returns>
public static int KnotSpanGivenN(int n, int degree, double u, KnotArray knots)
{
if (u > knots[n + 1] - Constants.EPSILON)
{
return(n);
}
if (u < knots[degree] + Constants.EPSILON)
{
return(degree);
}
var low = degree;
var high = n + 1;
int mid = (int)Math.Floor((decimal)(low + high) / 2);
while (u < knots[mid] || u >= knots[mid + 1])
{
if (u < knots[mid])
{
high = mid;
}
else
{
low = mid;
}
mid = (int)Math.Floor((decimal)(low + high) / 2);
}
return(mid);
}
public NurbsSurface(int degreeU, int degreeV, KnotArray knotsU, KnotArray knotsV, List <List <Point> > controlPoints)
{
DegreeU = degreeU;
DegreeV = degreeV;
KnotsU = knotsU;
KnotsV = knotsV;
ControlPoints = controlPoints;
}
public Volume(int degreeU, int degreeV, int degreeW, KnotArray knotsU, KnotArray knotsV, KnotArray knotsW, List <List <List <Point> > > controlPoints)
{
DegreeU = degreeU;
DegreeV = degreeV;
DegreeW = degreeW;
KnotsU = knotsU;
KnotsV = knotsV;
KnotsW = knotsW;
ControlPoints = controlPoints;
}
public static NurbsCurve Polyline(List <Vector> points)
{
KnotArray knots = new KnotArray()
{
0.0, 0.0
};
double lsum = 0.0;
for (int i = 0; i < points.Count - 1; i++)
{
lsum += Constants.DistanceTo(points[i], points[i + 1]);
knots.Add(lsum);
}
knots.Add(lsum);
var weights = points.Select(x => 1.0).ToList();
points.ForEach(x => weights.Add(1.0));
return(new NurbsCurve(1, knots, Eval.Homogenize1d(points, weights)));
}
public static NurbsCurve RationalBezierCurve(List <Vector> controlPoints, List <double> weights = null)
{
var degree = controlPoints.Count - 1;
var knots = new KnotArray();
for (int i = 0; i < degree + 1; i++)
{
knots.Add(0.0);
}
for (int i = 0; i < degree + 1; i++)
{
knots.Add(1.0);
}
if (weights == null)
{
weights = Sets.RepeatData(1.0, controlPoints.Count);
}
return(new NurbsCurve(degree, knots, Eval.Homogenize1d(controlPoints, weights)));
weights = Constants.Rep(controlPoints.Count, 1.0);
//return new NurbsCurveData(degree, knots, Eval.Homogenize1d(controlPoints, weights));
return(null);
}
/// <summary>
/// Insert a collectioin of knots on a curve
/// corresponds to Algorithm A5.2 (Piegl & Tiller)
/// </summary>
/// <param name="curve"></param>
/// <param name="knotsToInsert"></param>
/// <returns></returns>
public static NurbsCurve CurveKnotRefine(NurbsCurve curve, List <double> knotsToInsert)
{
if (knotsToInsert.Count == 0)
{
return(curve);
}
int degree = curve.Degree;
List <Vector> controlPoints = curve.ControlPoints;
KnotArray knots = curve.Knots;
int n = controlPoints.Count - 1;
int m = n + degree + 1;
int r = knotsToInsert.Count - 1;
int a = Eval.KnotSpan(degree, knotsToInsert[0], knots);
int b = Eval.KnotSpan(degree, knotsToInsert[r], knots);
List <Vector> controlPoints_post = new List <Vector>();
KnotArray knots_post = new KnotArray();
//new control points
for (int i = 0; i <= a - degree; i++)
{
controlPoints_post[i] = controlPoints[i];
}
for (int i = b - 1; i <= n; i++)
{
controlPoints_post[i + r + 1] = controlPoints[i];
}
//new knot vector
for (int i = 0; i <= a; i++)
{
knots_post[i] = knots[i];
}
for (int i = b + degree; i <= m; i++)
{
knots_post[i + r + 1] = knots[i];
}
int g = b + degree + 1;
int k = b + degree + r;
int j = r;
while (j >= 0)
{
while (knotsToInsert[j] <= knots[g] && g > a)
{
controlPoints_post[k - degree - 1] = controlPoints[g - degree - 1];
knots_post[k] = knots[g];
k--;
g--;
}
controlPoints_post[k - degree - 1] = controlPoints_post[k - degree];
for (int i = 1; i <= degree; i++)
{
int ind = k - degree + 1;
double alfa = knots_post[k + 1] - knotsToInsert[j];
if (Math.Abs(alfa) < Constants.EPSILON)
{
controlPoints_post[ind - 1] = controlPoints_post[ind];
}
else
{
alfa = alfa / (knots_post[k + 1] - knots[g - degree + 1]);
controlPoints_post[ind - 1] = (Vector)Constants.Addition(Constants.Multiplication(controlPoints_post[ind - 1], alfa), Constants.Multiplication(controlPoints_post[ind], 1.0 - alfa));
}
}
knots_post[k] = knotsToInsert[j];
k = k - 1;
j--;
}
return(new NurbsCurve(degree, knots_post, controlPoints_post));
}
/// <summary>
/// Reverse a knot vector
/// </summary>
/// <param name="knots">An array of knots</param>
/// <returns>The reversed array of knots</returns>
public static KnotArray KnotsReverse(KnotArray knots)
{
throw new NotImplementedException();
}
public NurbsCurve(int degree, KnotArray knots, List <Vector> controlPoints)
{
Degree = degree;
ControlPoints = controlPoints;
Knots = knots;
}
/// <summary>
/// Find the span on the knot Array without supplying n
/// </summary>
/// <param name="degree">integer degree of function</param>
/// <param name="u">float parameter</param>
/// <param name="knots">array of nondecreasing knot values</param>
/// <returns></returns>
public static int KnotSpan(int degree, double u, KnotArray knots)
{
return(KnotSpanGivenN(knots.Count - degree - 2, degree, u, knots));
}