public class KnotVector : List<double>, IList<double>, ICollection<double>, IReadOnlyList<double>, IReadOnlyCollection<double>, IEnumerable<double>, IList, ICollection, IEnumerableDefault constructor.
public KnotVector()Creates an instance of the knot vector from a list of double values.
public KnotVector(IEnumerable<double> values)| Type | Name | Description |
|---|---|---|
| System.Collections.Generic.IEnumerable<System.Double> | values | Set of knots. |
Creates an instance of the knot vector given degree, number of control points and whether it is clamped or unclamped.
public KnotVector(int degree, int numberOfControlPts, bool clamped = true)| Type | Name | Description |
|---|---|---|
| System.Int32 | degree | Degree of the curve. |
| System.Int32 | numberOfControlPts | Number of control points of the curve. |
| System.Boolean | clamped | If the curve is clamped or not. |
Creates a copy of the knotVector.
public KnotVector Copy()| Type | Description |
|---|---|
| KnotVector | The copy of the knotVector. |
Gets the domain of the knot vector.
public Interval GetDomain(int degree)| Type | Name | Description |
|---|---|---|
| System.Int32 | degree | The degree of the curve. |
| Type | Description |
|---|---|
| Interval | The domain. |
Checks if the knot is clamped, so if they are in the following structure.
[ (degree + 1 copies of the first knot), internal non-decreasing knots, (degree + 1 copies of the last knot) ].
public bool IsClamped(int degree)| Type | Name | Description |
|---|---|---|
| System.Int32 | degree | Curve degree. |
| Type | Description |
|---|---|
| System.Boolean | If true the knot is clamped, if false is unclamped. |
Checks if the knot is periodic, so if they are in the following structure.
[ (degree, negative values), internal non-decreasing knots between 0 and 1, (degree, positive values bigger than 1.0) ].
public bool IsPeriodic(int degree)| Type | Name | Description |
|---|---|---|
| System.Int32 | degree |
| Type | Description |
|---|---|
| System.Boolean | If true the knot is periodic, if false is clamped or unclamped. |
Checks the validity of the input knot vector.
Confirm the relations between degree (p), number of control points(n+1), and the number of knots (m+1).
Refer to The NURBS Book (2nd Edition), p.50 for details.
More specifically, this method checks if the knot vector is of the following structure:
The knot knots must be non-decreasing and of length (degree + 1) * 2 or greater
public bool IsValid(int degree, int numberOfControlPts)| Type | Name | Description |
|---|---|---|
| System.Int32 | degree | The degree of the curve. |
| System.Int32 | numberOfControlPts |
| Type | Description |
|---|---|
| System.Boolean | Whether the knots are valid. |
Returns the multiplicity values of the all knots in this knot vector.
public Dictionary<double, int> Multiplicities()| Type | Description |
|---|---|
| System.Collections.Generic.Dictionary<System.Double, System.Int32> | Dictionary of [knot, multiplicity]. |
Calculates the multiplicity of a knot.
public int Multiplicity(double knot)| Type | Name | Description |
|---|---|---|
| System.Double | knot | The index of the knot to determine multiplicity. |
| Type | Description |
|---|---|
| System.Int32 | The multiplicity of the knot, or 0 if the knot is not part of the knot vector. |
Normalizes the input knot vector to a range from 0.0 to 1.0.
public KnotVector Normalize()| Type | Description |
|---|---|
| KnotVector | Normalized knots vector. |
Performs a knot refinement on a curve, inserting knots and updating the control point locations.
Implementation of Algorithm A5.4 of The NURBS Book by Piegl and Tiller.
public static NurbsBase Refine(NurbsBase curve, IList<double> knotsToInsert)| Type | Name | Description |
|---|---|---|
| NurbsBase | curve | The curve object. |
| System.Collections.Generic.IList<System.Double> | knotsToInsert | The set of knots. |
| Type | Description |
|---|---|
| NurbsBase | A curve with refined knots. |
Performs a knot refinement on a surface by inserting knots at various parameters and updating the control point locations.
Implementation of Algorithm A5.5 of The NURBS Book by Piegl and Tiller.
ToDo: refactor this algo following the book.
public static NurbsSurface Refine(NurbsSurface surface, IList<double> knotsToInsert, SurfaceDirection direction)| Type | Name | Description |
|---|---|---|
| NurbsSurface | surface | The surface object to insert the knots. |
| System.Collections.Generic.IList<System.Double> | knotsToInsert | The set of knots to insert. |
| SurfaceDirection | direction | Whether to insert in the U or V direction of the surface. |
| Type | Description |
|---|---|
| NurbsSurface | A surface with the knots inserted. |
Reverses the order of the knot vector.
public static KnotVector Reverse(KnotVector knots)| Type | Name | Description |
|---|---|---|
| KnotVector | knots | Knot vectors to be reversed. |
| Type | Description |
|---|---|
| KnotVector | Reversed knot vectors. |
Finds the span of the knot vector from curve degree and a parameter u on the curve.
public int Span(int degree, double u)| Type | Name | Description |
|---|---|---|
| System.Int32 | degree | Curve degree. |
| System.Double | u | Parameter on curve. |
| Type | Description |
|---|---|
| System.Int32 | The index of the knot span. |
Finds the span on the knot vector of the given parameter.
Corresponds to algorithm 2.1 from the NURBS book by Piegl and Tiller.
public int Span(int n, int degree, double parameter)| Type | Name | Description |
|---|---|---|
| System.Int32 | n | Number of basis functions. |
| System.Int32 | degree | Degree of function. |
| System.Double | parameter | Parameter. |
| Type | Description |
|---|---|
| System.Int32 | The index of the knot span. |
Creates a text representation of the knot vector.
public override string ToString()| Type | Description |
|---|---|
| System.String | Knots in a string version. |
Generates a periodic uniform spaced knot vectors.
public static KnotVector UniformPeriodic(int degree, int numberOfControlPts)| Type | Name | Description |
|---|---|---|
| System.Int32 | degree | Degree. |
| System.Int32 | numberOfControlPts | Number of control points. |
| Type | Description |
|---|---|
| KnotVector |