A vector of knots in one dimension, with B-spline basis functions of a prescribed order.
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| | KnotVector () |
| | Create an empty KnotVector.
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| | KnotVector (std::istream &input) |
| | Create a KnotVector by reading data from stream input. Two integers are read, for order and number of control points.
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| | KnotVector (int order, int NCP) |
| | Create a KnotVector with undefined knots (initialized to -1) of order order and number of control points NCP.
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| | KnotVector (int order, const Vector &intervals, const Array< int > &continuity) |
| | Create a KnotVector by passing in a degree, a Vector of interval lengths of length n, and a list of continuity of length n + 1.
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| | KnotVector (const KnotVector &kv) |
| | Copy constructor.
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| KnotVector & | operator= (const KnotVector &kv) |
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| int | GetNE () const |
| | Return the number of elements, defined by distinct knots.
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| int | GetNCP () const |
| | Return the number of control points.
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| int | GetOrder () const |
| | Return the order.
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| int | Size () const |
| | Return the number of knots, including multiplicities.
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| void | GetElements () |
| | Count the number of elements.
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| bool | isElement (int i) const |
| | Return whether the knot index Order plus i is the beginning of an element.
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| int | GetNKS () const |
| | Return the number of control points minus the order. This is not the number of knot spans, but it gives the number of knots to be checked with isElement for non-empty knot spans (elements).
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| real_t | getKnotLocation (real_t xi, int ni) const |
| | Return the parameter for element reference coordinate xi in [0,1], for the element beginning at knot ni.
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| int | findKnotSpan (real_t u) const |
| | Return the index of the knot span containing parameter u.
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| void | CalcShape (Vector &shape, int i, real_t xi) const |
| | Calculate the nonvanishing shape function values in shape for the element corresponding to knot index i and element reference coordinate xi.
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| void | CalcDShape (Vector &grad, int i, real_t xi) const |
| | Calculate derivatives of the nonvanishing shape function values in grad for the element corresponding to knot index i and element reference coordinate xi.
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| void | CalcDnShape (Vector &gradn, int n, int i, real_t xi) const |
| | Calculate n-th derivatives (order n) of the nonvanishing shape function values in grad for the element corresponding to knot index i and element reference coordinate xi.
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| void | CalcD2Shape (Vector &grad2, int i, real_t xi) const |
| | Calculate second-order shape function derivatives, using CalcDnShape.
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| void | FindMaxima (Array< int > &ks, Vector &xi, Vector &u) const |
| | Gives the locations of the maxima of the KnotVector in reference space. The function gives the knot span ks, the coordinate in the knot span xi, and the coordinate of the maximum in parameter space u.
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| void | FindInterpolant (Array< Vector * > &x) |
| | Global curve interpolation through the points x (overwritten). x is an array with the length of the spatial dimension containing vectors with spatial coordinates. The control points of the interpolated curve are returned in x in the same form.
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| void | Difference (const KnotVector &kv, Vector &diff) const |
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| void | UniformRefinement (Vector &newknots, int rf) const |
| | Uniformly refine by factor rf, by inserting knots in each span.
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| void | Refinement (Vector &newknots, int rf) const |
| | Refine with refinement factor rf.
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| int | GetCoarseningFactor () const |
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| Vector | GetFineKnots (const int cf) const |
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| KnotVector * | DegreeElevate (int t) const |
| | Return a new KnotVector with elevated degree by repeating the endpoints of the KnotVector.
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| void | Flip () |
| | Reverse the knots.
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| void | Print (std::ostream &os) const |
| | Print the order, number of control points, and knots.
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| void | PrintFunctions (std::ostream &os, int samples=11) const |
| | Prints the non-zero shape functions and their first and second derivatives associated with the KnotVector per element. Use GetElements() to count the elements before using this function. samples is the number of samples of the shape functions per element.
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| | ~KnotVector () |
| | Destroys KnotVector.
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| real_t & | operator[] (int i) |
| | Access function to knot i.
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| const real_t & | operator[] (int i) const |
| | Const access function to knot i.
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A vector of knots in one dimension, with B-spline basis functions of a prescribed order.
- Note
- Order is defined in the sense of "The NURBS book" - 2nd ed - Piegl and Tiller, cf. section 2.2.
Definition at line 39 of file nurbs.hpp.
1.11.0