BSplineCurve.h

```
// Geometric Tools, LLC
// Copyright (c) 1998-2012
// Distributed under the Boost Software License, Version 1.0.
#pragma once
#include "NURBSGlobal.h"
#include "SingleCurve.h"
#include "BSplineBasis.h"
namespace NURBS
{
template <typename Real>
class BSplineCurve : public SingleCurve<Real>
{
public:
// Construction and destruction. The caller is responsible for deleting
// the input arrays if they were dynamically allocated. Internal copies
// of the arrays are made, so to dynamically change control points or
// knots you must use the 'SetControlPoint', 'GetControlPoint', and
// 'Knot' member functions.
// Uniform spline. The number of control points is n+1 >= 2. The degree
// of the B-spline is d and must satisfy 1 <= d <= n. The knots are
// implicitly calculated in [0,1]. If open is 'true', the spline is
// open and the knots are
// t[i] = 0, 0 <= i <= d
// (i-d)/(n+1-d), d+1 <= i <= n
// 1, n+1 <= i <= n+d+1
// If open is 'false', the spline is periodic and the knots are
// t[i] = (i-d)/(n+1-d), 0 <= i <= n+d+1
// If loop is 'true', extra control points are added to generate a closed
// curve. For an open spline, the control point array is reallocated and
// one extra control point is added, set to the first control point
// C[n+1] = C[0]. For a periodic spline, the control point array is
// reallocated and the first d points are replicated. In either case the
// knot array is calculated accordingly.
BSplineCurve (int numCtrlPoints, const Array1D_Vector3& ctrlPoint,
int degree, bool loop, bool open);
// Open, nonuniform spline. The knot array must have n-d elements. The
// elements must be nondecreasing. Each element must be in [0,1].
BSplineCurve (int numCtrlPoints, const Array1D_Vector3& ctrlPoint,
int degree, bool loop, const Real* knot);
int GetNumCtrlPoints () const;
int GetDegree () const;
bool IsOpen () const;
bool IsUniform () const;
bool IsLoop () const;
// Control points may be changed at any time. The input index should be
// valid (0 <= i <= n). If it is invalid, GetControlPoint returns a
// vector whose components are all MAX_REAL.
void SetControlPoint (int i, const Vector3& ctrl);
Vector3 GetControlPoint (int i) const;
// The knot values can be changed only if the basis function is nonuniform
// and the input index is valid (0 <= i <= n-d-1). If these conditions
// are not satisfied, GetKnot returns MAX_REAL.
void SetKnot (int i, Real knot);
Real GetKnot (int i) const;
Array1D_Real GetKnotVector(bool isInnerOnly = true);
// The spline is defined for 0 <= t <= 1. If a t-value is outside [0,1],
// an open spline clamps t to [0,1]. That is, if t > 1, t is set to 1;
// if t < 0, t is set to 0. A periodic spline wraps to to [0,1]. That
// is, if t is outside [0,1], then t is set to t-floor(t).
virtual Vector3 GetPosition (Real t) ;
virtual Vector3 GetFirstDerivative (Real t) ;
virtual Vector3 GetSecondDerivative (Real t) ;
virtual Vector3 GetThirdDerivative (Real t) ;
// If you need position and derivatives at the same time, it is more
// efficient to call these functions. Pass the addresses of those
// quantities whose values you want. You may pass 0 in any argument
// whose value you do not want.
void Get (Real t, Vector3* pos, Vector3* der1,
Vector3* der2, Vector3* der3);
// Access the basis function to compute it without control points. This
// is useful for least squares fitting of curves.
BSplineBasis<Real>& GetBasis ();
protected:
// Replicate the necessary number of control points when the Create
// function has loop equal to true, in which case the spline curve must
// be a closed curve.
void CreateControl (const Array1D_Vector3& ctrlPoint);
int mNumCtrlPoints;
Array1D_Vector3 mCtrlPoint; // ctrl[n+1]
bool mLoop;
BSplineBasis<Real> mBasis;
int mReplicate; // the number of replicated control points
};
typedef BSplineCurve<float> BSplineCurvef;
typedef BSplineCurve<double> BSplineCurved;
}
```