// Open, nonuniform spline, that takes external knot vector.
//
// if bIsInteriorKnot, the knot array must have n-d-1 elements, the standard start/end
// sequences of #degree 0/1 knots will be automatically added by internal BSplineBasis.
//
// if !bIsInteriorKnot, the knot array must have n+d+1 elements and is used directly.
//
// eg for 7 control points degree-3 curve the full knot vector would be [0 0 0 0 a b c 1 1 1 1],
// and the interior knot vector would be [a b c].
//
// The knot elements must be nondecreasing. Each element must be in [0,1]. Note that
// knot vectors can be arbitrary normalized by dividing by the largest knot, if
// you have a knot vector with values > 1
//
// loop=true duplicates the first control point to force loop closure, however this
// was broken in the WildMagic code because it didn't add a knot. I am not
// quite sure what to do here - a new non-1 knot value needs to be inserted for
// the previous last control point, somehow. Or perhaps the knot vector needs
// to be extended, ie the final degree-duplicate knots need value > 1?
//
// Currently to create a closed NURBS curve, the caller must handle this duplication
// themselves.
public NURBSCurve2(int numCtrlPoints, Vector2d[] ctrlPoint, double[] ctrlWeight, int degree, bool loop,
double[] knot, bool bIsInteriorKnot = true)
: base(0, 1)
{
if (numCtrlPoints < 2)
{
throw new Exception("NURBSCurve2(): only received " + numCtrlPoints + " control points!");
}
if (degree < 1 || degree > numCtrlPoints - 1)
{
throw new Exception("NURBSCurve2(): invalid degree " + degree);
}
// [RMS] loop mode doesn't work yet
if (loop == true)
{
throw new Exception("NURBSCUrve2(): loop mode is broken?");
}
mLoop = loop;
mNumCtrlPoints = numCtrlPoints;
mReplicate = (loop ? 1 : 0);
CreateControl(ctrlPoint, ctrlWeight);
mBasis = new BSplineBasis(mNumCtrlPoints + mReplicate, degree, knot, bIsInteriorKnot);
}
public BSplineBasis Clone()
{
var b2 = new BSplineBasis();
b2.mNumCtrlPoints = this.mNumCtrlPoints;
b2.mDegree = this.mDegree;
b2.mKnot = (double[])this.mKnot.Clone();
b2.mOpen = this.mOpen;
b2.mUniform = this.mUniform;
return(b2);
}
// Construction and destruction. Internal copies of the
// input arrays are made, so to dynamically change control points,
// control weights, or knots, you must use the 'SetControlPoint',
// 'GetControlPoint', 'SetControlWeight', 'GetControlWeight', and 'Knot'
// member functions.
// The homogeneous input points are (x,y,w) where the (x,y) values are
// stored in the ctrlPoint array and the w values are stored in the
// ctrlWeight array. The output points from curve evaluations are of
// the form (x',y') = (x/w,y/w).
// Uniform spline. The number of control points is n+1 >= 2. The degree
// of the 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.
//
// [RMS] "open" and "loop" are super-confusing here. Perhaps NURBSCurve2 should
// be refactored into several subclasses w/ different constructors, so that
// the naming makes sense?
public NURBSCurve2(int numCtrlPoints, Vector2d[] ctrlPoint, double[] ctrlWeight, int degree, bool loop, bool open)
: base(0, 1)
{
if (numCtrlPoints < 2)
{
throw new Exception("NURBSCurve2(): only received " + numCtrlPoints + " control points!");
}
if (degree < 1 || degree > numCtrlPoints - 1)
{
throw new Exception("NURBSCurve2(): invalid degree " + degree);
}
mLoop = loop;
mNumCtrlPoints = numCtrlPoints;
mReplicate = (loop ? (open ? 1 : degree) : 0);
CreateControl(ctrlPoint, ctrlWeight);
mBasis = new BSplineBasis(mNumCtrlPoints + mReplicate, degree, open);
}
