/*************************************************************************
* This function calculates tangent vector for a given value of parameter T
*
* INPUT PARAMETERS:
* P - parametric spline interpolant
* T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
* the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
* by making T=T-floor(T).
*
* OUTPUT PARAMETERS:
* X - X-component of tangent vector (normalized)
* Y - Y-component of tangent vector (normalized)
*
* NOTE:
* X^2+Y^2 is either 1 (for non-zero tangent vector) or 0.
*
*
* -- ALGLIB PROJECT --
* Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
public static void pspline2tangent(ref pspline2interpolant p,
double t,
ref double x,
ref double y)
{
double v = 0;
double v0 = 0;
double v1 = 0;
if (p.periodic)
{
t = t - (int)Math.Floor(t);
}
pspline2diff(ref p, t, ref v0, ref x, ref v1, ref y);
if ((double)(x) != (double)(0) | (double)(y) != (double)(0))
{
//
// this code is a bit more complex than X^2+Y^2 to avoid
// overflow for large values of X and Y.
//
v = apserv.safepythag2(x, y);
x = x / v;
y = y / v;
}
}
/*************************************************************************
* This function calculates arc length, i.e. length of curve between t=a
* and t=b.
*
* INPUT PARAMETERS:
* P - parametric spline interpolant
* A,B - parameter values corresponding to arc ends:
* B>A will result in positive length returned
* B<A will result in negative length returned
*
* RESULT:
* length of arc starting at T=A and ending at T=B.
*
*
* -- ALGLIB PROJECT --
* Copyright 30.05.2010 by Bochkanov Sergey
*************************************************************************/
public static double pspline2arclength(ref pspline2interpolant p,
double a,
double b)
{
double result = 0;
autogk.autogkstate state = new autogk.autogkstate();
autogk.autogkreport rep = new autogk.autogkreport();
double sx = 0;
double dsx = 0;
double d2sx = 0;
double sy = 0;
double dsy = 0;
double d2sy = 0;
autogk.autogksmooth(a, b, ref state);
while (autogk.autogkiteration(ref state))
{
spline1d.spline1ddiff(ref p.x, state.x, ref sx, ref dsx, ref d2sx);
spline1d.spline1ddiff(ref p.y, state.x, ref sy, ref dsy, ref d2sy);
state.f = apserv.safepythag2(dsx, dsy);
}
autogk.autogkresults(ref state, ref result, ref rep);
System.Diagnostics.Debug.Assert(rep.terminationtype > 0, "PSpline2ArcLength: internal error!");
return(result);
}
/*************************************************************************
* This function calculates the value of the parametric spline for a given
* value of parameter T
*
* INPUT PARAMETERS:
* P - parametric spline interpolant
* T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
* the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
* by making T=T-floor(T).
*
* OUTPUT PARAMETERS:
* X - X-position
* Y - Y-position
*
*
* -- ALGLIB PROJECT --
* Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
public static void pspline2calc(ref pspline2interpolant p,
double t,
ref double x,
ref double y)
{
if (p.periodic)
{
t = t - (int)Math.Floor(t);
}
x = spline1d.spline1dcalc(ref p.x, t);
y = spline1d.spline1dcalc(ref p.y, t);
}
/*************************************************************************
* This function calculates first and second derivative with respect to T.
*
* INPUT PARAMETERS:
* P - parametric spline interpolant
* T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
* the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
* by making T=T-floor(T).
*
* OUTPUT PARAMETERS:
* X - X-value
* DX - derivative
* D2X - second derivative
* Y - Y-value
* DY - derivative
* D2Y - second derivative
*
*
* -- ALGLIB PROJECT --
* Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
public static void pspline2diff2(ref pspline2interpolant p,
double t,
ref double x,
ref double dx,
ref double d2x,
ref double y,
ref double dy,
ref double d2y)
{
if (p.periodic)
{
t = t - (int)Math.Floor(t);
}
spline1d.spline1ddiff(ref p.x, t, ref x, ref dx, ref d2x);
spline1d.spline1ddiff(ref p.y, t, ref y, ref dy, ref d2y);
}
/*************************************************************************
* This function returns vector of parameter values correspoding to points.
*
* I.e. for P created from (X[0],Y[0])...(X[N-1],Y[N-1]) and U=TValues(P) we
* have
* (X[0],Y[0]) = PSpline2Calc(P,U[0]),
* (X[1],Y[1]) = PSpline2Calc(P,U[1]),
* (X[2],Y[2]) = PSpline2Calc(P,U[2]),
* ...
*
* INPUT PARAMETERS:
* P - parametric spline interpolant
*
* OUTPUT PARAMETERS:
* N - array size
* T - array[0..N-1]
*
*
* NOTES:
* for non-periodic splines U[0]=0, U[0]<U[1]<...<U[N-1], U[N-1]=1
* for periodic splines U[0]=0, U[0]<U[1]<...<U[N-1], U[N-1]<1
*
* -- ALGLIB PROJECT --
* Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
public static void pspline2parametervalues(ref pspline2interpolant p,
ref int n,
ref double[] t)
{
int i_ = 0;
System.Diagnostics.Debug.Assert(p.n >= 2, "PSpline2ParameterValues: internal error!");
n = p.n;
t = new double[n];
for (i_ = 0; i_ <= n - 1; i_++)
{
t[i_] = p.p[i_];
}
t[0] = 0;
if (!p.periodic)
{
t[n - 1] = 1;
}
}
/*************************************************************************
* This function builds periodic 2-dimensional parametric spline which
* starts at (X[0],Y[0]), goes through all points to (X[N-1],Y[N-1]) and then
* back to (X[0],Y[0]).
*
* INPUT PARAMETERS:
* XY - points, array[0..N-1,0..1].
* XY[I,0:1] corresponds to the Ith point.
* XY[N-1,0:1] must be different from XY[0,0:1].
* Order of points is important!
* N - points count, N>=3 for other types of splines.
* ST - spline type:
* 1 Catmull-Rom spline (Tension=0) with cyclic boundary conditions
* 2 cubic spline with cyclic boundary conditions
* PT - parameterization type:
* 0 uniform
* 1 chord length
* 2 centripetal
*
* OUTPUT PARAMETERS:
* P - parametric spline interpolant
*
*
* NOTES:
* this function assumes that there all consequent points are distinct.
* I.e. (x0,y0)<>(x1,y1), (x1,y1)<>(x2,y2), (x2,y2)<>(x3,y3) and so on.
* However, non-consequent points may coincide, i.e. we can have (x0,y0)=
* =(x2,y2).
* last point of sequence is NOT equal to the first point. You shouldn't
* make curve "explicitly periodic" by making them equal.
*
* -- ALGLIB PROJECT --
* Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
public static void pspline2buildperiodic(double[,] xy,
int n,
int st,
int pt,
ref pspline2interpolant p)
{
double[,] xyp = new double[0, 0];
double[] tmp = new double[0];
double v = 0;
int i = 0;
int i_ = 0;
xy = (double[, ])xy.Clone();
System.Diagnostics.Debug.Assert(st >= 1 & st <= 2, "PSpline2BuildPeriodic: incorrect spline type!");
System.Diagnostics.Debug.Assert(pt >= 0 & pt <= 2, "PSpline2BuildPeriodic: incorrect parameterization type!");
System.Diagnostics.Debug.Assert(n >= 3, "PSpline2BuildPeriodic: N<3!");
//
// Prepare
//
p.n = n;
p.periodic = true;
tmp = new double[n + 1];
xyp = new double[n + 1, 2];
for (i_ = 0; i_ <= n - 1; i_++)
{
xyp[i_, 0] = xy[i_, 0];
}
for (i_ = 0; i_ <= n - 1; i_++)
{
xyp[i_, 1] = xy[i_, 1];
}
for (i_ = 0; i_ <= 1; i_++)
{
xyp[n, i_] = xy[0, i_];
}
//
// Build parameterization, check that all parameters are distinct
//
pspline2par(ref xyp, n + 1, pt, ref p.p);
System.Diagnostics.Debug.Assert(apserv.apservaredistinct(p.p, n + 1), "PSpline2BuildPeriodic: consequent (or first and last) points are too close!");
//
// Build splines
//
if (st == 1)
{
for (i_ = 0; i_ <= n; i_++)
{
tmp[i_] = xyp[i_, 0];
}
spline1d.spline1dbuildcatmullrom(p.p, tmp, n + 1, -1, 0.0, ref p.x);
for (i_ = 0; i_ <= n; i_++)
{
tmp[i_] = xyp[i_, 1];
}
spline1d.spline1dbuildcatmullrom(p.p, tmp, n + 1, -1, 0.0, ref p.y);
}
if (st == 2)
{
for (i_ = 0; i_ <= n; i_++)
{
tmp[i_] = xyp[i_, 0];
}
spline1d.spline1dbuildcubic(p.p, tmp, n + 1, -1, 0.0, -1, 0.0, ref p.x);
for (i_ = 0; i_ <= n; i_++)
{
tmp[i_] = xyp[i_, 1];
}
spline1d.spline1dbuildcubic(p.p, tmp, n + 1, -1, 0.0, -1, 0.0, ref p.y);
}
}
/*************************************************************************
This function calculates arc length, i.e. length of curve between t=a
and t=b.
INPUT PARAMETERS:
P - parametric spline interpolant
A,B - parameter values corresponding to arc ends:
* B>A will result in positive length returned
* B<A will result in negative length returned
RESULT:
length of arc starting at T=A and ending at T=B.
-- ALGLIB PROJECT --
Copyright 30.05.2010 by Bochkanov Sergey
*************************************************************************/
public static double pspline2arclength(pspline2interpolant p,
double a,
double b)
{
double result = 0;
autogk.autogkstate state = new autogk.autogkstate();
autogk.autogkreport rep = new autogk.autogkreport();
double sx = 0;
double dsx = 0;
double d2sx = 0;
double sy = 0;
double dsy = 0;
double d2sy = 0;
autogk.autogksmooth(a, b, state);
while( autogk.autogkiteration(state) )
{
spline1d.spline1ddiff(p.x, state.x, ref sx, ref dsx, ref d2sx);
spline1d.spline1ddiff(p.y, state.x, ref sy, ref dsy, ref d2sy);
state.f = apserv.safepythag2(dsx, dsy);
}
autogk.autogkresults(state, ref result, rep);
alglib.ap.assert(rep.terminationtype>0, "PSpline2ArcLength: internal error!");
return result;
}
/*************************************************************************
This function calculates derivative, i.e. it returns (dX/dT,dY/dT).
INPUT PARAMETERS:
P - parametric spline interpolant
T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
by making T=T-floor(T).
OUTPUT PARAMETERS:
X - X-value
DX - X-derivative
Y - Y-value
DY - Y-derivative
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
public static void pspline2diff(ref pspline2interpolant p,
double t,
ref double x,
ref double dx,
ref double y,
ref double dy)
{
double d2s = 0;
if( p.periodic )
{
t = t-(int)Math.Floor(t);
}
spline1d.spline1ddiff(ref p.x, t, ref x, ref dx, ref d2s);
spline1d.spline1ddiff(ref p.y, t, ref y, ref dy, ref d2s);
}
/*************************************************************************
This function calculates tangent vector for a given value of parameter T
INPUT PARAMETERS:
P - parametric spline interpolant
T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
by making T=T-floor(T).
OUTPUT PARAMETERS:
X - X-component of tangent vector (normalized)
Y - Y-component of tangent vector (normalized)
NOTE:
X^2+Y^2 is either 1 (for non-zero tangent vector) or 0.
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
public static void pspline2tangent(pspline2interpolant p,
double t,
ref double x,
ref double y)
{
double v = 0;
double v0 = 0;
double v1 = 0;
x = 0;
y = 0;
if( p.periodic )
{
t = t-(int)Math.Floor(t);
}
pspline2diff(p, t, ref v0, ref x, ref v1, ref y);
if( (double)(x)!=(double)(0) || (double)(y)!=(double)(0) )
{
//
// this code is a bit more complex than X^2+Y^2 to avoid
// overflow for large values of X and Y.
//
v = apserv.safepythag2(x, y);
x = x/v;
y = y/v;
}
}
/*************************************************************************
This function calculates the value of the parametric spline for a given
value of parameter T
INPUT PARAMETERS:
P - parametric spline interpolant
T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
by making T=T-floor(T).
OUTPUT PARAMETERS:
X - X-position
Y - Y-position
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
public static void pspline2calc(pspline2interpolant p,
double t,
ref double x,
ref double y)
{
x = 0;
y = 0;
if( p.periodic )
{
t = t-(int)Math.Floor(t);
}
x = spline1d.spline1dcalc(p.x, t);
y = spline1d.spline1dcalc(p.y, t);
}
/*************************************************************************
This function returns vector of parameter values correspoding to points.
I.e. for P created from (X[0],Y[0])...(X[N-1],Y[N-1]) and U=TValues(P) we
have
(X[0],Y[0]) = PSpline2Calc(P,U[0]),
(X[1],Y[1]) = PSpline2Calc(P,U[1]),
(X[2],Y[2]) = PSpline2Calc(P,U[2]),
...
INPUT PARAMETERS:
P - parametric spline interpolant
OUTPUT PARAMETERS:
N - array size
T - array[0..N-1]
NOTES:
* for non-periodic splines U[0]=0, U[0]<U[1]<...<U[N-1], U[N-1]=1
* for periodic splines U[0]=0, U[0]<U[1]<...<U[N-1], U[N-1]<1
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
public static void pspline2parametervalues(pspline2interpolant p,
ref int n,
ref double[] t)
{
int i_ = 0;
n = 0;
t = new double[0];
alglib.ap.assert(p.n>=2, "PSpline2ParameterValues: internal error!");
n = p.n;
t = new double[n];
for(i_=0; i_<=n-1;i_++)
{
t[i_] = p.p[i_];
}
t[0] = 0;
if( !p.periodic )
{
t[n-1] = 1;
}
}
/*************************************************************************
This function builds periodic 2-dimensional parametric spline which
starts at (X[0],Y[0]), goes through all points to (X[N-1],Y[N-1]) and then
back to (X[0],Y[0]).
INPUT PARAMETERS:
XY - points, array[0..N-1,0..1].
XY[I,0:1] corresponds to the Ith point.
XY[N-1,0:1] must be different from XY[0,0:1].
Order of points is important!
N - points count, N>=3 for other types of splines.
ST - spline type:
* 1 Catmull-Rom spline (Tension=0) with cyclic boundary conditions
* 2 cubic spline with cyclic boundary conditions
PT - parameterization type:
* 0 uniform
* 1 chord length
* 2 centripetal
OUTPUT PARAMETERS:
P - parametric spline interpolant
NOTES:
* this function assumes that there all consequent points are distinct.
I.e. (x0,y0)<>(x1,y1), (x1,y1)<>(x2,y2), (x2,y2)<>(x3,y3) and so on.
However, non-consequent points may coincide, i.e. we can have (x0,y0)=
=(x2,y2).
* last point of sequence is NOT equal to the first point. You shouldn't
make curve "explicitly periodic" by making them equal.
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
public static void pspline2buildperiodic(double[,] xy,
int n,
int st,
int pt,
pspline2interpolant p)
{
double[,] xyp = new double[0,0];
double[] tmp = new double[0];
int i_ = 0;
xy = (double[,])xy.Clone();
alglib.ap.assert(st>=1 && st<=2, "PSpline2BuildPeriodic: incorrect spline type!");
alglib.ap.assert(pt>=0 && pt<=2, "PSpline2BuildPeriodic: incorrect parameterization type!");
alglib.ap.assert(n>=3, "PSpline2BuildPeriodic: N<3!");
//
// Prepare
//
p.n = n;
p.periodic = true;
tmp = new double[n+1];
xyp = new double[n+1, 2];
for(i_=0; i_<=n-1;i_++)
{
xyp[i_,0] = xy[i_,0];
}
for(i_=0; i_<=n-1;i_++)
{
xyp[i_,1] = xy[i_,1];
}
for(i_=0; i_<=1;i_++)
{
xyp[n,i_] = xy[0,i_];
}
//
// Build parameterization, check that all parameters are distinct
//
pspline2par(xyp, n+1, pt, ref p.p);
alglib.ap.assert(apserv.aredistinct(p.p, n+1), "PSpline2BuildPeriodic: consequent (or first and last) points are too close!");
//
// Build splines
//
if( st==1 )
{
for(i_=0; i_<=n;i_++)
{
tmp[i_] = xyp[i_,0];
}
spline1d.spline1dbuildcatmullrom(p.p, tmp, n+1, -1, 0.0, p.x);
for(i_=0; i_<=n;i_++)
{
tmp[i_] = xyp[i_,1];
}
spline1d.spline1dbuildcatmullrom(p.p, tmp, n+1, -1, 0.0, p.y);
}
if( st==2 )
{
for(i_=0; i_<=n;i_++)
{
tmp[i_] = xyp[i_,0];
}
spline1d.spline1dbuildcubic(p.p, tmp, n+1, -1, 0.0, -1, 0.0, p.x);
for(i_=0; i_<=n;i_++)
{
tmp[i_] = xyp[i_,1];
}
spline1d.spline1dbuildcubic(p.p, tmp, n+1, -1, 0.0, -1, 0.0, p.y);
}
}
/*************************************************************************
This function builds non-periodic 2-dimensional parametric spline which
starts at (X[0],Y[0]) and ends at (X[N-1],Y[N-1]).
INPUT PARAMETERS:
XY - points, array[0..N-1,0..1].
XY[I,0:1] corresponds to the Ith point.
Order of points is important!
N - points count, N>=5 for Akima splines, N>=2 for other types of
splines.
ST - spline type:
* 0 Akima spline
* 1 parabolically terminated Catmull-Rom spline (Tension=0)
* 2 parabolically terminated cubic spline
PT - parameterization type:
* 0 uniform
* 1 chord length
* 2 centripetal
OUTPUT PARAMETERS:
P - parametric spline interpolant
NOTES:
* this function assumes that there all consequent points are distinct.
I.e. (x0,y0)<>(x1,y1), (x1,y1)<>(x2,y2), (x2,y2)<>(x3,y3) and so on.
However, non-consequent points may coincide, i.e. we can have (x0,y0)=
=(x2,y2).
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
public static void pspline2build(double[,] xy,
int n,
int st,
int pt,
pspline2interpolant p)
{
double[] tmp = new double[0];
int i_ = 0;
xy = (double[,])xy.Clone();
alglib.ap.assert(st>=0 && st<=2, "PSpline2Build: incorrect spline type!");
alglib.ap.assert(pt>=0 && pt<=2, "PSpline2Build: incorrect parameterization type!");
if( st==0 )
{
alglib.ap.assert(n>=5, "PSpline2Build: N<5 (minimum value for Akima splines)!");
}
else
{
alglib.ap.assert(n>=2, "PSpline2Build: N<2!");
}
//
// Prepare
//
p.n = n;
p.periodic = false;
tmp = new double[n];
//
// Build parameterization, check that all parameters are distinct
//
pspline2par(xy, n, pt, ref p.p);
alglib.ap.assert(apserv.aredistinct(p.p, n), "PSpline2Build: consequent points are too close!");
//
// Build splines
//
if( st==0 )
{
for(i_=0; i_<=n-1;i_++)
{
tmp[i_] = xy[i_,0];
}
spline1d.spline1dbuildakima(p.p, tmp, n, p.x);
for(i_=0; i_<=n-1;i_++)
{
tmp[i_] = xy[i_,1];
}
spline1d.spline1dbuildakima(p.p, tmp, n, p.y);
}
if( st==1 )
{
for(i_=0; i_<=n-1;i_++)
{
tmp[i_] = xy[i_,0];
}
spline1d.spline1dbuildcatmullrom(p.p, tmp, n, 0, 0.0, p.x);
for(i_=0; i_<=n-1;i_++)
{
tmp[i_] = xy[i_,1];
}
spline1d.spline1dbuildcatmullrom(p.p, tmp, n, 0, 0.0, p.y);
}
if( st==2 )
{
for(i_=0; i_<=n-1;i_++)
{
tmp[i_] = xy[i_,0];
}
spline1d.spline1dbuildcubic(p.p, tmp, n, 0, 0.0, 0, 0.0, p.x);
for(i_=0; i_<=n-1;i_++)
{
tmp[i_] = xy[i_,1];
}
spline1d.spline1dbuildcubic(p.p, tmp, n, 0, 0.0, 0, 0.0, p.y);
}
}
public override alglib.apobject make_copy()
{
pspline2interpolant _result = new pspline2interpolant();
_result.n = n;
_result.periodic = periodic;
_result.p = (double[])p.Clone();
_result.x = (spline1d.spline1dinterpolant)x.make_copy();
_result.y = (spline1d.spline1dinterpolant)y.make_copy();
return _result;
}
/*************************************************************************
This function calculates first and second derivative with respect to T.
INPUT PARAMETERS:
P - parametric spline interpolant
T - point:
* T in [0,1] corresponds to interval spanned by points
* for non-periodic splines T<0 (or T>1) correspond to parts of
the curve before the first (after the last) point
* for periodic splines T<0 (or T>1) are projected into [0,1]
by making T=T-floor(T).
OUTPUT PARAMETERS:
X - X-value
DX - derivative
D2X - second derivative
Y - Y-value
DY - derivative
D2Y - second derivative
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
public static void pspline2diff2(pspline2interpolant p,
double t,
ref double x,
ref double dx,
ref double d2x,
ref double y,
ref double dy,
ref double d2y)
{
x = 0;
dx = 0;
d2x = 0;
y = 0;
dy = 0;
d2y = 0;
if( p.periodic )
{
t = t-(int)Math.Floor(t);
}
spline1d.spline1ddiff(p.x, t, ref x, ref dx, ref d2x);
spline1d.spline1ddiff(p.y, t, ref y, ref dy, ref d2y);
}
/*************************************************************************
* This function builds non-periodic 2-dimensional parametric spline which
* starts at (X[0],Y[0]) and ends at (X[N-1],Y[N-1]).
*
* INPUT PARAMETERS:
* XY - points, array[0..N-1,0..1].
* XY[I,0:1] corresponds to the Ith point.
* Order of points is important!
* N - points count, N>=5 for Akima splines, N>=2 for other types of
* splines.
* ST - spline type:
* 0 Akima spline
* 1 parabolically terminated Catmull-Rom spline (Tension=0)
* 2 parabolically terminated cubic spline
* PT - parameterization type:
* 0 uniform
* 1 chord length
* 2 centripetal
*
* OUTPUT PARAMETERS:
* P - parametric spline interpolant
*
*
* NOTES:
* this function assumes that there all consequent points are distinct.
* I.e. (x0,y0)<>(x1,y1), (x1,y1)<>(x2,y2), (x2,y2)<>(x3,y3) and so on.
* However, non-consequent points may coincide, i.e. we can have (x0,y0)=
* =(x2,y2).
*
* -- ALGLIB PROJECT --
* Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
public static void pspline2build(double[,] xy,
int n,
int st,
int pt,
ref pspline2interpolant p)
{
double[] tmp = new double[0];
double v = 0;
int i = 0;
int i_ = 0;
xy = (double[, ])xy.Clone();
System.Diagnostics.Debug.Assert(st >= 0 & st <= 2, "PSpline2Build: incorrect spline type!");
System.Diagnostics.Debug.Assert(pt >= 0 & pt <= 2, "PSpline2Build: incorrect parameterization type!");
if (st == 0)
{
System.Diagnostics.Debug.Assert(n >= 5, "PSpline2Build: N<5 (minimum value for Akima splines)!");
}
else
{
System.Diagnostics.Debug.Assert(n >= 2, "PSpline2Build: N<2!");
}
//
// Prepare
//
p.n = n;
p.periodic = false;
tmp = new double[n];
//
// Build parameterization, check that all parameters are distinct
//
pspline2par(ref xy, n, pt, ref p.p);
System.Diagnostics.Debug.Assert(apserv.apservaredistinct(p.p, n), "PSpline2Build: consequent points are too close!");
//
// Build splines
//
if (st == 0)
{
for (i_ = 0; i_ <= n - 1; i_++)
{
tmp[i_] = xy[i_, 0];
}
spline1d.spline1dbuildakima(p.p, tmp, n, ref p.x);
for (i_ = 0; i_ <= n - 1; i_++)
{
tmp[i_] = xy[i_, 1];
}
spline1d.spline1dbuildakima(p.p, tmp, n, ref p.y);
}
if (st == 1)
{
for (i_ = 0; i_ <= n - 1; i_++)
{
tmp[i_] = xy[i_, 0];
}
spline1d.spline1dbuildcatmullrom(p.p, tmp, n, 0, 0.0, ref p.x);
for (i_ = 0; i_ <= n - 1; i_++)
{
tmp[i_] = xy[i_, 1];
}
spline1d.spline1dbuildcatmullrom(p.p, tmp, n, 0, 0.0, ref p.y);
}
if (st == 2)
{
for (i_ = 0; i_ <= n - 1; i_++)
{
tmp[i_] = xy[i_, 0];
}
spline1d.spline1dbuildcubic(p.p, tmp, n, 0, 0.0, 0, 0.0, ref p.x);
for (i_ = 0; i_ <= n - 1; i_++)
{
tmp[i_] = xy[i_, 1];
}
spline1d.spline1dbuildcubic(p.p, tmp, n, 0, 0.0, 0, 0.0, ref p.y);
}
}
/*************************************************************************
This function returns vector of parameter values correspoding to points.
I.e. for P created from (X[0],Y[0])...(X[N-1],Y[N-1]) and U=TValues(P) we
have
(X[0],Y[0]) = PSpline2Calc(P,U[0]),
(X[1],Y[1]) = PSpline2Calc(P,U[1]),
(X[2],Y[2]) = PSpline2Calc(P,U[2]),
...
INPUT PARAMETERS:
P - parametric spline interpolant
OUTPUT PARAMETERS:
N - array size
T - array[0..N-1]
NOTES:
* for non-periodic splines U[0]=0, U[0]<U[1]<...<U[N-1], U[N-1]=1
* for periodic splines U[0]=0, U[0]<U[1]<...<U[N-1], U[N-1]<1
-- ALGLIB PROJECT --
Copyright 28.05.2010 by Bochkanov Sergey
*************************************************************************/
public static void pspline2parametervalues(ref pspline2interpolant p,
ref int n,
ref double[] t)
{
int i_ = 0;
System.Diagnostics.Debug.Assert(p.n>=2, "PSpline2ParameterValues: internal error!");
n = p.n;
t = new double[n];
for(i_=0; i_<=n-1;i_++)
{
t[i_] = p.p[i_];
}
t[0] = 0;
if( !p.periodic )
{
t[n-1] = 1;
}
}