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/*
* Copyright (C) 1998, 2000-2007, 2010, 2011, 2012, 2013 SINTEF ICT,
* Applied Mathematics, Norway.
*
* Contact information: E-mail: tor.dokken@sintef.no
* SINTEF ICT, Department of Applied Mathematics,
* P.O. Box 124 Blindern,
* 0314 Oslo, Norway.
*
* This file is part of SISL.
*
* SISL is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License as
* published by the Free Software Foundation, either version 3 of the
* License, or (at your option) any later version.
*
* SISL is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Affero General Public License for more details.
*
* You should have received a copy of the GNU Affero General Public
* License along with SISL. If not, see
* <http://www.gnu.org/licenses/>.
*
* In accordance with Section 7(b) of the GNU Affero General Public
* License, a covered work must retain the producer line in every data
* file that is created or manipulated using SISL.
*
* Other Usage
* You can be released from the requirements of the license by purchasing
* a commercial license. Buying such a license is mandatory as soon as you
* develop commercial activities involving the SISL library without
* disclosing the source code of your own applications.
*
* This file may be used in accordance with the terms contained in a
* written agreement between you and SINTEF ICT.
*/
#include "sisl-copyright.h"
#define S1357
#include "sislP.h"
#if defined(SISLNEEDPROTOTYPES)
void
s1357(double epoint[],int inbpnt,int idim,int ntype[],double epar[],
int icnsta,int icnend,int iopen,int ik,double astpar,
double *cendpar,SISLCurve **rc,double **gpar,int *jnbpar,int *jstat)
#else
void s1357(epoint,inbpnt,idim,ntype,epar,icnsta,icnend,iopen,ik,astpar,
cendpar,rc,gpar,jnbpar,jstat)
double epoint[];
int inbpnt;
int idim;
int ntype[];
double epar[];
int icnsta;
int icnend;
int iopen;
int ik;
double astpar;
double *cendpar;
SISLCurve **rc;
double **gpar;
int *jnbpar;
int *jstat;
#endif
/*
*************************************************************************
*
* Purpose: To calculate a B-spline curve interpolating a set of points.
* The points can be assigned a tangent (derivative).
* The curve can be closed or open. If end-conditions are
* conflicting, the condition closed curve rules out other
* end conditions.
* The parametrization is given by the array Epar.
*
* Input:
* Epoint - Array (length idim*inbpnt) containing the points/
* derivatives to be interpolated.
* Inbpnt - No. of points/derivatives in the epoint array.
* Idim - The dimension of the space in which the points lie.
* ntype - Array (length inbpnt) containing type indicator for
* points/derivatives/second-derivatives:
* 1 - Ordinary point.
* 2 - Knuckle point. (Is treated as an ordinary point.)
* 3 - Derivative to next point.
* 4 - Derivative to prior point.
* ( 5 - Second derivative to next point. )
* ( 6 - Second derivative to prior point. )
* 13 - Start-point of tangent to next point.
* 14 - End-point of tangent to prior point.
* Epar - Array containing the wanted parametrization. Only parameter
* values corresponding to position points are given.
* For closed curves, one additional parameter value
* must be spesified. The last entry contains
* the parametrization of the repeted start point.
* (if the endpoint is equal to the startpoint of
* the interpolation the lenght of the array should
* be equal to inpt1 also in the closed case).
* Icnsta - Additional condition at the start of the curve:
* 0 : No additional condition.
* 1 : Zero curvature at start.
* Icnend - Additional condition at the end of the curve:
* 0 : No additional condition.
* 1 : Zero curvature at end.
* Iopen - Flag telling if the curve should be open or closed:
* 1 : The curve should be open.
* 0 : The curve should be closed.
* -1 : The curve should be closed and periodic.
* Ik - The order of the B-spline curve to be produced.
* Astpar - Parameter-value to be used at the start of the curve.
*
* Output:
* Jstat - status variable:
* < 0 : Error.
* = 0 : Ok.
* > 0 : Warning.
* cendpar - Parameter-value used at the end of the curve.
* Rc - Pointer to output-curve.
* Gpar - Pointer to the parameter-values of the points in
* the curve. Represented only once, although derivatives
* and second-derivatives will have the same parameter-
* value as the points.
* Jnbpar - No. of different parameter-values.
*
* Method: First the parametrization of the curve and the type
* specification of points/derivatives are checked and/or
* corrected. Then the knots are calculated, and the
* interpolation is performed.
*
* Calls: s1907,s1908,s1902,s1891,s1713,s1750,s6err.
*
* Written by: Trond Vidar Stensby, SI, 1991-07
* The Fortran routine, p19539, is written by: T. Dokken SI.
* Bug fix: Michael Floater, 82.9.93. The construction of gpar and *jnbpar
* at the end of the routine was incorrect.
* REWISED BY: Vibeke Skytt, 03.94. This routine corresponds to s1358,
* but differ in the use of the parameter
* iopen and the input array ntype is of
* type int.
* REWISED BY: Johannes Kaasa, 01.98. Made sure the start and end points
* are correct in the periodic case. I also made proper
* handling when the order is higher than the number of
* interpolation points.
*****************************************************************
*/
{
int kpos = 0;
SISLCurve *qc = SISL_NULL; /* Temporary SISLCurves. */
SISLCurve *qc2 = SISL_NULL;
SISLCurve *dummy = SISL_NULL;
int *ltype = SISL_NULL; /* Type of interpolation condition
(temporary) */
int *ltype2 = SISL_NULL; /* Type of interpolation condition (finial) */
int *sder = SISL_NULL; /* Vector of derivative indicators. */
int knpt; /* Number of interpolation conditions. */
int kordr; /* Local order. */
int kstat; /* Status variable. */
int kn; /* Number of coefficients of B-spline curve.*/
int ki, kj, kl; /* Loop control variable. */
int kright = 1; /* One equation system to solve in
interpolation. */
int knlr = 0; /* Indicates shape of interpolation matrix. */
int knrc = 0; /* Indicates shape of interpolation matrix. */
int kopen; /* Local open/closed parameter. Closed,
non-periodic is treated as an open curve.*/
int kpair; /* Pair order or not. */
int kcont; /* Continuity in start/end point. */
int kleft; /* Pointer into knot array. */
int klast1, klast2; /* Last element in array. */
double split_par; /* Splitting parameter. */
double tdiff; /* Length of parameter interval. */
double *lpar = SISL_NULL; /* Parameter values. (temporary) */
double *lcond = SISL_NULL; /* Interpolation conditions. (temporary) */
double *sknot = SISL_NULL; /* Knot vector. */
double *spar = SISL_NULL; /* Parameter valued. (finial) */
double *scond = SISL_NULL; /* Interpolation conditions. (finial) */
double *scoef = SISL_NULL; /* Coefficients of curve. */
double *temp = SISL_NULL; /* Temporary storage. */
*jstat = 0;
/* If necessary reduce the order. */
kordr = MIN (ik, inbpnt);
/* Set local open/closed parameter. */
kopen = (iopen == SISL_CRV_PERIODIC) ? 0 : 1;
/* Check pair order or not. */
kpair = (kordr % 2 == 0) ? 1 : 0;
/* Transform interpolation conditions. */
s1907 (epoint, ntype, epar, iopen, icnsta, icnend, inbpnt,
idim, &lcond, <ype, &lpar,&knpt, &kstat);
if (kstat < 0) goto error;
/* Test interpolation conditions, and adjust the input conditions
if necessary. */
s1908 (lcond, ltype, lpar, knpt, kordr, idim, iopen, &scond, <ype2,
&spar, &knpt, &kstat);
if (kstat < 0) goto error;
/* Allocate scratch for derivative indicator. */
sder = newarray (knpt, INT);
if (sder == SISL_NULL) goto err101;
for (ki = 0; ki < knpt; ki++)
sder[ki] = abs (ltype2[ki]);
if (iopen == SISL_CRV_PERIODIC)
{
knlr = kordr / 2;
knrc = kordr - knlr - 1;
knpt--;
}
/* Produce knot vector. */
s1902 (lpar, knpt, kordr, kopen, &sknot, &kstat);
if (kstat < 0) goto error;
/* Perform interpolation. */
s1891 (spar, scond, idim, knpt, kright, sder, kopen, sknot,
&scoef, &kn, kordr, knlr, knrc, &kstat);
if (kstat < 0) goto error;
/* Corrected start and end for odd order periodic curves. */
if (iopen == SISL_CRV_PERIODIC && kpair)
{
if ((temp = newarray(idim, double)) == SISL_NULL)
goto err101;
/* Find number of present starting knots. */
ki = 0;
while (sknot[ki] < epar[0]) ki++;
klast1 = kn + kordr - 1;
klast2 = idim*(kn - 1);
tdiff = lpar[knpt] - lpar[0];
for ( ; ki < (kordr - 1); ki++)
{
temp[0] = sknot[knpt - 1] - tdiff;
for (kj = klast1; kj > 0; kj--)
sknot[kj] = sknot[kj - 1];
sknot[0] = temp[0];
for (kl = 0; kl < idim; kl++)
temp[kl] = scoef[(knpt - 1)*idim + kl];
for (kj = klast2; kj > 0; kj -= idim)
{
for (kl = 0; kl < idim; kl++)
scoef[kj + kl] = scoef[kj - idim + kl];
}
for (kl = 0; kl < idim; kl++)
scoef[kl] = temp[kl];
}
}
/* Express the curve as a curve object. */
qc = newCurve (kn, kordr, sknot, scoef, 1, idim, 1);
if (qc == SISL_NULL) goto err101;
qc->cuopen = iopen;
/* Corrected start and end for even order periodic curves. */
if (iopen == SISL_CRV_PERIODIC && !kpair &&
fabs(qc->et[qc->ik - 1] - epar[0]) > REL_PAR_RES)
{
/* Shift the start/end point. */
split_par = epar[0];
while (split_par < qc->et[qc->ik-1])
split_par += (qc->et[qc->in] - qc->et[qc->ik-1]);
while (split_par > qc->et[qc->in])
split_par -= (qc->et[qc->in] - qc->et[qc->ik-1]);
s1710(qc, split_par, &qc2, &dummy, &kstat);
if (kstat != 2) goto error;
tdiff = qc2->et[qc2->ik - 1] - epar[0];
if (fabs(tdiff) > REL_PAR_RES)
{
for (ki = 0; ki < (qc2->in + qc2->ik); ki++)
qc2->et[ki] -= tdiff;
}
/* qc2 is represented on a closed basis, and flagged
as SISL_CRV_CLOSED. We have to open it again. First
find the continuity in the new end point. */
kcont = qc->ik - 1 - max(s6knotmult(qc->et, qc->ik, qc->in,
&kleft, epar[0], &kstat), 1);
if (kstat < 0) goto error;
make_cv_cyclic(qc2, kcont, &kstat);
if (kstat < 0) goto error;
if (qc != SISL_NULL) freeCurve (qc);
qc = qc2;
qc2 = SISL_NULL;
}
if (kordr < ik)
{
/* The order of the curve is less than expected. Increase the order. */
qc2 = SISL_NULL;
s1750 (qc, ik, &qc2, &kstat);
if (kstat < 0) goto error;
if (qc != SISL_NULL) freeCurve (qc);
qc = qc2;
qc2 = SISL_NULL;
}
/* Set open/closed parameter of curve. */
qc->cuopen = iopen;
/* Set end of parameter interval. */
*cendpar = *(qc->et + qc->in);
/* Interpolation performed. */
/* Find distinct parameter values. */
*gpar = lpar;
/* Bug fix, MSF, 28.9.93. Change
*jnbpar = 1;
to: */
*jnbpar = 0;
for (ki = 1; ki<knpt; ki++)
{
if (spar[ki - 1] < spar[ki])
/* Bug fix. MSF, 28.9.93 Change (*gpar)[(*jnbpar)++] = spar[ki]; to: */
(*gpar)[(*jnbpar)++] = spar[ki-1];
}
/* Bug fix. MSF, 28.9.93 Change (*gpar)[(*jnbpar)++] = spar[ki]; to: */
(*gpar)[(*jnbpar)++] = spar[ki-1];
*rc = qc;
goto out;
/* Error in scratch allocation. */
err101:
*jstat = -101;
s6err ("s1357", *jstat, kpos);
goto out;
/* Error in lower level routine. */
error:
*jstat = kstat;
s6err ("s1357", *jstat, kpos);
goto out;
out:
/* Free scratch occupied by local arrays. */
if (scond != SISL_NULL) freearray (scond);
if (scoef != SISL_NULL) freearray (scoef);
if (sder != SISL_NULL) freearray (sder);
if (ltype != SISL_NULL) freearray (ltype);
if (ltype2 != SISL_NULL) freearray (ltype2);
if (lcond != SISL_NULL) freearray (lcond);
if (sknot != SISL_NULL) freearray (sknot);
if (spar != SISL_NULL) freearray (spar);
if (temp != SISL_NULL) freearray (temp);
return;
}
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