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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"
/*
*
* $Id: s1306.c,v 1.2 2001-03-19 15:58:43 afr Exp $
*
*/
#define S1306
#include "sislP.h"
#if defined(SISLNEEDPROTOTYPES)
void
s1306(double ep[],double eparp[],double eimpli[],int ideg,
double egeo3d[],double egeop[],int *jstat)
#else
void s1306(ep,eparp,eimpli,ideg,egeo3d,egeop,jstat)
double ep[];
double eparp[];
double eimpli[];
int ideg;
double egeo3d[];
double egeop[];
int *jstat;
#endif
/*
*********************************************************************
*
* PURPOSE : To calculate the radius of curvature at the intersection
* point between a B-spline surface and an implicit represented
* surface. The first and second derivatives
* of the intersection point in the B-spline surface are give as
* input. All coordinates are assumed to be in 3-D.
*
*
*
* INPUT : ep - 0-2 order derivatives of B-spline surface.
* For ideg=1,2 and 1001 the sequence is position,
* first derivative in first parameter direction,
* first derivative in second parameter direction,
* (2,0) derivative, (1,1) derivative, (0,2) derivative
* and normal. (21 numbers)
* For ideg=1003,1004,1005 the second derivatives are followed
* by the third derivatives and the normal (33 numbers)
* Compatible with output of s1421
* eparp - Parameter pair in B-spline surface of point
* eimpli - Description of the implicit surface
* ideg - The degree of the implicit surface
* ideg=1: Plane
* ideg=2; Quadric surface
* ideg=1001: Torus surface
* ideg=1003: Silhouette line parallel projection
* ideg=1004: Silhouette line perspective projection
* ideg=1005: Silhouette line circular projection
*
*
* OUTPUT :
* jstat - status messages
* = 11 : Fuzzy singular intersection point found
* = 10 : Singular intersection point found
* = 2 : Singular intersection point found
* = 1 : Curvature radius infinit
* = 0 : ok, curvature radius
* < 0 : error
* egeo3d - 3-D geometry description of the intersection. The
* array contains: position, unit tangent, curvature
* and radius of curvature. (A total of 10 numbers)
* A radius of curvature =-1, indicates that the radius
* of curvature is infinit.
* egeop - Description of the intersection in the parameter plane
* of the B-spline surface. The array contains: position,
* unit tangent, curvature and radius of curvature.
* (A total of 7 numbers)
*
* METHOD : We put the parametric surface into the implicit equation
* and get a function f(s,t)=0. By assuming that u and v are
* function s of a variable u we get:
*
* f(s(u),y(u)) = 0
*
* By making the derivative with respect to u we get:
*
* f s + f t = 0
* s u t u
*
* By assuming that u=s or u=t, we get one derivative equal
* to 1, and the other can be calculated. By taking one more
* derivative with respect to u we get:
*
* 2 2
* f s + 2 f s t + f s + f t + f t = 0.
* ss u st u u s uu tt u t uu
*
* Since s=u or t=u we know that one of the double derivatives
* is zero and the other can be caluclated.
*
* Based on these derivatives in the parameter plane the
* derivatives of the intersection curve with respect to u can
* be calculated, and futher on the actual curvature of the
* intersection curve at the input point.
*
* In the case that both f = 0 and f = 0 the second equation
* s t
* can be used for calculating s and t
* u u.
*
* USE: This function is only working in 3-D
*
* REFERENCES :
*-
* CALLS : s6scpr,fabs,s1307,s6err
*
*
* WRITTEN BY : Tor Dokken, SI, Oslo , Norway, 30 May 1988
* Revised by : Tor Dokken, SI, Oslo, March 1989.
* Initiating tangent etc. to 0 when singular point found
* Revised by : Mike Floater, SI, 1991-01
* Add perspective and circular silhouettes (ideg=1004,ideg=1005)
*
*********************************************************************
*/
{
int fuzzy_sing = FALSE;
int sing = FALSE;
int kstat = 0; /* Local status variable */
int ki,kj,kl; /* Control variables in loop */
int kpos = 0; /* Position of error */
int ksize; /* Number of doubles for storage of derivateves
and normal vector */
int ksizem3; /* ksize - 3 */
double *sps; /* Pointer to dP/ds */
double *spt; /* Pointer to dP/dt */
double *spss; /* Pointer to ddP/(dsds) */
double *spst; /* Pointer to ddP/(dsdt) */
double *sptt; /* Pointer to ddP/(dtdt) */
double tfs,tft,tfss; /* Derivatives of parametric surface put into */
double tfst,tftt; /* the implicit equation */
double tsu,ttu,tsuu,ttuu;/* Derivatives of parameter direction */
double sder[6]; /* Derivatives of parametric surface */
double snorm[3]; /* Normal vector of implicit surface at ep */
double sp[9]; /* Points, first and second deriv. of intcur */
/* If ideg=1,2 or 1001 then only derivatives up to second order
are calculated, then 18 doubles for derivatives and 3 for the
normal vector are to be used for calculation of points in the
spline surface. For ideg=1003,1004,1005 we have a silhouette curve and
derivatives up to the third are to be calculated,
thus 30 +3 a total of 33 doubles are to be calculated */
if (ideg==1003 || ideg==1004 || ideg==1005)
{
ksize = 33;
}
else
{
ksize = 21;
}
ksizem3 = ksize -3;
/* Calculated derivatives of the parametric surface put into the implicit
surface at the point ep */
s1331(ep,eimpli,ideg,2,sder,snorm,&kstat);
if (kstat<0) goto error;
tfs = sder[1];
tft = sder[2];
tfss = sder[3];
tfst = sder[4];
tftt = sder[5];
/* Calculate ds/du and dt/du */
/* UJK, aug.92 */
/* if (DEQUAL(tfs,(double)0.0) &&
DEQUAL(tft,(double)0.0) ) */
/* UJK, 13.08.93, save suzzy singular information. */
if (fabs(tfs) < 0.000001 &&
fabs(tft) < 0.000001) fuzzy_sing = TRUE;
else
fuzzy_sing = FALSE;
if (DEQUAL((double)1.0 + tfs,(double)1.0) &&
DEQUAL((double)1.0 + tft,(double)1.0) )
{
double tdum1,tdum2,tafss,tafst,taftt;
/* Singular point found, copy position and derivative value of input to
output, if not second order derivatives uniqely describes a tangent*/
memcopy(egeo3d,ep,3,DOUBLE);
memcopy(egeop,eparp,2,DOUBLE);
tafss = fabs(tfss);
tafst = fabs(tfst);
taftt = fabs(tftt);
tdum1 = tfst*tfst - tfss*tftt;
tdum2 = MAX(tafss,taftt);
tdum2 = MAX(tafst,tdum2);
for (ki=3 ; ki<10 ; ki++) egeo3d[ki] = DZERO;
for (ki=2 ; ki<7 ; ki++) egeop[ki] = DZERO;
if (DEQUAL(tdum2+tdum1,tdum2) &&
(DNEQUAL(tafss+tafst,tafst) || DNEQUAL(taftt+tafst,tafst)) )
{
/* A unique tangent can be calculated */
if (tafss>taftt)
{
tsu = -tfst/tfss;
ttu = 1;
}
else
{
tsu = 1;
ttu = -tfst/tftt;
}
tsuu = 0.0;
ttuu = 0.0;
/* Flag singular case */
sing = TRUE;
}
else
{
/* A tangent can not be calulated */
goto war02;
}
}
else
{
/* A noneisngular point found */
if (fabs(tfs) > fabs(tft))
{
/* Use u=t */
tsu = -tft/tfs;
ttu = (double)1.0;
tsuu = -(tfss*tsu*tsu + (double)2.0*tfst*tsu*ttu + tftt*ttu*ttu)/tfs;
ttuu = (double)0.0;
}
else
{
/* Use u=t */
tsu = (double)1.0;
ttu = -tfs/tft;
tsuu = (double)0.0;
ttuu = -(tfss*tsu*tsu + (double)2.0*tfst*tsu*ttu + tftt*ttu*ttu)/tft;
}
}
/* The calculation of the derivatives of one parameter direction with
respect to the other is dependent on the degree of the implicit equation*/
/* Set local pointers */
sps = ep + 3;
spt = ep + 6;
spss = ep + 9;
spst = ep + 12;
sptt = ep + 15;
/* Make description of intersection point in 3-D including
curvature and radius of curvature, first make description of
intersection point in parameter plane */
/* We will now express the intersection curve locally as a function
* of a w-parameter.
*
* c(w) = p(s(w),t(w))
*
* This gives the derivative
*
*
* c' = P s' + P t'
* s t
*
* And the second derivative
*
* 2 2
* c" = P s' + 2P s't' + P t' + P s" + P t"
* ss st tt s t
*/
for (ki=0,kj=3,kl=6 ; ki<3 ; ki++,kj++,kl++)
{
/* Copy position */
sp[ki] = ep[ki];
/* Make tangent */
sp[kj] = sps[ki]*tsu + spt[ki]*ttu;
/* Make curvature */
sp[kl] = spss[ki]*tsu*tsu + (double)2.0*spst[ki]*tsu*ttu +
sptt[ki]*ttu*ttu + sps[ki]*tsuu + spt[ki]*ttuu;
}
/* Make 3-D curvature and radius of curvature */
s1307(sp,3,egeo3d,&kstat);
if (kstat < 0 )goto error;
/* Make description of intersection point in parameter plane including
curvature and radius of curvature, first make description of
intersection point in parameter plane */
sp[0] = eparp[0];
sp[1] = eparp[1];
sp[2] = tsu;
sp[3] = ttu;
sp[4] = tsuu;
sp[5] = ttuu;
s1307(sp,2,egeop,&kstat);
if (kstat < 0) goto error;
/* Everyting is ok */
*jstat = 0;
goto out;
/* SISLPoint lying on torus axis */
war02: *jstat=2;
goto out;
/* Error in lower level function */
error:
*jstat = kstat;
s6err("s1306",*jstat,kpos);
goto out;
out:
if (sing && *jstat>=0) *jstat = 10;
else if (fuzzy_sing && *jstat>=0) *jstat = 11;
return;
}
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