1 /*
2 * Copyright (C) 1998, 2000-2007, 2010, 2011, 2012, 2013 SINTEF ICT,
3 * Applied Mathematics, Norway.
4 *
5 * Contact information: E-mail: tor.dokken@sintef.no
6 * SINTEF ICT, Department of Applied Mathematics,
7 * P.O. Box 124 Blindern,
8 * 0314 Oslo, Norway.
9 *
10 * This file is part of SISL.
11 *
12 * SISL is free software: you can redistribute it and/or modify
13 * it under the terms of the GNU Affero General Public License as
14 * published by the Free Software Foundation, either version 3 of the
15 * License, or (at your option) any later version.
16 *
17 * SISL is distributed in the hope that it will be useful,
18 * but WITHOUT ANY WARRANTY; without even the implied warranty of
19 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20 * GNU Affero General Public License for more details.
21 *
22 * You should have received a copy of the GNU Affero General Public
23 * License along with SISL. If not, see
24 * <http://www.gnu.org/licenses/>.
25 *
26 * In accordance with Section 7(b) of the GNU Affero General Public
27 * License, a covered work must retain the producer line in every data
28 * file that is created or manipulated using SISL.
29 *
30 * Other Usage
31 * You can be released from the requirements of the license by purchasing
32 * a commercial license. Buying such a license is mandatory as soon as you
33 * develop commercial activities involving the SISL library without
34 * disclosing the source code of your own applications.
35 *
36 * This file may be used in accordance with the terms contained in a
37 * written agreement between you and SINTEF ICT.
38 */
39
40 #include "sisl-copyright.h"
41
42 /*
43 *
44 * $Id: s2500.c,v 1.8 2001-03-19 15:58:59 afr Exp $
45 *
46 */
47
48
49 #define S2500
50
51 #include "sislP.h"
52
53 #if defined(SISLNEEDPROTOTYPES)
54 void
s2500(SISLSurf * surf,int ider,int iside1,int iside2,double parvalue[],int * leftknot1,int * leftknot2,double * gaussian,int * jstat)55 s2500(SISLSurf *surf, int ider, int iside1, int iside2, double parvalue[],
56 int *leftknot1,int *leftknot2, double *gaussian, int *jstat)
57 #else
58 void s2500(surf, ider, iside1, iside2, parvalue, leftknot1, leftknot2, gaussian, jstat)
59 SISLSurf *surf;
60 int ider;
61 int iside1;
62 int iside2;
63 double parvalue[];
64 int *leftknot1;
65 int *leftknot2;
66 double *gaussian;
67 int *jstat;
68 #endif
69 /*
70 ***************************************************************************
71 *
72 ***************************************************************************
73 * PURPOSE : To compute the Gaussian K(u,v) of a Surface for given
74 * values (u,v) = (parvalue[0],parvalue[1]), where:
75 *
76 * et1[leftknot1] <= parvalue[0] < et1[leftknot1+1],
77 * et2[leftknot2] <= parvalue[1] < et2[leftknot2+1].
78 * See also s2501().
79 *
80 * INPUT :
81 * surf - Pointer to the surface to evaluate.
82 * ider - Number of derivatives to calculate.
83 * Only implemented for ider=0.
84 * < 0 : No derivative calculated.
85 * = 0 : Position calculated.
86 * = 1 : Position and first derivative calculated.
87 * etc.
88 * iside1 - Indicator telling if the derivatives in the first
89 * parameter direction is to be calculated from the
90 * left or from the right:
91 * < 0 calculate derivative from the left hand side
92 * >= 0 calculate derivative from the right hand side.
93 * iside2 - Indicator telling if the derivatives in the second
94 * parameter direction is to be calculated from the
95 * left or from the right:
96 * < 0 calculate derivative from the left hand side
97 * >= 0 calculate derivative from the right hand side.
98 * parvalue - Parameter-value at which to evaluate. Dimension of
99 * parvalue is 2.
100 *
101 * INPUT/OUTPUT :
102 * leftknot1 - Pointer to the interval in the knot vector in the
103 * first parameter direction where parvalue[0] is found,
104 * that is:
105 * et1[leftknot1] <= parvalue[0] < et1[leftknot1+1].
106 * leftknot1 should be set equal to zero at the first call
107 * to the routine.
108 *
109 * leftknot2 - Pointer to the interval in the knot vector in the
110 * second parameter direction where parvalue[1] is found,
111 * that is:
112 * et2[leftknot2] <= parvalue[1] < et2[leftknot2+1].
113 * leftknot2 should be set equal to zero at the first call
114 * to the routine.
115 *
116 * OUTPUT :
117 * gaussian - Gaussian of the surface in (u,v) =
118 * (parvalue[0],parvalue[1]).
119 * jstat - Status messages
120 * = 2 : Surface is degenerate at the point, that is,
121 * the surface is not regular at this point.
122 * = 1 : Surface is close to degenerate at the point.
123 * Angle between tangents is less than the angular
124 * tolerance.
125 * = 0 : Ok.
126 * < 0 : Error.
127 *
128 * METHOD : The Gaussian is given by
129 *
130 * K(x,y) = (hxx*hyy-hxy^2)/((1+hx^2+hy^2)^2),
131 *
132 * if the surface (h(x,y)) is 1D, and
133 *
134 * K(u,v) = (eg-f*f)/(EG-F*F),
135 *
136 * if the surface (X(u,v)) is 3D. The variables E,F,G,e,f and g
137 * are the coefficients of the first and second fundamental form.
138 * They are given by: e = <N,Xuu>, f = <N,Xuv>, g = <N,Xvv>,
139 * E = <Xu,Xu>, F = <Xu,Xv> and G = <Xv,Xv>. The routine will
140 * test if the surface is degenerate (not regular) or close to
141 * degenerate. Call s2501().
142 *
143 * REFERENCES : Differential Geometry of Curves and Surfaces,
144 * (Manfredo P. Do Carmo, Prentice Hall,
145 * ISBN: 0-13-212589-7).
146 *-
147 * CALLS : s1422() and s2501().
148 *
149 * LIMITATIONS :
150 * (i) If the surface is degenerated (not regular) at the point
151 * (u,v), it makes no sense to speak about the Gaussian
152 * K(u,v). The routine returns jstat = 2.
153 * (ii) If the surface is closed to degenerate, the Gaussian
154 * K(u,v) can be numerical instable. The routine returns
155 * jstat = 1.
156 * (iii) If the surface is Cr the curvature calculated is C(r-2).
157 * (iv) The dimension of the space in which the surface lies must
158 * be 1,2 or 3.
159 *
160 *
161 * WRITTEN BY : Geir Westgaard, SINTEF, Oslo, Norway. Date: 1995-1
162 * CORRECTED BY : Ulf J Krystad, SINTEF, Oslo, Norway. Date: 1995-1
163 * Added ider, iside1 and iside2 parameters.
164 ******************************************************************************
165 */
166 {
167 int kwarn = 0; /* Local staus variable(warning). */
168 int kistat = 0; /* Local staus variable. */
169 double derive[18]; /* Array containing the computed derivatives. */
170 double normal[3]; /* Array containing the computed normalvektor. */
171
172
173 if (ider != 0) goto err178;
174
175
176 if (surf == SISL_NULL) goto err150;
177 else
178 {
179 /* Compute derivates and normal. */
180
181 s1422(surf,2,iside1,iside2,parvalue,leftknot1,leftknot2,derive,normal,&kistat);
182 if (kistat > 0) kwarn=kistat;
183
184 if (kistat < 0) /* Error in lower level routine. */
185 {
186 goto error;
187 }
188 else if (kistat != 2) /* The surface is not degenerate */
189 {
190 s2501(surf, ider, derive, normal, gaussian, &kistat);
191
192 if (kistat < 0)
193 goto error;
194 }
195 else if (kistat == 2) /* The surface is degenerated. */
196 {
197 *gaussian = 0.0;
198 goto war002;
199 }
200
201 }
202
203
204 /* Successful computations */
205
206 *jstat = kwarn;
207 goto out;
208
209
210 /* The surface is degenerated at (u,v) */
211 war002:
212 *jstat = 2;
213 goto out;
214
215 /* Error. Input (surface) pointer is SISL_NULL. */
216 err150:
217 *jstat = -150;
218 s6err("s2500", *jstat, 0);
219 goto out;
220
221 /* Illegal derivative requested. */
222 err178:
223 *jstat = -178;
224 s6err("s2500",*jstat,0);
225 goto out;
226 /* Error in lower level routine. */
227
228 error:
229 *jstat = kistat;
230 s6err("s2500",*jstat,0);
231 goto out;
232
233
234 out:
235
236 return;
237
238 }
239