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nubspline_eval_std_s.h
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1
2// einspline: a library for creating and evaluating B-splines //
3// Copyright (C) 2007 Kenneth P. Esler, Jr. //
4// //
5// This program is free software; you can redistribute it and/or modify //
6// it under the terms of the GNU General Public License as published by //
7// the Free Software Foundation; either version 2 of the License, or //
8// (at your option) any later version. //
9// //
10// This program is distributed in the hope that it will be useful, //
11// but WITHOUT ANY WARRANTY; without even the implied warranty of //
12// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the //
13// GNU General Public License for more details. //
14// //
15// You should have received a copy of the GNU General Public License //
16// along with this program; if not, write to the Free Software //
17// Foundation, Inc., 51 Franklin Street, Fifth Floor, //
18// Boston, MA 02110-1301 USA //
20
21#ifndef NUBSPLINE_EVAL_STD_S_H
22#define NUBSPLINE_EVAL_STD_S_H
23
24#include <math.h>
25#include <stdio.h>
26#include "nubspline_structs.h"
27
28/************************************************************/
29/* 1D single-precision, real evaulation functions */
30/************************************************************/
31
32/* Value only */
33inline void
34eval_NUBspline_1d_s (NUBspline_1d_s * restrict spline,
35 double x, float* restrict val)
36{
37 float bfuncs[4];
38 int i = get_NUBasis_funcs_s (spline->x_basis, x, bfuncs);
39 float* restrict coefs = spline->coefs;
40 *val = (coefs[i+0]*bfuncs[0] +coefs[i+1]*bfuncs[1] +
41 coefs[i+2]*bfuncs[2] +coefs[i+3]*bfuncs[3]);
42}
43
44/* Value and first derivative */
45inline void
46eval_NUBspline_1d_s_vg (NUBspline_1d_s * restrict spline, double x,
47 float* restrict val, float* restrict grad)
48{
49 float bfuncs[4], dbfuncs[4];
50 int i = get_NUBasis_dfuncs_s (spline->x_basis, x, bfuncs, dbfuncs);
51 float* restrict coefs = spline->coefs;
52 *val = (coefs[i+0]* bfuncs[0] + coefs[i+1]* bfuncs[1] +
53 coefs[i+2]* bfuncs[2] + coefs[i+3]* bfuncs[3]);
54 *grad = (coefs[i+0]*dbfuncs[0] + coefs[i+1]*dbfuncs[1] +
55 coefs[i+2]*dbfuncs[2] + coefs[i+3]*dbfuncs[3]);
56}
57
58/* Value, first derivative, and second derivative */
59inline void
60eval_NUBspline_1d_s_vgl (NUBspline_1d_s * restrict spline, double x,
61 float* restrict val, float* restrict grad,
62 float* restrict lapl)
63{
64 float bfuncs[4], dbfuncs[4], d2bfuncs[4];
65 int i = get_NUBasis_d2funcs_s (spline->x_basis, x, bfuncs, dbfuncs, d2bfuncs);
66 float* restrict coefs = spline->coefs;
67 *val = (coefs[i+0]* bfuncs[0] + coefs[i+1]* bfuncs[1] +
68 coefs[i+2]* bfuncs[2] + coefs[i+3]* bfuncs[3]);
69 *grad = (coefs[i+0]* dbfuncs[0] + coefs[i+1]* dbfuncs[1] +
70 coefs[i+2]* dbfuncs[2] + coefs[i+3]* dbfuncs[3]);
71 *lapl = (coefs[i+0]*d2bfuncs[0] + coefs[i+1]*d2bfuncs[1] +
72 coefs[i+2]*d2bfuncs[2] + coefs[i+3]*d2bfuncs[3]);
73
74}
75
76inline void
77eval_NUBspline_1d_s_vgh (NUBspline_1d_s * restrict spline, double x,
78 float* restrict val, float* restrict grad,
79 float* restrict hess)
80{
81 eval_NUBspline_1d_s_vgl (spline, x, val, grad, hess);
82}
83
84/************************************************************/
85/* 2D single-precision, real evaulation functions */
86/************************************************************/
87
88/* Value only */
89inline void
90eval_NUBspline_2d_s (NUBspline_2d_s * restrict spline,
91 double x, double y, float* restrict val)
92{
93 float a[4], b[4];
94 int ix = get_NUBasis_funcs_s (spline->x_basis, x, a);
95 int iy = get_NUBasis_funcs_s (spline->y_basis, y, b);
96
97 float* restrict coefs = spline->coefs;
98
99 int xs = spline->x_stride;
100#define C(i,j) coefs[(ix+(i))*xs+iy+(j)]
101 *val = (a[0]*(C(0,0)*b[0]+C(0,1)*b[1]+C(0,2)*b[2]+C(0,3)*b[3])+
102 a[1]*(C(1,0)*b[0]+C(1,1)*b[1]+C(1,2)*b[2]+C(1,3)*b[3])+
103 a[2]*(C(2,0)*b[0]+C(2,1)*b[1]+C(2,2)*b[2]+C(2,3)*b[3])+
104 a[3]*(C(3,0)*b[0]+C(3,1)*b[1]+C(3,2)*b[2]+C(3,3)*b[3]));
105#undef C
106
107}
108
109
110/* Value and gradient */
111inline void
112eval_NUBspline_2d_s_vg (NUBspline_2d_s * restrict spline,
113 double x, double y,
114 float* restrict val, float* restrict grad)
115{
116 float a[4], b[4], da[4], db[4];
117 int ix = get_NUBasis_dfuncs_s (spline->x_basis, x, a, da);
118 int iy = get_NUBasis_dfuncs_s (spline->y_basis, y, b, db);
119
120 float* restrict coefs = spline->coefs;
121
122 int xs = spline->x_stride;
123#define C(i,j) coefs[(ix+(i))*xs+iy+(j)]
124 *val = (a[0]*(C(0,0)*b[0]+C(0,1)*b[1]+C(0,2)*b[2]+C(0,3)*b[3])+
125 a[1]*(C(1,0)*b[0]+C(1,1)*b[1]+C(1,2)*b[2]+C(1,3)*b[3])+
126 a[2]*(C(2,0)*b[0]+C(2,1)*b[1]+C(2,2)*b[2]+C(2,3)*b[3])+
127 a[3]*(C(3,0)*b[0]+C(3,1)*b[1]+C(3,2)*b[2]+C(3,3)*b[3]));
128 grad[0] = (da[0]*(C(0,0)*b[0]+C(0,1)*b[1]+C(0,2)*b[2]+C(0,3)*b[3])+
129 da[1]*(C(1,0)*b[0]+C(1,1)*b[1]+C(1,2)*b[2]+C(1,3)*b[3])+
130 da[2]*(C(2,0)*b[0]+C(2,1)*b[1]+C(2,2)*b[2]+C(2,3)*b[3])+
131 da[3]*(C(3,0)*b[0]+C(3,1)*b[1]+C(3,2)*b[2]+C(3,3)*b[3]));
132 grad[1] = (a[0]*(C(0,0)*db[0]+C(0,1)*db[1]+C(0,2)*db[2]+C(0,3)*db[3])+
133 a[1]*(C(1,0)*db[0]+C(1,1)*db[1]+C(1,2)*db[2]+C(1,3)*db[3])+
134 a[2]*(C(2,0)*db[0]+C(2,1)*db[1]+C(2,2)*db[2]+C(2,3)*db[3])+
135 a[3]*(C(3,0)*db[0]+C(3,1)*db[1]+C(3,2)*db[2]+C(3,3)*db[3]));
136#undef C
137}
138
139/* Value, gradient, and laplacian */
140inline void
141eval_NUBspline_2d_s_vgl (NUBspline_2d_s * restrict spline,
142 double x, double y, float* restrict val,
143 float* restrict grad, float* restrict lapl)
144{
145 float a[4], b[4], da[4], db[4], d2a[4], d2b[4], bc[4];
146 int ix = get_NUBasis_d2funcs_s (spline->x_basis, x, a, da, d2a);
147 int iy = get_NUBasis_d2funcs_s (spline->y_basis, y, b, db, d2b);
148
149 float* restrict coefs = spline->coefs;
150
151 int xs = spline->x_stride;
152#define C(i,j) coefs[(ix+(i))*xs+iy+(j)]
153 bc[0] = (C(0,0)*b[0]+C(0,1)*b[1]+C(0,2)*b[2]+C(0,3)*b[3]);
154 bc[1] = (C(1,0)*b[0]+C(1,1)*b[1]+C(1,2)*b[2]+C(1,3)*b[3]);
155 bc[2] = (C(2,0)*b[0]+C(2,1)*b[1]+C(2,2)*b[2]+C(2,3)*b[3]);
156 bc[3] = (C(3,0)*b[0]+C(3,1)*b[1]+C(3,2)*b[2]+C(3,3)*b[3]);
157 *val = (a[0]*bc[0] + a[1]*bc[1] + a[2]*bc[2] + a[3]*bc[3]);
158 grad[0] = (da[0]*bc[0] + da[1]*bc[1] + da[2]*bc[2] + da[3]*bc[3]);
159 grad[1] = (a[0]*(C(0,0)*db[0]+C(0,1)*db[1]+C(0,2)*db[2]+C(0,3)*db[3])+
160 a[1]*(C(1,0)*db[0]+C(1,1)*db[1]+C(1,2)*db[2]+C(1,3)*db[3])+
161 a[2]*(C(2,0)*db[0]+C(2,1)*db[1]+C(2,2)*db[2]+C(2,3)*db[3])+
162 a[3]*(C(3,0)*db[0]+C(3,1)*db[1]+C(3,2)*db[2]+C(3,3)*db[3]));
163 *lapl = (d2a[0]*bc[0] + d2a[1]*bc[1] + d2a[2]*bc[2] + d2a[3]*bc[3]+
164 a[0]*(C(0,0)*d2b[0]+C(0,1)*d2b[1]+C(0,2)*d2b[2]+C(0,3)*d2b[3])+
165 a[1]*(C(1,0)*d2b[0]+C(1,1)*d2b[1]+C(1,2)*d2b[2]+C(1,3)*d2b[3])+
166 a[2]*(C(2,0)*d2b[0]+C(2,1)*d2b[1]+C(2,2)*d2b[2]+C(2,3)*d2b[3])+
167 a[3]*(C(3,0)*d2b[0]+C(3,1)*d2b[1]+C(3,2)*d2b[2]+C(3,3)*d2b[3]));
168
169#undef C
170}
171
172/* Value, gradient, and Hessian */
173inline void
174eval_NUBspline_2d_s_vgh (NUBspline_2d_s * restrict spline,
175 double x, double y, float* restrict val,
176 float* restrict grad, float* restrict hess)
177{
178 float a[4], b[4], da[4], db[4], d2a[4], d2b[4], bc[4];
179 int ix = get_NUBasis_d2funcs_s (spline->x_basis, x, a, da, d2a);
180 int iy = get_NUBasis_d2funcs_s (spline->y_basis, y, b, db, d2b);
181
182 float* restrict coefs = spline->coefs;
183
184 int xs = spline->x_stride;
185#define C(i,j) coefs[(ix+(i))*xs+iy+(j)]
186 bc[0] = (C(0,0)*b[0]+C(0,1)*b[1]+C(0,2)*b[2]+C(0,3)*b[3]);
187 bc[1] = (C(1,0)*b[0]+C(1,1)*b[1]+C(1,2)*b[2]+C(1,3)*b[3]);
188 bc[2] = (C(2,0)*b[0]+C(2,1)*b[1]+C(2,2)*b[2]+C(2,3)*b[3]);
189 bc[3] = (C(3,0)*b[0]+C(3,1)*b[1]+C(3,2)*b[2]+C(3,3)*b[3]);
190 *val = (a[0]*bc[0] + a[1]*bc[1] + a[2]*bc[2] + a[3]*bc[3]);
191 grad[0] = (da[0]*bc[0] + da[1]*bc[1] + da[2]*bc[2] + da[3]*bc[3]);
192 grad[1] = (a[0]*(C(0,0)*db[0]+C(0,1)*db[1]+C(0,2)*db[2]+C(0,3)*db[3])+
193 a[1]*(C(1,0)*db[0]+C(1,1)*db[1]+C(1,2)*db[2]+C(1,3)*db[3])+
194 a[2]*(C(2,0)*db[0]+C(2,1)*db[1]+C(2,2)*db[2]+C(2,3)*db[3])+
195 a[3]*(C(3,0)*db[0]+C(3,1)*db[1]+C(3,2)*db[2]+C(3,3)*db[3]));
196 hess[0] = (d2a[0]*bc[0] + d2a[1]*bc[1] + d2a[2]*bc[2] + d2a[3]*bc[3]);
197 hess[1] = (da[0]*(C(0,0)*db[0]+C(0,1)*db[1]+C(0,2)*db[2]+C(0,3)*db[3])+
198 da[1]*(C(1,0)*db[0]+C(1,1)*db[1]+C(1,2)*db[2]+C(1,3)*db[3])+
199 da[2]*(C(2,0)*db[0]+C(2,1)*db[1]+C(2,2)*db[2]+C(2,3)*db[3])+
200 da[3]*(C(3,0)*db[0]+C(3,1)*db[1]+C(3,2)*db[2]+C(3,3)*db[3]));
201 hess[3] = (a[0]*(C(0,0)*d2b[0]+C(0,1)*d2b[1]+C(0,2)*d2b[2]+C(0,3)*d2b[3])+
202 a[1]*(C(1,0)*d2b[0]+C(1,1)*d2b[1]+C(1,2)*d2b[2]+C(1,3)*d2b[3])+
203 a[2]*(C(2,0)*d2b[0]+C(2,1)*d2b[1]+C(2,2)*d2b[2]+C(2,3)*d2b[3])+
204 a[3]*(C(3,0)*d2b[0]+C(3,1)*d2b[1]+C(3,2)*d2b[2]+C(3,3)*d2b[3]));
205 hess[2] = hess[1];
206
207#undef C
208}
209
210
211/************************************************************/
212/* 3D single-precision, real evaulation functions */
213/************************************************************/
214
215/* Value only */
216inline void
217eval_NUBspline_3d_s (NUBspline_3d_s * restrict spline,
218 double x, double y, double z,
219 float* restrict val)
220{
221
222 float a[4], b[4], c[4];
223 int ix = get_NUBasis_funcs_s (spline->x_basis, x, a);
224 int iy = get_NUBasis_funcs_s (spline->y_basis, y, b);
225 int iz = get_NUBasis_funcs_s (spline->z_basis, z, c);
226 float* restrict coefs = spline->coefs;
227
228 int xs = spline->x_stride;
229 int ys = spline->y_stride;
230#define P(i,j,k) coefs[(ix+(i))*xs+(iy+(j))*ys+(iz+(k))]
231 *val = (a[0]*(b[0]*(P(0,0,0)*c[0]+P(0,0,1)*c[1]+P(0,0,2)*c[2]+P(0,0,3)*c[3])+
232 b[1]*(P(0,1,0)*c[0]+P(0,1,1)*c[1]+P(0,1,2)*c[2]+P(0,1,3)*c[3])+
233 b[2]*(P(0,2,0)*c[0]+P(0,2,1)*c[1]+P(0,2,2)*c[2]+P(0,2,3)*c[3])+
234 b[3]*(P(0,3,0)*c[0]+P(0,3,1)*c[1]+P(0,3,2)*c[2]+P(0,3,3)*c[3]))+
235 a[1]*(b[0]*(P(1,0,0)*c[0]+P(1,0,1)*c[1]+P(1,0,2)*c[2]+P(1,0,3)*c[3])+
236 b[1]*(P(1,1,0)*c[0]+P(1,1,1)*c[1]+P(1,1,2)*c[2]+P(1,1,3)*c[3])+
237 b[2]*(P(1,2,0)*c[0]+P(1,2,1)*c[1]+P(1,2,2)*c[2]+P(1,2,3)*c[3])+
238 b[3]*(P(1,3,0)*c[0]+P(1,3,1)*c[1]+P(1,3,2)*c[2]+P(1,3,3)*c[3]))+
239 a[2]*(b[0]*(P(2,0,0)*c[0]+P(2,0,1)*c[1]+P(2,0,2)*c[2]+P(2,0,3)*c[3])+
240 b[1]*(P(2,1,0)*c[0]+P(2,1,1)*c[1]+P(2,1,2)*c[2]+P(2,1,3)*c[3])+
241 b[2]*(P(2,2,0)*c[0]+P(2,2,1)*c[1]+P(2,2,2)*c[2]+P(2,2,3)*c[3])+
242 b[3]*(P(2,3,0)*c[0]+P(2,3,1)*c[1]+P(2,3,2)*c[2]+P(2,3,3)*c[3]))+
243 a[3]*(b[0]*(P(3,0,0)*c[0]+P(3,0,1)*c[1]+P(3,0,2)*c[2]+P(3,0,3)*c[3])+
244 b[1]*(P(3,1,0)*c[0]+P(3,1,1)*c[1]+P(3,1,2)*c[2]+P(3,1,3)*c[3])+
245 b[2]*(P(3,2,0)*c[0]+P(3,2,1)*c[1]+P(3,2,2)*c[2]+P(3,2,3)*c[3])+
246 b[3]*(P(3,3,0)*c[0]+P(3,3,1)*c[1]+P(3,3,2)*c[2]+P(3,3,3)*c[3])));
247#undef P
248
249}
250
251/* Value and gradient */
252inline void
253eval_NUBspline_3d_s_vg (NUBspline_3d_s * restrict spline,
254 double x, double y, double z,
255 float* restrict val, float* restrict grad)
256{
257 float a[4], b[4], c[4], da[4], db[4], dc[4],
258 cP[16], bcP[4], dbcP[4];
259 int ix = get_NUBasis_dfuncs_s (spline->x_basis, x, a, da);
260 int iy = get_NUBasis_dfuncs_s (spline->y_basis, y, b, db);
261 int iz = get_NUBasis_dfuncs_s (spline->z_basis, z, c, dc);
262 float* restrict coefs = spline->coefs;
263
264 int xs = spline->x_stride;
265 int ys = spline->y_stride;
266#define P(i,j,k) coefs[(ix+(i))*xs+(iy+(j))*ys+(iz+(k))]
267 cP[ 0] = (P(0,0,0)*c[0]+P(0,0,1)*c[1]+P(0,0,2)*c[2]+P(0,0,3)*c[3]);
268 cP[ 1] = (P(0,1,0)*c[0]+P(0,1,1)*c[1]+P(0,1,2)*c[2]+P(0,1,3)*c[3]);
269 cP[ 2] = (P(0,2,0)*c[0]+P(0,2,1)*c[1]+P(0,2,2)*c[2]+P(0,2,3)*c[3]);
270 cP[ 3] = (P(0,3,0)*c[0]+P(0,3,1)*c[1]+P(0,3,2)*c[2]+P(0,3,3)*c[3]);
271 cP[ 4] = (P(1,0,0)*c[0]+P(1,0,1)*c[1]+P(1,0,2)*c[2]+P(1,0,3)*c[3]);
272 cP[ 5] = (P(1,1,0)*c[0]+P(1,1,1)*c[1]+P(1,1,2)*c[2]+P(1,1,3)*c[3]);
273 cP[ 6] = (P(1,2,0)*c[0]+P(1,2,1)*c[1]+P(1,2,2)*c[2]+P(1,2,3)*c[3]);
274 cP[ 7] = (P(1,3,0)*c[0]+P(1,3,1)*c[1]+P(1,3,2)*c[2]+P(1,3,3)*c[3]);
275 cP[ 8] = (P(2,0,0)*c[0]+P(2,0,1)*c[1]+P(2,0,2)*c[2]+P(2,0,3)*c[3]);
276 cP[ 9] = (P(2,1,0)*c[0]+P(2,1,1)*c[1]+P(2,1,2)*c[2]+P(2,1,3)*c[3]);
277 cP[10] = (P(2,2,0)*c[0]+P(2,2,1)*c[1]+P(2,2,2)*c[2]+P(2,2,3)*c[3]);
278 cP[11] = (P(2,3,0)*c[0]+P(2,3,1)*c[1]+P(2,3,2)*c[2]+P(2,3,3)*c[3]);
279 cP[12] = (P(3,0,0)*c[0]+P(3,0,1)*c[1]+P(3,0,2)*c[2]+P(3,0,3)*c[3]);
280 cP[13] = (P(3,1,0)*c[0]+P(3,1,1)*c[1]+P(3,1,2)*c[2]+P(3,1,3)*c[3]);
281 cP[14] = (P(3,2,0)*c[0]+P(3,2,1)*c[1]+P(3,2,2)*c[2]+P(3,2,3)*c[3]);
282 cP[15] = (P(3,3,0)*c[0]+P(3,3,1)*c[1]+P(3,3,2)*c[2]+P(3,3,3)*c[3]);
283
284 bcP[0] = ( b[0]*cP[ 0] + b[1]*cP[ 1] + b[2]*cP[ 2] + b[3]*cP[ 3]);
285 bcP[1] = ( b[0]*cP[ 4] + b[1]*cP[ 5] + b[2]*cP[ 6] + b[3]*cP[ 7]);
286 bcP[2] = ( b[0]*cP[ 8] + b[1]*cP[ 9] + b[2]*cP[10] + b[3]*cP[11]);
287 bcP[3] = ( b[0]*cP[12] + b[1]*cP[13] + b[2]*cP[14] + b[3]*cP[15]);
288
289 dbcP[0] = ( db[0]*cP[ 0] + db[1]*cP[ 1] + db[2]*cP[ 2] + db[3]*cP[ 3]);
290 dbcP[1] = ( db[0]*cP[ 4] + db[1]*cP[ 5] + db[2]*cP[ 6] + db[3]*cP[ 7]);
291 dbcP[2] = ( db[0]*cP[ 8] + db[1]*cP[ 9] + db[2]*cP[10] + db[3]*cP[11]);
292 dbcP[3] = ( db[0]*cP[12] + db[1]*cP[13] + db[2]*cP[14] + db[3]*cP[15]);
293
294 *val = ( a[0]*bcP[0] + a[1]*bcP[1] + a[2]*bcP[2] + a[3]*bcP[3]);
295 grad[0] = (da[0]*bcP[0] + da[1]*bcP[1] + da[2]*bcP[2] + da[3]*bcP[3]);
296 grad[1] = (a[0]*dbcP[0] + a[1]*dbcP[1] + a[2]*dbcP[2] + a[3]*dbcP[3]);
297 grad[2] =
298 (a[0]*(b[0]*(P(0,0,0)*dc[0]+P(0,0,1)*dc[1]+P(0,0,2)*dc[2]+P(0,0,3)*dc[3])+
299 b[1]*(P(0,1,0)*dc[0]+P(0,1,1)*dc[1]+P(0,1,2)*dc[2]+P(0,1,3)*dc[3])+
300 b[2]*(P(0,2,0)*dc[0]+P(0,2,1)*dc[1]+P(0,2,2)*dc[2]+P(0,2,3)*dc[3])+
301 b[3]*(P(0,3,0)*dc[0]+P(0,3,1)*dc[1]+P(0,3,2)*dc[2]+P(0,3,3)*dc[3]))+
302 a[1]*(b[0]*(P(1,0,0)*dc[0]+P(1,0,1)*dc[1]+P(1,0,2)*dc[2]+P(1,0,3)*dc[3])+
303 b[1]*(P(1,1,0)*dc[0]+P(1,1,1)*dc[1]+P(1,1,2)*dc[2]+P(1,1,3)*dc[3])+
304 b[2]*(P(1,2,0)*dc[0]+P(1,2,1)*dc[1]+P(1,2,2)*dc[2]+P(1,2,3)*dc[3])+
305 b[3]*(P(1,3,0)*dc[0]+P(1,3,1)*dc[1]+P(1,3,2)*dc[2]+P(1,3,3)*dc[3]))+
306 a[2]*(b[0]*(P(2,0,0)*dc[0]+P(2,0,1)*dc[1]+P(2,0,2)*dc[2]+P(2,0,3)*dc[3])+
307 b[1]*(P(2,1,0)*dc[0]+P(2,1,1)*dc[1]+P(2,1,2)*dc[2]+P(2,1,3)*dc[3])+
308 b[2]*(P(2,2,0)*dc[0]+P(2,2,1)*dc[1]+P(2,2,2)*dc[2]+P(2,2,3)*dc[3])+
309 b[3]*(P(2,3,0)*dc[0]+P(2,3,1)*dc[1]+P(2,3,2)*dc[2]+P(2,3,3)*dc[3]))+
310 a[3]*(b[0]*(P(3,0,0)*dc[0]+P(3,0,1)*dc[1]+P(3,0,2)*dc[2]+P(3,0,3)*dc[3])+
311 b[1]*(P(3,1,0)*dc[0]+P(3,1,1)*dc[1]+P(3,1,2)*dc[2]+P(3,1,3)*dc[3])+
312 b[2]*(P(3,2,0)*dc[0]+P(3,2,1)*dc[1]+P(3,2,2)*dc[2]+P(3,2,3)*dc[3])+
313 b[3]*(P(3,3,0)*dc[0]+P(3,3,1)*dc[1]+P(3,3,2)*dc[2]+P(3,3,3)*dc[3])));
314#undef P
315
316}
317
318
319
320/* Value, gradient, and laplacian */
321inline void
322eval_NUBspline_3d_s_vgl (NUBspline_3d_s * restrict spline,
323 double x, double y, double z,
324 float* restrict val, float* restrict grad, float* restrict lapl)
325{
326 float a[4], b[4], c[4], da[4], db[4], dc[4],
327 d2a[4], d2b[4], d2c[4], cP[16], dcP[16], bcP[4], dbcP[4], d2bcP[4], bdcP[4];
328
329 int ix = get_NUBasis_d2funcs_s (spline->x_basis, x, a, da, d2a);
330 int iy = get_NUBasis_d2funcs_s (spline->y_basis, y, b, db, d2b);
331 int iz = get_NUBasis_d2funcs_s (spline->z_basis, z, c, dc, d2c);
332
333 float* restrict coefs = spline->coefs;
334 int xs = spline->x_stride;
335 int ys = spline->y_stride;
336#define P(i,j,k) coefs[(ix+(i))*xs+(iy+(j))*ys+(iz+(k))]
337 cP[ 0] = (P(0,0,0)*c[0]+P(0,0,1)*c[1]+P(0,0,2)*c[2]+P(0,0,3)*c[3]);
338 cP[ 1] = (P(0,1,0)*c[0]+P(0,1,1)*c[1]+P(0,1,2)*c[2]+P(0,1,3)*c[3]);
339 cP[ 2] = (P(0,2,0)*c[0]+P(0,2,1)*c[1]+P(0,2,2)*c[2]+P(0,2,3)*c[3]);
340 cP[ 3] = (P(0,3,0)*c[0]+P(0,3,1)*c[1]+P(0,3,2)*c[2]+P(0,3,3)*c[3]);
341 cP[ 4] = (P(1,0,0)*c[0]+P(1,0,1)*c[1]+P(1,0,2)*c[2]+P(1,0,3)*c[3]);
342 cP[ 5] = (P(1,1,0)*c[0]+P(1,1,1)*c[1]+P(1,1,2)*c[2]+P(1,1,3)*c[3]);
343 cP[ 6] = (P(1,2,0)*c[0]+P(1,2,1)*c[1]+P(1,2,2)*c[2]+P(1,2,3)*c[3]);
344 cP[ 7] = (P(1,3,0)*c[0]+P(1,3,1)*c[1]+P(1,3,2)*c[2]+P(1,3,3)*c[3]);
345 cP[ 8] = (P(2,0,0)*c[0]+P(2,0,1)*c[1]+P(2,0,2)*c[2]+P(2,0,3)*c[3]);
346 cP[ 9] = (P(2,1,0)*c[0]+P(2,1,1)*c[1]+P(2,1,2)*c[2]+P(2,1,3)*c[3]);
347 cP[10] = (P(2,2,0)*c[0]+P(2,2,1)*c[1]+P(2,2,2)*c[2]+P(2,2,3)*c[3]);
348 cP[11] = (P(2,3,0)*c[0]+P(2,3,1)*c[1]+P(2,3,2)*c[2]+P(2,3,3)*c[3]);
349 cP[12] = (P(3,0,0)*c[0]+P(3,0,1)*c[1]+P(3,0,2)*c[2]+P(3,0,3)*c[3]);
350 cP[13] = (P(3,1,0)*c[0]+P(3,1,1)*c[1]+P(3,1,2)*c[2]+P(3,1,3)*c[3]);
351 cP[14] = (P(3,2,0)*c[0]+P(3,2,1)*c[1]+P(3,2,2)*c[2]+P(3,2,3)*c[3]);
352 cP[15] = (P(3,3,0)*c[0]+P(3,3,1)*c[1]+P(3,3,2)*c[2]+P(3,3,3)*c[3]);
353
354 dcP[ 0] = (P(0,0,0)*dc[0]+P(0,0,1)*dc[1]+P(0,0,2)*dc[2]+P(0,0,3)*dc[3]);
355 dcP[ 1] = (P(0,1,0)*dc[0]+P(0,1,1)*dc[1]+P(0,1,2)*dc[2]+P(0,1,3)*dc[3]);
356 dcP[ 2] = (P(0,2,0)*dc[0]+P(0,2,1)*dc[1]+P(0,2,2)*dc[2]+P(0,2,3)*dc[3]);
357 dcP[ 3] = (P(0,3,0)*dc[0]+P(0,3,1)*dc[1]+P(0,3,2)*dc[2]+P(0,3,3)*dc[3]);
358 dcP[ 4] = (P(1,0,0)*dc[0]+P(1,0,1)*dc[1]+P(1,0,2)*dc[2]+P(1,0,3)*dc[3]);
359 dcP[ 5] = (P(1,1,0)*dc[0]+P(1,1,1)*dc[1]+P(1,1,2)*dc[2]+P(1,1,3)*dc[3]);
360 dcP[ 6] = (P(1,2,0)*dc[0]+P(1,2,1)*dc[1]+P(1,2,2)*dc[2]+P(1,2,3)*dc[3]);
361 dcP[ 7] = (P(1,3,0)*dc[0]+P(1,3,1)*dc[1]+P(1,3,2)*dc[2]+P(1,3,3)*dc[3]);
362 dcP[ 8] = (P(2,0,0)*dc[0]+P(2,0,1)*dc[1]+P(2,0,2)*dc[2]+P(2,0,3)*dc[3]);
363 dcP[ 9] = (P(2,1,0)*dc[0]+P(2,1,1)*dc[1]+P(2,1,2)*dc[2]+P(2,1,3)*dc[3]);
364 dcP[10] = (P(2,2,0)*dc[0]+P(2,2,1)*dc[1]+P(2,2,2)*dc[2]+P(2,2,3)*dc[3]);
365 dcP[11] = (P(2,3,0)*dc[0]+P(2,3,1)*dc[1]+P(2,3,2)*dc[2]+P(2,3,3)*dc[3]);
366 dcP[12] = (P(3,0,0)*dc[0]+P(3,0,1)*dc[1]+P(3,0,2)*dc[2]+P(3,0,3)*dc[3]);
367 dcP[13] = (P(3,1,0)*dc[0]+P(3,1,1)*dc[1]+P(3,1,2)*dc[2]+P(3,1,3)*dc[3]);
368 dcP[14] = (P(3,2,0)*dc[0]+P(3,2,1)*dc[1]+P(3,2,2)*dc[2]+P(3,2,3)*dc[3]);
369 dcP[15] = (P(3,3,0)*dc[0]+P(3,3,1)*dc[1]+P(3,3,2)*dc[2]+P(3,3,3)*dc[3]);
370
371 bcP[0] = ( b[0]*cP[ 0] + b[1]*cP[ 1] + b[2]*cP[ 2] + b[3]*cP[ 3]);
372 bcP[1] = ( b[0]*cP[ 4] + b[1]*cP[ 5] + b[2]*cP[ 6] + b[3]*cP[ 7]);
373 bcP[2] = ( b[0]*cP[ 8] + b[1]*cP[ 9] + b[2]*cP[10] + b[3]*cP[11]);
374 bcP[3] = ( b[0]*cP[12] + b[1]*cP[13] + b[2]*cP[14] + b[3]*cP[15]);
375
376 dbcP[0] = ( db[0]*cP[ 0] + db[1]*cP[ 1] + db[2]*cP[ 2] + db[3]*cP[ 3]);
377 dbcP[1] = ( db[0]*cP[ 4] + db[1]*cP[ 5] + db[2]*cP[ 6] + db[3]*cP[ 7]);
378 dbcP[2] = ( db[0]*cP[ 8] + db[1]*cP[ 9] + db[2]*cP[10] + db[3]*cP[11]);
379 dbcP[3] = ( db[0]*cP[12] + db[1]*cP[13] + db[2]*cP[14] + db[3]*cP[15]);
380
381 bdcP[0] = ( b[0]*dcP[ 0] + b[1]*dcP[ 1] + b[2]*dcP[ 2] + b[3]*dcP[ 3]);
382 bdcP[1] = ( b[0]*dcP[ 4] + b[1]*dcP[ 5] + b[2]*dcP[ 6] + b[3]*dcP[ 7]);
383 bdcP[2] = ( b[0]*dcP[ 8] + b[1]*dcP[ 9] + b[2]*dcP[10] + b[3]*dcP[11]);
384 bdcP[3] = ( b[0]*dcP[12] + b[1]*dcP[13] + b[2]*dcP[14] + b[3]*dcP[15]);
385
386 d2bcP[0] = ( d2b[0]*cP[ 0] + d2b[1]*cP[ 1] + d2b[2]*cP[ 2] + d2b[3]*cP[ 3]);
387 d2bcP[1] = ( d2b[0]*cP[ 4] + d2b[1]*cP[ 5] + d2b[2]*cP[ 6] + d2b[3]*cP[ 7]);
388 d2bcP[2] = ( d2b[0]*cP[ 8] + d2b[1]*cP[ 9] + d2b[2]*cP[10] + d2b[3]*cP[11]);
389 d2bcP[3] = ( d2b[0]*cP[12] + d2b[1]*cP[13] + d2b[2]*cP[14] + d2b[3]*cP[15]);
390
391
392 *val =
393 ( a[0]*bcP[0] + a[1]*bcP[1] + a[2]*bcP[2] + a[3]*bcP[3]);
394
395 grad[0] =
396 (da[0]*bcP[0] + da[1]*bcP[1] + da[2]*bcP[2] + da[3]*bcP[3]);
397 grad[1] =
398 (a[0]*dbcP[0] + a[1]*dbcP[1] + a[2]*dbcP[2] + a[3]*dbcP[3]);
399 grad[2] =
400 (a[0]*bdcP[0] + a[1]*bdcP[1] + a[2]*bdcP[2] + a[3]*bdcP[3]);
401
402 *lapl = (d2a[0]*bcP[0] + d2a[1]*bcP[1] + d2a[2]*bcP[2] + d2a[3]*bcP[3])
403 + (a[0]*d2bcP[0] + a[1]*d2bcP[1] + a[2]*d2bcP[2] + a[3]*d2bcP[3]) +
404 (a[0]*(b[0]*(P(0,0,0)*d2c[0]+P(0,0,1)*d2c[1]+P(0,0,2)*d2c[2]+P(0,0,3)*d2c[3])+
405 b[1]*(P(0,1,0)*d2c[0]+P(0,1,1)*d2c[1]+P(0,1,2)*d2c[2]+P(0,1,3)*d2c[3])+
406 b[2]*(P(0,2,0)*d2c[0]+P(0,2,1)*d2c[1]+P(0,2,2)*d2c[2]+P(0,2,3)*d2c[3])+
407 b[3]*(P(0,3,0)*d2c[0]+P(0,3,1)*d2c[1]+P(0,3,2)*d2c[2]+P(0,3,3)*d2c[3]))+
408 a[1]*(b[0]*(P(1,0,0)*d2c[0]+P(1,0,1)*d2c[1]+P(1,0,2)*d2c[2]+P(1,0,3)*d2c[3])+
409 b[1]*(P(1,1,0)*d2c[0]+P(1,1,1)*d2c[1]+P(1,1,2)*d2c[2]+P(1,1,3)*d2c[3])+
410 b[2]*(P(1,2,0)*d2c[0]+P(1,2,1)*d2c[1]+P(1,2,2)*d2c[2]+P(1,2,3)*d2c[3])+
411 b[3]*(P(1,3,0)*d2c[0]+P(1,3,1)*d2c[1]+P(1,3,2)*d2c[2]+P(1,3,3)*d2c[3]))+
412 a[2]*(b[0]*(P(2,0,0)*d2c[0]+P(2,0,1)*d2c[1]+P(2,0,2)*d2c[2]+P(2,0,3)*d2c[3])+
413 b[1]*(P(2,1,0)*d2c[0]+P(2,1,1)*d2c[1]+P(2,1,2)*d2c[2]+P(2,1,3)*d2c[3])+
414 b[2]*(P(2,2,0)*d2c[0]+P(2,2,1)*d2c[1]+P(2,2,2)*d2c[2]+P(2,2,3)*d2c[3])+
415 b[3]*(P(2,3,0)*d2c[0]+P(2,3,1)*d2c[1]+P(2,3,2)*d2c[2]+P(2,3,3)*d2c[3]))+
416 a[3]*(b[0]*(P(3,0,0)*d2c[0]+P(3,0,1)*d2c[1]+P(3,0,2)*d2c[2]+P(3,0,3)*d2c[3])+
417 b[1]*(P(3,1,0)*d2c[0]+P(3,1,1)*d2c[1]+P(3,1,2)*d2c[2]+P(3,1,3)*d2c[3])+
418 b[2]*(P(3,2,0)*d2c[0]+P(3,2,1)*d2c[1]+P(3,2,2)*d2c[2]+P(3,2,3)*d2c[3])+
419 b[3]*(P(3,3,0)*d2c[0]+P(3,3,1)*d2c[1]+P(3,3,2)*d2c[2]+P(3,3,3)*d2c[3])));
420#undef P
421
422}
423
424
425
426
427
428/* Value, gradient, and Hessian */
429inline void
430eval_NUBspline_3d_s_vgh (NUBspline_3d_s * restrict spline,
431 double x, double y, double z,
432 float* restrict val, float* restrict grad, float* restrict hess)
433{
434 float a[4], b[4], c[4], da[4], db[4], dc[4],
435 d2a[4], d2b[4], d2c[4], cP[16], dcP[16], d2cP[16], bcP[4], dbcP[4],
436 d2bcP[4], dbdcP[4], bd2cP[4], bdcP[4];
437 int ix = get_NUBasis_d2funcs_s (spline->x_basis, x, a, da, d2a);
438 int iy = get_NUBasis_d2funcs_s (spline->y_basis, y, b, db, d2b);
439 int iz = get_NUBasis_d2funcs_s (spline->z_basis, z, c, dc, d2c);
440
441 int xs = spline->x_stride;
442 int ys = spline->y_stride;
443 float* restrict coefs = spline->coefs;
444#define P(i,j,k) coefs[(ix+(i))*xs+(iy+(j))*ys+(iz+(k))]
445 cP[ 0] = (P(0,0,0)*c[0]+P(0,0,1)*c[1]+P(0,0,2)*c[2]+P(0,0,3)*c[3]);
446 cP[ 1] = (P(0,1,0)*c[0]+P(0,1,1)*c[1]+P(0,1,2)*c[2]+P(0,1,3)*c[3]);
447 cP[ 2] = (P(0,2,0)*c[0]+P(0,2,1)*c[1]+P(0,2,2)*c[2]+P(0,2,3)*c[3]);
448 cP[ 3] = (P(0,3,0)*c[0]+P(0,3,1)*c[1]+P(0,3,2)*c[2]+P(0,3,3)*c[3]);
449 cP[ 4] = (P(1,0,0)*c[0]+P(1,0,1)*c[1]+P(1,0,2)*c[2]+P(1,0,3)*c[3]);
450 cP[ 5] = (P(1,1,0)*c[0]+P(1,1,1)*c[1]+P(1,1,2)*c[2]+P(1,1,3)*c[3]);
451 cP[ 6] = (P(1,2,0)*c[0]+P(1,2,1)*c[1]+P(1,2,2)*c[2]+P(1,2,3)*c[3]);
452 cP[ 7] = (P(1,3,0)*c[0]+P(1,3,1)*c[1]+P(1,3,2)*c[2]+P(1,3,3)*c[3]);
453 cP[ 8] = (P(2,0,0)*c[0]+P(2,0,1)*c[1]+P(2,0,2)*c[2]+P(2,0,3)*c[3]);
454 cP[ 9] = (P(2,1,0)*c[0]+P(2,1,1)*c[1]+P(2,1,2)*c[2]+P(2,1,3)*c[3]);
455 cP[10] = (P(2,2,0)*c[0]+P(2,2,1)*c[1]+P(2,2,2)*c[2]+P(2,2,3)*c[3]);
456 cP[11] = (P(2,3,0)*c[0]+P(2,3,1)*c[1]+P(2,3,2)*c[2]+P(2,3,3)*c[3]);
457 cP[12] = (P(3,0,0)*c[0]+P(3,0,1)*c[1]+P(3,0,2)*c[2]+P(3,0,3)*c[3]);
458 cP[13] = (P(3,1,0)*c[0]+P(3,1,1)*c[1]+P(3,1,2)*c[2]+P(3,1,3)*c[3]);
459 cP[14] = (P(3,2,0)*c[0]+P(3,2,1)*c[1]+P(3,2,2)*c[2]+P(3,2,3)*c[3]);
460 cP[15] = (P(3,3,0)*c[0]+P(3,3,1)*c[1]+P(3,3,2)*c[2]+P(3,3,3)*c[3]);
461
462 dcP[ 0] = (P(0,0,0)*dc[0]+P(0,0,1)*dc[1]+P(0,0,2)*dc[2]+P(0,0,3)*dc[3]);
463 dcP[ 1] = (P(0,1,0)*dc[0]+P(0,1,1)*dc[1]+P(0,1,2)*dc[2]+P(0,1,3)*dc[3]);
464 dcP[ 2] = (P(0,2,0)*dc[0]+P(0,2,1)*dc[1]+P(0,2,2)*dc[2]+P(0,2,3)*dc[3]);
465 dcP[ 3] = (P(0,3,0)*dc[0]+P(0,3,1)*dc[1]+P(0,3,2)*dc[2]+P(0,3,3)*dc[3]);
466 dcP[ 4] = (P(1,0,0)*dc[0]+P(1,0,1)*dc[1]+P(1,0,2)*dc[2]+P(1,0,3)*dc[3]);
467 dcP[ 5] = (P(1,1,0)*dc[0]+P(1,1,1)*dc[1]+P(1,1,2)*dc[2]+P(1,1,3)*dc[3]);
468 dcP[ 6] = (P(1,2,0)*dc[0]+P(1,2,1)*dc[1]+P(1,2,2)*dc[2]+P(1,2,3)*dc[3]);
469 dcP[ 7] = (P(1,3,0)*dc[0]+P(1,3,1)*dc[1]+P(1,3,2)*dc[2]+P(1,3,3)*dc[3]);
470 dcP[ 8] = (P(2,0,0)*dc[0]+P(2,0,1)*dc[1]+P(2,0,2)*dc[2]+P(2,0,3)*dc[3]);
471 dcP[ 9] = (P(2,1,0)*dc[0]+P(2,1,1)*dc[1]+P(2,1,2)*dc[2]+P(2,1,3)*dc[3]);
472 dcP[10] = (P(2,2,0)*dc[0]+P(2,2,1)*dc[1]+P(2,2,2)*dc[2]+P(2,2,3)*dc[3]);
473 dcP[11] = (P(2,3,0)*dc[0]+P(2,3,1)*dc[1]+P(2,3,2)*dc[2]+P(2,3,3)*dc[3]);
474 dcP[12] = (P(3,0,0)*dc[0]+P(3,0,1)*dc[1]+P(3,0,2)*dc[2]+P(3,0,3)*dc[3]);
475 dcP[13] = (P(3,1,0)*dc[0]+P(3,1,1)*dc[1]+P(3,1,2)*dc[2]+P(3,1,3)*dc[3]);
476 dcP[14] = (P(3,2,0)*dc[0]+P(3,2,1)*dc[1]+P(3,2,2)*dc[2]+P(3,2,3)*dc[3]);
477 dcP[15] = (P(3,3,0)*dc[0]+P(3,3,1)*dc[1]+P(3,3,2)*dc[2]+P(3,3,3)*dc[3]);
478
479 d2cP[ 0] = (P(0,0,0)*d2c[0]+P(0,0,1)*d2c[1]+P(0,0,2)*d2c[2]+P(0,0,3)*d2c[3]);
480 d2cP[ 1] = (P(0,1,0)*d2c[0]+P(0,1,1)*d2c[1]+P(0,1,2)*d2c[2]+P(0,1,3)*d2c[3]);
481 d2cP[ 2] = (P(0,2,0)*d2c[0]+P(0,2,1)*d2c[1]+P(0,2,2)*d2c[2]+P(0,2,3)*d2c[3]);
482 d2cP[ 3] = (P(0,3,0)*d2c[0]+P(0,3,1)*d2c[1]+P(0,3,2)*d2c[2]+P(0,3,3)*d2c[3]);
483 d2cP[ 4] = (P(1,0,0)*d2c[0]+P(1,0,1)*d2c[1]+P(1,0,2)*d2c[2]+P(1,0,3)*d2c[3]);
484 d2cP[ 5] = (P(1,1,0)*d2c[0]+P(1,1,1)*d2c[1]+P(1,1,2)*d2c[2]+P(1,1,3)*d2c[3]);
485 d2cP[ 6] = (P(1,2,0)*d2c[0]+P(1,2,1)*d2c[1]+P(1,2,2)*d2c[2]+P(1,2,3)*d2c[3]);
486 d2cP[ 7] = (P(1,3,0)*d2c[0]+P(1,3,1)*d2c[1]+P(1,3,2)*d2c[2]+P(1,3,3)*d2c[3]);
487 d2cP[ 8] = (P(2,0,0)*d2c[0]+P(2,0,1)*d2c[1]+P(2,0,2)*d2c[2]+P(2,0,3)*d2c[3]);
488 d2cP[ 9] = (P(2,1,0)*d2c[0]+P(2,1,1)*d2c[1]+P(2,1,2)*d2c[2]+P(2,1,3)*d2c[3]);
489 d2cP[10] = (P(2,2,0)*d2c[0]+P(2,2,1)*d2c[1]+P(2,2,2)*d2c[2]+P(2,2,3)*d2c[3]);
490 d2cP[11] = (P(2,3,0)*d2c[0]+P(2,3,1)*d2c[1]+P(2,3,2)*d2c[2]+P(2,3,3)*d2c[3]);
491 d2cP[12] = (P(3,0,0)*d2c[0]+P(3,0,1)*d2c[1]+P(3,0,2)*d2c[2]+P(3,0,3)*d2c[3]);
492 d2cP[13] = (P(3,1,0)*d2c[0]+P(3,1,1)*d2c[1]+P(3,1,2)*d2c[2]+P(3,1,3)*d2c[3]);
493 d2cP[14] = (P(3,2,0)*d2c[0]+P(3,2,1)*d2c[1]+P(3,2,2)*d2c[2]+P(3,2,3)*d2c[3]);
494 d2cP[15] = (P(3,3,0)*d2c[0]+P(3,3,1)*d2c[1]+P(3,3,2)*d2c[2]+P(3,3,3)*d2c[3]);
495
496 bcP[0] = ( b[0]*cP[ 0] + b[1]*cP[ 1] + b[2]*cP[ 2] + b[3]*cP[ 3]);
497 bcP[1] = ( b[0]*cP[ 4] + b[1]*cP[ 5] + b[2]*cP[ 6] + b[3]*cP[ 7]);
498 bcP[2] = ( b[0]*cP[ 8] + b[1]*cP[ 9] + b[2]*cP[10] + b[3]*cP[11]);
499 bcP[3] = ( b[0]*cP[12] + b[1]*cP[13] + b[2]*cP[14] + b[3]*cP[15]);
500
501 dbcP[0] = ( db[0]*cP[ 0] + db[1]*cP[ 1] + db[2]*cP[ 2] + db[3]*cP[ 3]);
502 dbcP[1] = ( db[0]*cP[ 4] + db[1]*cP[ 5] + db[2]*cP[ 6] + db[3]*cP[ 7]);
503 dbcP[2] = ( db[0]*cP[ 8] + db[1]*cP[ 9] + db[2]*cP[10] + db[3]*cP[11]);
504 dbcP[3] = ( db[0]*cP[12] + db[1]*cP[13] + db[2]*cP[14] + db[3]*cP[15]);
505
506 bdcP[0] = ( b[0]*dcP[ 0] + b[1]*dcP[ 1] + b[2]*dcP[ 2] + b[3]*dcP[ 3]);
507 bdcP[1] = ( b[0]*dcP[ 4] + b[1]*dcP[ 5] + b[2]*dcP[ 6] + b[3]*dcP[ 7]);
508 bdcP[2] = ( b[0]*dcP[ 8] + b[1]*dcP[ 9] + b[2]*dcP[10] + b[3]*dcP[11]);
509 bdcP[3] = ( b[0]*dcP[12] + b[1]*dcP[13] + b[2]*dcP[14] + b[3]*dcP[15]);
510
511 bd2cP[0] = ( b[0]*d2cP[ 0] + b[1]*d2cP[ 1] + b[2]*d2cP[ 2] + b[3]*d2cP[ 3]);
512 bd2cP[1] = ( b[0]*d2cP[ 4] + b[1]*d2cP[ 5] + b[2]*d2cP[ 6] + b[3]*d2cP[ 7]);
513 bd2cP[2] = ( b[0]*d2cP[ 8] + b[1]*d2cP[ 9] + b[2]*d2cP[10] + b[3]*d2cP[11]);
514 bd2cP[3] = ( b[0]*d2cP[12] + b[1]*d2cP[13] + b[2]*d2cP[14] + b[3]*d2cP[15]);
515
516 d2bcP[0] = ( d2b[0]*cP[ 0] + d2b[1]*cP[ 1] + d2b[2]*cP[ 2] + d2b[3]*cP[ 3]);
517 d2bcP[1] = ( d2b[0]*cP[ 4] + d2b[1]*cP[ 5] + d2b[2]*cP[ 6] + d2b[3]*cP[ 7]);
518 d2bcP[2] = ( d2b[0]*cP[ 8] + d2b[1]*cP[ 9] + d2b[2]*cP[10] + d2b[3]*cP[11]);
519 d2bcP[3] = ( d2b[0]*cP[12] + d2b[1]*cP[13] + d2b[2]*cP[14] + d2b[3]*cP[15]);
520
521 dbdcP[0] = ( db[0]*dcP[ 0] + db[1]*dcP[ 1] + db[2]*dcP[ 2] + db[3]*dcP[ 3]);
522 dbdcP[1] = ( db[0]*dcP[ 4] + db[1]*dcP[ 5] + db[2]*dcP[ 6] + db[3]*dcP[ 7]);
523 dbdcP[2] = ( db[0]*dcP[ 8] + db[1]*dcP[ 9] + db[2]*dcP[10] + db[3]*dcP[11]);
524 dbdcP[3] = ( db[0]*dcP[12] + db[1]*dcP[13] + db[2]*dcP[14] + db[3]*dcP[15]);
525
526 *val = a[0]*bcP[0] + a[1]*bcP[1] + a[2]*bcP[2] + a[3]*bcP[3];
527 grad[0] = (da[0] *bcP[0] + da[1]*bcP[1] + da[2]*bcP[2] + da[3]*bcP[3]);
528 grad[1] = (a[0]*dbcP[0] + a[1]*dbcP[1] + a[2]*dbcP[2] + a[3]*dbcP[3]);
529 grad[2] = (a[0]*bdcP[0] + a[1]*bdcP[1] + a[2]*bdcP[2] + a[3]*bdcP[3]);
530 // d2x
531 hess[0] = (d2a[0]*bcP[0] + d2a[1]*bcP[1] + d2a[2]*bcP[2] + d2a[3]*bcP[3]);
532 // dx dy
533 hess[1] = (da[0]*dbcP[0] + da[1]*dbcP[1] + da[1]*dbcP[1] + da[1]*dbcP[1]);
534 hess[3] = hess[1];
535 // dx dz;
536 hess[2] = (da[0]*bdcP[0] + da[1]*bdcP[1] + da[1]*bdcP[1] + da[1]*bdcP[1]);
537 hess[6] = hess[2];
538 // d2y
539 hess[4] = (a[0]*d2bcP[0] + a[1]*d2bcP[1] + a[2]*d2bcP[2] + a[3]*d2bcP[3]);
540 // dy dz
541 hess[5] = (a[0]*dbdcP[0] + a[1]*dbdcP[1] + a[2]*dbdcP[2] + a[3]*dbdcP[3]);
542 hess[7] = hess[5];
543 // d2z
544 hess[8] = (a[0]*bd2cP[0] + a[1]*bd2cP[1] + a[2]*bd2cP[2] + a[3]*bd2cP[3]);
545#undef P
546
547}
548
549#endif
restrict
#define restrict
Definition local_definitions.h:4
get_NUBasis_dfuncs_s
int get_NUBasis_dfuncs_s(NUBasis *restrict basis, double x, float bfuncs[4], float dbfuncs[4])
Definition nubasis.cpp:121
get_NUBasis_funcs_s
int get_NUBasis_funcs_s(NUBasis *restrict basis, double x, float bfuncs[4])
Definition nubasis.cpp:71
get_NUBasis_d2funcs_s
int get_NUBasis_d2funcs_s(NUBasis *restrict basis, double x, float bfuncs[4], float dbfuncs[4], float d2bfuncs[4])
Definition nubasis.cpp:183
eval_NUBspline_1d_s
void eval_NUBspline_1d_s(NUBspline_1d_s *restrict spline, double x, float *restrict val)
Definition nubspline_eval_std_s.h:34
eval_NUBspline_3d_s_vgl
void eval_NUBspline_3d_s_vgl(NUBspline_3d_s *restrict spline, double x, double y, double z, float *restrict val, float *restrict grad, float *restrict lapl)
Definition nubspline_eval_std_s.h:322
C
#define C(i, j)
eval_NUBspline_2d_s_vg
void eval_NUBspline_2d_s_vg(NUBspline_2d_s *restrict spline, double x, double y, float *restrict val, float *restrict grad)
Definition nubspline_eval_std_s.h:112
eval_NUBspline_3d_s
void eval_NUBspline_3d_s(NUBspline_3d_s *restrict spline, double x, double y, double z, float *restrict val)
Definition nubspline_eval_std_s.h:217
P
#define P(i, j, k)
eval_NUBspline_3d_s_vg
void eval_NUBspline_3d_s_vg(NUBspline_3d_s *restrict spline, double x, double y, double z, float *restrict val, float *restrict grad)
Definition nubspline_eval_std_s.h:253
eval_NUBspline_2d_s
void eval_NUBspline_2d_s(NUBspline_2d_s *restrict spline, double x, double y, float *restrict val)
Definition nubspline_eval_std_s.h:90
eval_NUBspline_3d_s_vgh
void eval_NUBspline_3d_s_vgh(NUBspline_3d_s *restrict spline, double x, double y, double z, float *restrict val, float *restrict grad, float *restrict hess)
Definition nubspline_eval_std_s.h:430
eval_NUBspline_1d_s_vg
void eval_NUBspline_1d_s_vg(NUBspline_1d_s *restrict spline, double x, float *restrict val, float *restrict grad)
Definition nubspline_eval_std_s.h:46
eval_NUBspline_1d_s_vgh
void eval_NUBspline_1d_s_vgh(NUBspline_1d_s *restrict spline, double x, float *restrict val, float *restrict grad, float *restrict hess)
Definition nubspline_eval_std_s.h:77
eval_NUBspline_2d_s_vgl
void eval_NUBspline_2d_s_vgl(NUBspline_2d_s *restrict spline, double x, double y, float *restrict val, float *restrict grad, float *restrict lapl)
Definition nubspline_eval_std_s.h:141
eval_NUBspline_2d_s_vgh
void eval_NUBspline_2d_s_vgh(NUBspline_2d_s *restrict spline, double x, double y, float *restrict val, float *restrict grad, float *restrict hess)
Definition nubspline_eval_std_s.h:174
eval_NUBspline_1d_s_vgl
void eval_NUBspline_1d_s_vgl(NUBspline_1d_s *restrict spline, double x, float *restrict val, float *restrict grad, float *restrict lapl)
Definition nubspline_eval_std_s.h:60
nubspline_structs.h
NUBspline_1d_s
Definition nubspline_structs.h:61
NUBspline_2d_s
Definition nubspline_structs.h:71
NUBspline_3d_s
Definition nubspline_structs.h:82