1 // ******************************************************************************
2 //
3 // Title: Force Field X.
4 // Description: Force Field X - Software for Molecular Biophysics.
5 // Copyright: Copyright (c) Michael J. Schnieders 2001-2024.
6 //
7 // This file is part of Force Field X.
8 //
9 // Force Field X is free software; you can redistribute it and/or modify it
10 // under the terms of the GNU General Public License version 3 as published by
11 // the Free Software Foundation.
12 //
13 // Force Field X is distributed in the hope that it will be useful, but WITHOUT
14 // ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
15 // FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
16 // details.
17 //
18 // You should have received a copy of the GNU General Public License along with
19 // Force Field X; if not, write to the Free Software Foundation, Inc., 59 Temple
20 // Place, Suite 330, Boston, MA 02111-1307 USA
21 //
22 // Linking this library statically or dynamically with other modules is making a
23 // combined work based on this library. Thus, the terms and conditions of the
24 // GNU General Public License cover the whole combination.
25 //
26 // As a special exception, the copyright holders of this library give you
27 // permission to link this library with independent modules to produce an
28 // executable, regardless of the license terms of these independent modules, and
29 // to copy and distribute the resulting executable under terms of your choice,
30 // provided that you also meet, for each linked independent module, the terms
31 // and conditions of the license of that module. An independent module is a
32 // module which is not derived from or based on this library. If you modify this
33 // library, you may extend this exception to your version of the library, but
34 // you are not obligated to do so. If you do not wish to do so, delete this
35 // exception statement from your version.
36 //
37 // ******************************************************************************
38 package ffx.numerics.spline;
39
40 import javax.annotation.Nullable;
41
42 /**
43 * TriCubicSpline class.
44 *
45 * @author Timothy D. Fenn
46 * @see <a href="http://www.cs.cmu.edu/~fp/courses/graphics/asst5/catmullRom.pdf"
47 * target="_blank">Catmull-Rom splines</a>
48 * @since 1.0
49 */
50 public class TriCubicSpline {
51
52 /**
53 * Tau for the smoothing matrix.
54 */
55 private static final double tau = 0.25;
56 /**
57 * Smoothing matrix: Catmull-Rom spline with tau=0.25
58 */
59 private static final double[][] catmullRomMat =
60 new double[][]{
61 {0.0, 1.0, 0.0, 0.0},
62 {-tau, 0.0, tau, 0.0},
63 {2.0 * tau, tau - 3.0, 3.0 - 2.0 * tau, -tau},
64 {-tau, 2.0 - tau, tau - 2.0, tau}
65 };
66
67 private final double[] p;
68 private final double[] q;
69 private final double[] r;
70 private final double[] u;
71 private final double[] v;
72 private final double[] w;
73 private final double[] dp;
74 private final double[] dq;
75 private final double[] dr;
76 private final double[] du;
77 private final double[] dv;
78 private final double[] dw;
79
80 /**
81 * Initialize Spline function.
82 */
83 public TriCubicSpline() {
84 dw = new double[4];
85 dv = new double[4];
86 du = new double[4];
87 dr = new double[4];
88 dq = new double[4];
89 dp = new double[4];
90 w = new double[4];
91 v = new double[4];
92 u = new double[4];
93 r = new double[4];
94 q = new double[4];
95 p = new double[4];
96 }
97
98 /**
99 * Determine the spline value at a given point.
100 *
101 * @param dx delta between point and previous grid point in X
102 * @param dy delta between point and previous grid point in Y
103 * @param dz delta between point and previous grid point in Z
104 * @param scalar 3d array in x,y,z order of 3D scalar data
105 * @param g gradient array (can be null)
106 * @return the interpolated scalar value at the requested point
107 */
108 public double spline(double dx, double dy, double dz, double[][][] scalar, @Nullable double[] g) {
109
110 // p(s) = u . catmull-rom matrix . p^T applied in 3 dimensions (u, v, w)
111 u[0] = 1.0;
112 v[0] = 1.0;
113 w[0] = 1.0;
114 for (int i = 1; i < 4; i++) {
115 u[i] = u[i - 1] * dx;
116 v[i] = v[i - 1] * dy;
117 w[i] = w[i - 1] * dz;
118 }
119
120 // Derivatives
121 du[0] = dv[0] = dw[0] = 0.0;
122 du[1] = dv[1] = dw[1] = 1.0;
123 du[2] = 2.0 * dx;
124 du[3] = 3.0 * dx * dx;
125 dv[2] = 2.0 * dy;
126 dv[3] = 3.0 * dy * dy;
127 dw[2] = 2.0 * dz;
128 dw[3] = 3.0 * dz * dz;
129
130 // vec4mat4 - could put this in VectorMath class
131 for (int i = 0; i < 4; i++) {
132 p[i] = q[i] = r[i] = 0.0;
133 dp[i] = dq[i] = dr[i] = 0.0;
134 for (int j = 0; j < 4; j++) {
135 p[i] += u[j] * catmullRomMat[j][i];
136 q[i] += v[j] * catmullRomMat[j][i];
137 r[i] += w[j] * catmullRomMat[j][i];
138 dp[i] += du[j] * catmullRomMat[j][i];
139 dq[i] += dv[j] * catmullRomMat[j][i];
140 dr[i] += dw[j] * catmullRomMat[j][i];
141 }
142 }
143
144 // Tensor products
145 double sum = 0.0;
146 double gx = 0.0, gy = 0.0, gz = 0.0;
147 for (int i = 0; i < 4; i++) {
148 for (int j = 0; j < 4; j++) {
149 for (int k = 0; k < 4; k++) {
150 sum += p[i] * q[j] * r[k] * scalar[i][j][k];
151 gx += dp[i] * q[j] * r[k] * scalar[i][j][k];
152 gy += p[i] * dq[j] * r[k] * scalar[i][j][k];
153 gz += p[i] * q[j] * dr[k] * scalar[i][j][k];
154 }
155 }
156 }
157
158 if (g != null) {
159 g[0] = gx;
160 g[1] = gy;
161 g[2] = gz;
162 }
163
164 return sum;
165 }
166 }