1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
|
//
// Copyright 2005 by Johannes Hofmann
//
// This library is free software; you can redistribute it and/or
// modify it under the terms of the GNU Library General Public
// License as published by the Free Software Foundation; either
// version 2 of the License, or (at your option) any later version.
//
// This library 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
// Library General Public License for more details.
//
// You should have received a copy of the GNU Library General Public
// License along with this library; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
// USA.
//
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
extern "C" {
#include <ccmath.h>
}
#include "ProjectionTangential.H"
static int opt_step(double *tan_nick_view,
double *tan_dir_view,
double *n_scale,
double tan_dir_m1,
double tan_nick_m1,
double tan_dir_m2,
double tan_nick_m2,
double d_m1_2, double d_m2_2, double d_m1_m2_2);
static double
comp_tilt(double tan_nick_view, double tan_dir_view, double n_scale,
double tan_nick_m, double tan_dir_m,
double x, double y, double pi_d);
int
ProjectionTangential::comp_params(const Hill *m1, const Hill *m2, ViewParams *parms) {
const Hill *tmp;
double a_center_tmp, scale_tmp, a_nick_tmp;
scale_tmp = comp_scale(m1->alph, m2->alph, m1->x, m2->x);
if (isnan(scale_tmp) || scale_tmp < 100.0) {
// try again with mountains swapped
tmp = m1;
m1 = m2;
m2 = tmp;
scale_tmp = comp_scale(m1->alph, m2->alph, m1->x, m2->x);
}
a_center_tmp = comp_center_angle(m1->alph, m2->alph, m1->x, m2->x);
a_nick_tmp = atan ((m1->y + tan(m1->a_nick) * parms->scale) /
(parms->scale - m1->y * tan(m1->a_nick)));
if (isnan(a_center_tmp) || isnan(scale_tmp) ||
scale_tmp < 100.0 || isnan(a_nick_tmp)) {
return 1;
} else {
parms->a_center = a_center_tmp;
parms->scale = scale_tmp;
parms->a_nick = a_nick_tmp;
optimize(m1, m2, parms);
return 0;
}
}
double
ProjectionTangential::angle_dist(double a1, double a2) {
double ret;
a1 = fmod(a1, 2.0 * pi_d);
if (a1 < 0.0) {
a1 = a1 + 2.0 * pi_d;
}
a2 = fmod(a2, 2.0 * pi_d);
if (a2 < 0.0) {
a2 = a2 + 2.0 * pi_d;
}
ret = fabs(a1 - a2);
if (ret > pi_d) {
ret = 2.0 * pi_d - ret;
}
return ret;
}
int
ProjectionTangential::optimize(const Hill *m1, const Hill *m2, ViewParams *parms) {
int i;
double tan_nick_view, tan_dir_view, n_scale;
double tan_nick_m1, tan_dir_m1;
double tan_nick_m2, tan_dir_m2;
double d_m1_2, d_m2_2, d_m1_m2_2;
d_m1_2 = pow(m1->x, 2.0) + pow(m1->y, 2.0);
d_m2_2 = pow(m2->x, 2.0) + pow(m2->y, 2.0);
d_m1_m2_2 = pow(m1->x - m2->x, 2.0) + pow(m1->y - m2->y, 2.0);
tan_nick_view = tan(parms->a_nick);
tan_dir_view = tan(parms->a_center);
n_scale = parms->scale;
tan_dir_m1 = tan(m1->alph);
tan_nick_m1 = tan(m1->a_nick);
tan_dir_m2 = tan(m2->alph);
tan_nick_m2 = tan(m2->a_nick);
for (i=0; i<5; i++) {
opt_step(&tan_nick_view, &tan_dir_view, &n_scale,
tan_dir_m1, tan_nick_m1, tan_dir_m2, tan_nick_m2,
d_m1_2, d_m2_2, d_m1_m2_2);
}
if (isnan(tan_dir_view) || isnan(tan_nick_view) || isnan(n_scale)) {
fprintf(stderr, "No solution found.\n");
return 1;
}
parms->a_center = atan(tan_dir_view);
parms->a_nick = atan(tan_nick_view);
if (parms->a_center > 2.0 * pi_d) {
parms->a_center = parms->a_center - 2.0 * pi_d;
} else if (parms->a_center < 0.0) {
parms->a_center = parms->a_center + 2.0 * pi_d;
}
// atan(tan_dir_view) is not the only possible solution.
// Choose the one which is close to m1->alph.
if (angle_dist(parms->a_center, m1->alph) > pi_d/2.0) {
parms->a_center = parms->a_center + pi_d;
}
parms->scale = n_scale;
// use the point with greater distance from center for tilt computation
if (d_m1_2 > d_m2_2) {
parms->a_tilt = comp_tilt(tan_nick_view, tan_dir_view, n_scale,
tan_nick_m1, tan_dir_m1,
(double) m1->x, (double) m1->y, pi_d);
} else {
parms->a_tilt = comp_tilt(tan_nick_view, tan_dir_view, n_scale,
tan_nick_m2, tan_dir_m2,
(double) m2->x, (double) m2->y, pi_d);
}
return 0;
}
void
ProjectionTangential::get_coordinates(double a_view, double a_nick,
const ViewParams *parms, double *x, double *y) {
double x_tmp, y_tmp;
x_tmp = tan(a_view) * parms->scale;
y_tmp = - (tan(a_nick - parms->a_nick) * parms->scale);
// rotate by a_tilt;
*x = x_tmp * cos(parms->a_tilt) - y_tmp * sin(parms->a_tilt);
*y = x_tmp * sin(parms->a_tilt) + y_tmp * cos(parms->a_tilt);
}
double
ProjectionTangential::comp_center_angle(double a1, double a2, double d1, double d2) {
double sign1 = 1.0;
double tan_acenter, tan_a1, tan_a2, a_center;
tan_a1 = tan(a1);
tan_a2 = tan(a2);
tan_acenter = (((pow(((pow((1.0 + (tan_a1 * tan_a2)), 2.0) * ((d1 * d1) + (d2 * d2))) + (2.0 * d1 * d2 * ((2.0 * ((tan_a2 * tan_a1) - (tan_a2 * tan_a2))) - ((tan_a1 * tan_a1) * (2.0 + (tan_a2 * tan_a2))) - 1.0))), (1.0 / 2.0)) * sign1) + ((1.0 - (tan_a1 * tan_a2)) * (d1 - d2))) / (2.0 * ((d2 * tan_a2) - (d1 * tan_a1))));
a_center = atan(tan_acenter);
if (a_center > 2.0 * pi_d) {
a_center = a_center - 2.0 * pi_d;
} else if (a_center < 0.0) {
a_center = a_center + 2.0 * pi_d;
}
// atan(tan_dir_view) is not the only possible solution.
// Choose the one which is close to m1->alph.
if (fabs(a_center - a1) > pi_d/2.0) {
a_center = a_center + pi_d;
}
return a_center;
}
double
ProjectionTangential::comp_scale(double a1, double a2, double d1, double d2) {
double sign1 = 1.0;
double sc, tan_a1, tan_a2;
tan_a1 = tan(a1);
tan_a2 = tan(a2);
sc = ((((1.0 + (tan_a1 * tan_a2)) * (d1 - d2)) - (sign1 * pow((((1.0 + pow((tan_a1 * tan_a2), 2.0)) * ((d1 * d1) + (d2 * d2))) + (2.0 * ((tan_a1 * tan_a2 * pow((d1 + d2), 2.0)) - (d1 * d2 * (((tan_a1 * tan_a1) * (2.0 + (tan_a2 * tan_a2))) + 1.0 + (2.0 * (tan_a2 * tan_a2))))))), (1.0 / 2.0)))) / (2.0 * (tan_a1 - tan_a2)));
return sc;
}
static int
get_matrix(double m[],
double tan_nick_view, double tan_dir_view, double n_scale,
double tan_dir_m1, double tan_nick_m1,
double tan_dir_m2, double tan_nick_m2) {
m[0] = pow(n_scale,2.0)*(1.0/pow((tan_nick_m1*tan_nick_view + 1.0),2.0)*(2.0*tan_nick_m1 - 2.0 * tan_nick_view) + 2.0*tan_nick_m1*pow((tan_nick_m1 - tan_nick_view), 2.0)/pow((tan_nick_m1*tan_nick_view + 1.0), 3.0));
m[1] = pow(n_scale, 2.0) *(1.0/pow((tan_dir_m1*tan_dir_view + 1.0), 2.0) * (2.0*tan_dir_m1 - 2.0*tan_dir_view) + 2.0*tan_dir_m1*pow((tan_dir_m1 - tan_dir_view),2.0) / pow((tan_dir_m1*tan_dir_view + 1.0), 3.0));
m[2] = -2.0*n_scale*(pow((tan_dir_m1 - tan_dir_view), 2.0)/pow((tan_dir_m1*tan_dir_view + 1.0), 2.0) + pow((tan_nick_m1 - tan_nick_view), 2.0)/pow((tan_nick_m1*tan_nick_view + 1.0), 2.0));
m[3] = pow(n_scale, 2.0)*(1.0/pow((tan_nick_m2*tan_nick_view + 1.0), 2.0)*(2.0*tan_nick_m2 - 2.0*tan_nick_view) + 2.0*tan_nick_m2*pow((tan_nick_m2 - tan_nick_view), 2.0)/pow((tan_nick_m2*tan_nick_view + 1.0), 3.0));
m[4] = pow(n_scale, 2.0)*(1.0/pow((tan_dir_m2*tan_dir_view + 1.0), 2.0)*(2.0*tan_dir_m2 - 2.0*tan_dir_view) + 2.0*tan_dir_m2*pow((tan_dir_m2 - tan_dir_view), 2.0)/pow((tan_dir_m2*tan_dir_view + 1.0), 3.0));
m[5] = -2.0*n_scale*(pow((tan_dir_m2 - tan_dir_view), 2.0)/pow((tan_dir_m2*tan_dir_view + 1.0), 2.0) + pow((tan_nick_m2 - tan_nick_view), 2.0)/pow((tan_nick_m2*tan_nick_view + 1.0), 2.0));
m[6] = 2.0*(n_scale*(tan_nick_m1 - tan_nick_view)/(tan_nick_m1*tan_nick_view + 1.0) - n_scale*(tan_nick_m2 - tan_nick_view)/(tan_nick_m2*tan_nick_view + 1.0))*(n_scale/(tan_nick_m1*tan_nick_view + 1.0) - n_scale/(tan_nick_m2*tan_nick_view + 1.0) + tan_nick_m1*n_scale*(tan_nick_m1 - tan_nick_view)/pow((tan_nick_m1*tan_nick_view + 1.0), 2.0) - tan_nick_m2*n_scale*(tan_nick_m2 - tan_nick_view)/pow((tan_nick_m2*tan_nick_view + 1.0),2.0));
m[7] = 2.0*(n_scale*(tan_dir_m1 - tan_dir_view)/(tan_dir_m1*tan_dir_view + 1.0) - n_scale*(tan_dir_m2 - tan_dir_view)/(tan_dir_m2*tan_dir_view + 1.0))*(n_scale/(tan_dir_m1*tan_dir_view + 1.0) - n_scale/(tan_dir_m2*tan_dir_view + 1.0) + tan_dir_m1*n_scale*(tan_dir_m1 - tan_dir_view)/pow((tan_dir_m1*tan_dir_view + 1.0), 2.0) - tan_dir_m2*n_scale*(tan_dir_m2 - tan_dir_view)/pow((tan_dir_m2*tan_dir_view + 1.0), 2.0));
m[8] = - 2.0*(n_scale*(tan_dir_m1 - tan_dir_view)/(tan_dir_m1*tan_dir_view + 1.0) - n_scale*(tan_dir_m2 - tan_dir_view)/(tan_dir_m2*tan_dir_view + 1.0))*((tan_dir_m1 - tan_dir_view)/(tan_dir_m1*tan_dir_view + 1.0) - (tan_dir_m2 - tan_dir_view)/(tan_dir_m2*tan_dir_view + 1.0)) - 2.0*(n_scale*(tan_nick_m1 - tan_nick_view)/(tan_nick_m1*tan_nick_view + 1.0) - n_scale*(tan_nick_m2 - tan_nick_view)/(tan_nick_m2*tan_nick_view + 1.0))*((tan_nick_m1 - tan_nick_view)/(tan_nick_m1*tan_nick_view + 1.0) - (tan_nick_m2 - tan_nick_view)/(tan_nick_m2*tan_nick_view + 1.0));
return 0;
}
static int opt_step(double *tan_nick_view,
double *tan_dir_view,
double *n_scale,
double tan_dir_m1,
double tan_nick_m1,
double tan_dir_m2,
double tan_nick_m2,
double d_m1_2, double d_m2_2, double d_m1_m2_2) {
double a[9];
double b[3];
double a_x0[3], f_x0 [3], x0[3];
int ret;
get_matrix(a, *tan_nick_view, *tan_dir_view, *n_scale,
tan_dir_m1, tan_nick_m1, tan_dir_m2, tan_nick_m2);
f_x0[0] = d_m1_2 - (pow((*tan_nick_view-tan_nick_m1),2.0)/pow((tan_nick_m1**tan_nick_view+1), 2.0)+pow((*tan_dir_view-tan_dir_m1),2.0)/pow((tan_dir_m1**tan_dir_view+1),2.0))*pow(*n_scale, 2.0);
f_x0[1] = d_m2_2 - (pow((*tan_nick_view-tan_nick_m2),2.0)/pow((tan_nick_m2**tan_nick_view+1),2.0)+pow((*tan_dir_view-tan_dir_m2),2.0)/pow((tan_dir_m2**tan_dir_view+1),2.0))*pow(*n_scale, 2.0);
f_x0[2] = d_m1_m2_2 - (pow((- (((*tan_dir_view - tan_dir_m1) * *n_scale) / (tan_dir_m1 * *tan_dir_view + 1.0)) + (((*tan_dir_view - tan_dir_m2) * *n_scale) / (tan_dir_m2 * *tan_dir_view + 1))), 2.0) + pow((- (((*tan_nick_view - tan_nick_m1) * *n_scale) / (tan_nick_m1 * *tan_nick_view + 1)) + ((*tan_nick_view - tan_nick_m2) * *n_scale) / (tan_nick_m2 * *tan_nick_view + 1)), 2.0));
x0[0] = *tan_nick_view;
x0[1] = *tan_dir_view;
x0[2] = *n_scale;
rmmult(a_x0, a, x0, 3, 3, 1);
b[0] = a_x0[0] - f_x0[0];
b[1] = a_x0[1] - f_x0[1];
b[2] = a_x0[2] - f_x0[2];
ret = solv(a, b, 3);
*tan_nick_view = b[0];
*tan_dir_view = b[1];
*n_scale = b[2];
return 0;
}
static double
comp_tilt(double tan_nick_view, double tan_dir_view, double n_scale,
double tan_nick_m, double tan_dir_m,
double x, double y, double pi_d) {
double y_tmp, x_tmp, sin_a_tilt1, sin_a_tilt2, sin_a_tilt, res;
y_tmp = - (((tan_nick_view - tan_nick_m) * n_scale) /
(tan_nick_m * tan_nick_view + 1));
x_tmp = - (((tan_dir_view - tan_dir_m) * n_scale) /
(tan_dir_m * tan_dir_view + 1));
sin_a_tilt1 = - (y * - pow(x*x + y*y - y_tmp*y_tmp, 0.5) - x * y_tmp) /
(x*x + y*y);
sin_a_tilt2 = - (y * pow(x*x + y*y - y_tmp*y_tmp, 0.5) - x * y_tmp) /
(x*x + y*y);
sin_a_tilt = fabs(sin_a_tilt1) < fabs(sin_a_tilt2)?sin_a_tilt1:sin_a_tilt2;
res = asin(sin_a_tilt);
if (res > pi_d / 4.0) {
res = res - pi_d / 2.0;
} else if (res < -pi_d / 4.0) {
res = res + pi_d / 2.0;
}
return res;
}
|
