27b826a8
 David Mayerich
added a spherical...
|
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
|
#ifndef STIM_SPH_HARMONICS
#define STIM_SPH_HARMONICS
#include <GL/gl.h>
#include <stim/gl/error.h>
#include <stim/visualization/colormap.h>
#include <vector>
#define PI 3.14159
#define WIRE_SCALE 1.001
namespace stim{
class sph_harmonics{
private:
double* func; //stores the raw function data (samples at each point)
GLuint color_tex; //texture map that acts as a colormap for the spherical function
unsigned int N; //resolution of the spherical grid
std::vector<double> C; //list of SH coefficients
//evaluates an associated Legendre polynomial (-l <= m <= l)
double P(int l,int m,double x)
{
// evaluate an Associated Legendre Polynomial P(l,m,x) at x
double pmm = 1.0;
if(m>0) {
double somx2 = sqrt((1.0-x)*(1.0+x));
double fact = 1.0;
for(int i=1; i<=m; i++) {
pmm *= (-fact) * somx2;
fact += 2.0;
}
}
if(l==m) return pmm;
double pmmp1 = x * (2.0*m+1.0) * pmm;
if(l==m+1) return pmmp1;
double pll = 0.0;
for(int ll=m+2; ll<=l; ++ll) {
pll = ( (2.0*ll-1.0)*x*pmmp1-(ll+m-1.0)*pmm ) / (ll-m);
pmm = pmmp1;
pmmp1 = pll;
}
return pll;
}
//recursively calculate a factorial given a positive integer n
unsigned int factorial(unsigned int n) {
if (n == 0)
return 1;
return n * factorial(n - 1);
}
//calculate the SH scaling constant
double K(int l, int m){
// renormalisation constant for SH function
double temp = ((2.0*l+1.0)*factorial(l-m)) / (4.0*PI*factorial(l+m));
return sqrt(temp);
}
//calculate the value of the SH basis function (l, m) at (theta, phi)
//here, theta = [0, PI], phi = [0, 2*PI]
double SH(int l, int m, double theta, double phi){
// return a point sample of a Spherical Harmonic basis function
// l is the band, range [0..N]
// m in the range [-l..l]
// theta in the range [0..Pi]
// phi in the range [0..2*Pi]
const double sqrt2 = sqrt(2.0);
if(m==0) return K(l,0)*P(l,m,cos(theta));
else if(m>0) return sqrt2*K(l,m)*cos(m*phi)*P(l,m,cos(theta));
else return sqrt2*K(l,-m)*sin(-m*phi)*P(l,-m,cos(theta));
}
void gen_function(){
//initialize the function to zero
memset(func, 0, sizeof(double) * N * N);
double theta, phi;
double result;
int l, m;
l = m = 0;
for(unsigned int c = 0; c < C.size(); c++){
for(unsigned int xi = 0; xi < N; xi++)
for(unsigned int yi = 0; yi < N; yi++){
theta = (2 * PI) * ((double)xi / (N-1));
phi = PI * ((double)yi / (N-1));
result = C[c] * SH(l, m, phi, theta); //phi and theta are reversed here (damn physicists)
func[yi * N + xi] += result;
}
m++; //increment m
//if we're in a new tier, increment l and set m = -l
if(m > l){
l++;
m = -l;
}
}
}
void gl_prep_draw(){
//enable depth testing
//this has to be used instead of culling because the sphere can have negative values
glEnable(GL_DEPTH_TEST);
glDepthMask(GL_TRUE);
glEnable(GL_TEXTURE_2D); //enable 2D texture mapping
}
//draw a texture mapped sphere representing the function surface
void gl_draw_sphere() {
//PI is used to convert from spherical to cartesian coordinates
//const double PI = 3.14159;
//bind the 2D texture representing the color map
glBindTexture(GL_TEXTURE_2D, color_tex);
//Draw the Sphere
int i, j;
for(i = 1; i <= N-1; i++) {
double phi0 = PI * ((double) (i - 1) / (N-1));
double phi1 = PI * ((double) i / (N-1));
glBegin(GL_QUAD_STRIP);
for(j = 0; j <= N; j++) {
//calculate the indices into the function array
int phi0_i = i-1;
int phi1_i = i;
int theta_i = j;
if(theta_i == N)
theta_i = 0;
double v0 = func[phi0_i * N + theta_i];
double v1 = func[phi1_i * N + theta_i];
v0 = fabs(v0);
v1 = fabs(v1);
double theta = 2 * PI * (double) (j - 1) / N;
double x0 = v0 * cos(theta) * sin(phi0);
double y0 = v0 * sin(theta) * sin(phi0);
double z0 = v0 * cos(phi0);
double x1 = v1 * cos(theta) * sin(phi1);
double y1 = v1 * sin(theta) * sin(phi1);
double z1 = v1 * cos(phi1);
glTexCoord2f(theta / (2 * PI), phi0 / PI);
glVertex3f(x0, y0, z0);
glTexCoord2f(theta / (2 * PI), phi1 / PI);
glVertex3f(x1, y1, z1);
}
glEnd();
}
}
//draw a wire frame sphere representing the function surface
void gl_draw_wireframe() {
//PI is used to convert from spherical to cartesian coordinates
//const double PI = 3.14159;
//bind the 2D texture representing the color map
glDisable(GL_TEXTURE_2D);
glColor3f(0.0f, 0.0f, 0.0f);
//Draw the Sphere
int i, j;
for(i = 1; i <= N-1; i++) {
double phi0 = PI * ((double) (i - 1) / (N-1));
double phi1 = PI * ((double) i / (N-1));
glBegin(GL_LINE_STRIP);
for(j = 0; j <= N; j++) {
//calculate the indices into the function array
int phi0_i = i-1;
int phi1_i = i;
int theta_i = j;
if(theta_i == N)
theta_i = 0;
double v0 = func[phi0_i * N + theta_i];
double v1 = func[phi1_i * N + theta_i];
v0 = fabs(v0);
v1 = fabs(v1);
double theta = 2 * PI * (double) (j - 1) / N;
double x0 = WIRE_SCALE * v0 * cos(theta) * sin(phi0);
double y0 = WIRE_SCALE * v0 * sin(theta) * sin(phi0);
double z0 = WIRE_SCALE * v0 * cos(phi0);
double x1 = WIRE_SCALE * v1 * cos(theta) * sin(phi1);
double y1 = WIRE_SCALE * v1 * sin(theta) * sin(phi1);
double z1 = WIRE_SCALE * v1 * cos(phi1);
glTexCoord2f(theta / (2 * PI), phi0 / PI);
glVertex3f(x0, y0, z0);
glTexCoord2f(theta / (2 * PI), phi1 / PI);
glVertex3f(x1, y1, z1);
}
glEnd();
}
}
void init(unsigned int n){
//set the sphere resolution
N = n;
//allocate space for the color map
unsigned int bytes = N * N * sizeof(unsigned char) * 3;
unsigned char* color_image;
color_image = (unsigned char*) malloc(bytes);
//allocate space for the function
func = (double*) malloc(N * N * sizeof(double));
//generate a function (temporary)
gen_function();
//generate a colormap from the function
stim::cpu2cpu<double>(func, color_image, N*N, stim::cmBrewer);
//prep everything for drawing
gl_prep_draw();
//generate an OpenGL texture map in the current context
glGenTextures(1, &color_tex);
//bind the texture
glBindTexture(GL_TEXTURE_2D, color_tex);
//copy the color data from the buffer to the GPU
glTexImage2D(GL_TEXTURE_2D, 0, GL_RGB, N, N, 0, GL_RGB, GL_UNSIGNED_BYTE, color_image);
//initialize all of the texture parameters
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_REPEAT);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
glTexEnvf(GL_TEXTURE_ENV, GL_TEXTURE_ENV_MODE, GL_REPLACE);
//free the buffer
free(color_image);
}
public:
void glRender(){
//set all OpenGL parameters required for drawing
gl_prep_draw();
//draw the sphere
gl_draw_sphere();
//gl_draw_wireframe();
}
void glInit(unsigned int n){
init(n);
}
void push(double c){
C.push_back(c);
}
}; //end class sph_harmonics
}
#endif
|
