aboutsummaryrefslogtreecommitdiff
path: root/attic/dave/AffineSolve.c.CHARLES
blob: cb62ef6fd1b2033a6860602100eee5ea176fa28a (plain)
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
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
//
//  main.c
//  Aff
//  Created by user on 3/2/17.
//  Copyright © 2017 user. All rights reserved.
//

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <math.h>
#include "dclapack.h"

#define LH_ID    1
#define NUM_HMD 32

#define MAX_POINTS 128
//#define _ABS(a)  ( (a)<=0 ? -(a) : (a) )
#define _SIGN(a) ( (a)<=0 ? -1.0f : 1.0f )
#define RANDF  ( (float)rand() / (float)RAND_MAX )
#define PI 3.14159265358979323846264

#define STEP_SIZE_ROT 1.0
#define STEP_SIZE_POS 1.0
#define FALLOFF   0.99999
#define NITER     2000000
#define TOO_SMALL 0.0001
#define ORTHOG_PENALTY   1.0

float hmd_pos[NUM_HMD][3];
void ReadHmdPoints()
{
    int i;
    FILE *fin = fopen("HMD_points.csv","r");
    if (fin==NULL) {
        printf("ERROR: could not open HMD_points.csv for reading\n");
        exit(1);
    }
    
    for (i=0; i<NUM_HMD; i++) {
        fscanf(fin, "%f %f %f", &(hmd_pos[i][0]), &(hmd_pos[i][1]), &(hmd_pos[i][2]));
    }
    
    fclose(fin);
}

float hmd_angle[NUM_HMD][2];
void ReadPtinfo()
{
    // Initialize to -9999
    int i;
    for (i=0; i<NUM_HMD; i++) { hmd_angle[i][0]=-9999.0; hmd_angle[i][1]=-9999.0; }

    // Read ptinfo.csv
    FILE *fin = fopen("ptinfo.csv", "r");
    if (fin==NULL) { printf("ERROR: could not open ptinfo.csv for reading\n"); exit(1); }
    while (!feof(fin))
    {
        // Read the angle
        int sen,lh,axis,count;
        float angle, avglen, stddevang, stddevlen;
        float max_outlier_length, max_outlier_angle;
        int rt = fscanf( fin, "%d %d %d %d %f %f %f %f %f %f\n",
                        &sen, &lh, &axis, &count,
                        &angle, &avglen, &stddevang, &stddevlen,
                        &max_outlier_length, &max_outlier_angle);
        if (rt != 10) { break; }
        
        // If it's valid, store in the result
        if (lh == LH_ID && sen < NUM_HMD) {
            hmd_angle[sen][axis] = angle;
        }
    }
    fclose(fin);
}

#define PRINT_MAT(A,M,N) { \
    int m,n; \
    printf(#A "\n"); \
    for (m=0; m<M; m++) { \
        for (n=0; n<N; n++) { \
            printf("%f\t", A[m][n]); \
        } \
        printf("\n"); \
    } \
}

#define CrossProduct(ox,oy,oz,a,b,c,x,y,z) { \
    ox=(b)*(z)-(c)*(y); \
    oy=(c)*(x)-(a)*(z); \
    oz=(a)*(y)-(b)*(x); }

void OrthoSolve(
    float T[4][4],               // OUTPUT: 4x4 transformation matrix
    FLOAT S_out[2][MAX_POINTS],  // OUTPUT:  array of screenspace points
    FLOAT S_in[2][MAX_POINTS],   // INPUT:  array of screenspace points
    FLOAT X_in[3][MAX_POINTS],   // INPUT:  array of offsets
    int nPoints)
{
    int i,j,k;
    FLOAT R[3][3];           // OUTPUT: 3x3 rotation matrix
    FLOAT trans[3];          // INPUT:  x,y,z translation vector

    //--------------------
    // Remove the center of the HMD offsets, and the screen space
    //--------------------
    FLOAT xbar[3] = {0.0, 0.0, 0.0};
    FLOAT sbar[2] = {0.0, 0.0};
    FLOAT S[2][MAX_POINTS];
    FLOAT X[3][MAX_POINTS];
    FLOAT inv_nPoints = 1.0 / nPoints;
    for (i=0; i<nPoints; i++) {
        xbar[0] += X_in[0][i];
        xbar[1] += X_in[1][i];
        xbar[2] += X_in[2][i];
        sbar[0] += S_in[0][i];
        sbar[1] += S_in[1][i];        
    }
    for (j=0; j<3; j++) { xbar[j] *= inv_nPoints; }
    for (j=0; j<2; j++) { sbar[j] *= inv_nPoints; }
    for (i=0; i<nPoints; i++) {
        X[0][i] = X_in[0][i] - xbar[0];
        X[1][i] = X_in[1][i] - xbar[1];
        X[2][i] = X_in[2][i] - xbar[2];
        S[0][i] = S_in[0][i] - sbar[0];
        S[1][i] = S_in[1][i] - sbar[1];
    }
    
    //--------------------
    // Solve for the morph matrix
    //  S = M X
    // thus
    // (SX^t)(XX^t)^-1 = M
    //--------------------
    FLOAT Xt[MAX_POINTS][3];
    FLOAT XXt[3][3];
    FLOAT invXXt[3][3];
    FLOAT SXt[2][3];
    FLOAT M[2][3];           // Morph matrix! (2 by 3)
    TRANSP(X,Xt,3,nPoints);
    MUL(X,Xt,XXt,3,nPoints,3);
    MUL(S,Xt,SXt,2,nPoints,3);
    INV(XXt,invXXt,3);
    MUL(SXt,invXXt,M,2,3,3);
//PRINT(M,2,3);

// Double checking work
FLOAT S_morph[2][MAX_POINTS];
MUL(M,X,S_morph,2,3,nPoints);
for (i=0; i<nPoints; i++) { S_morph[0][i]+=sbar[0]; S_morph[1][i]+=sbar[1]; }

    //--------------------
    // Solve for the non-trivial vector
    //  uf -- vector that goes into the camera
    //--------------------
    FLOAT uM[3][3] = {
        { M[0][0], M[0][1], M[0][2] },
        { M[1][0], M[1][1], M[1][2] },
        { 3.14567, -1.2345, 4.32567 } };      // Morph matrix with appended row
//PRINT(uM,3,3);
// ToDo: Pick a number for the bottom that is NOT linearly separable with M[0] and M[1]
    FLOAT B[3][1] = { {0.0}, {0.0}, {1.0} };
    FLOAT inv_uM[3][3];
    FLOAT uf[3][1];
    INV(uM,inv_uM,3);
    MUL(inv_uM,B,uf,3,3,1);
    
    //--------------------
    // Solve for unit length vector
    //  f that goes into the camera
    //--------------------
    FLOAT uf_len = sqrt( uf[0][0]*uf[0][0] + uf[1][0]*uf[1][0] + uf[2][0]*uf[2][0] );
    FLOAT f[3][1] = { {uf[0][0]/uf_len}, {uf[1][0]/uf_len}, {uf[2][0]/uf_len} };
	printf( "FFF: {%f %f %f}: %f\n", f[0][0], f[1][0], f[2][0], uf_len );
//PRINT(uf,3,1);
//PRINT(f,3,1);

//FLOAT check[3][1];
//MUL(uM,uf,check,3,3,1);
//PRINT(check,3,1);

    //--------------------
    // take cross products to get vectors u,r
    //--------------------
    FLOAT u[3][1], r[3][1];
    CrossProduct(u[0][0],u[1][0],u[2][0],f[0][0],f[1][0],f[2][0],1.0,0.0,0.0);
    FLOAT inv_ulen = 1.0 / sqrt( u[0][0]*u[0][0] + u[1][0]*u[1][0] + u[2][0]*u[2][0] );
    u[0][0]*=inv_ulen; u[1][0]*=inv_ulen; u[2][0]*=inv_ulen;
    CrossProduct(r[0][0],r[1][0],r[2][0],f[0][0],f[1][0],f[2][0],u[0][0],u[1][0],u[2][0]);
//PRINT(u,3,1);
//PRINT(r,3,1);

    //--------------------
    // Use morph matrix to get screen space
    //  uhat,rhat
    //--------------------
    FLOAT uhat[2][1], rhat[2][1], fhat[2][1];
    MUL(M,f,fhat,2,3,1);
    MUL(M,u,uhat,2,3,1);
    MUL(M,r,rhat,2,3,1);
    FLOAT fhat_len = sqrt( fhat[0][0]*fhat[0][0] + fhat[1][0]*fhat[1][0] );
    FLOAT uhat_len = sqrt( uhat[0][0]*uhat[0][0] + uhat[1][0]*uhat[1][0] );
    FLOAT rhat_len = sqrt( rhat[0][0]*rhat[0][0] + rhat[1][0]*rhat[1][0] );
    FLOAT urhat_len = 0.5 * (uhat_len + rhat_len);
/*    
printf("fhat %f %f (len %f)\n", fhat[0][0], fhat[1][0], fhat_len);
printf("uhat %f %f (len %f)\n", uhat[0][0], uhat[1][0], uhat_len);
printf("rhat %f %f (len %f)\n", rhat[0][0], rhat[1][0], rhat_len);
*/
    FLOAT ydist1 = 1.0 /  uhat_len; //0.25*PI / uhat_len;
    FLOAT ydist2 = 1.0 /  rhat_len; //0.25*PI / rhat_len;
    FLOAT ydist  = 1.0 / urhat_len;
    printf("ydist1 %f ydist2 %f ydist %f  FH: %f\n", ydist1, ydist2, ydist, fhat_len);

    //--------------------
    // Rescale the axies to be of the proper length
    //--------------------
    FLOAT x[3][1] = { {M[0][0]*ydist}, {0.0}, {M[1][0]*ydist} };
    FLOAT y[3][1] = { {M[0][1]*ydist}, {0.0}, {M[1][1]*ydist} };
    FLOAT z[3][1] = { {M[0][2]*ydist}, {0.0}, {M[1][2]*ydist} };
printf( "YDIST: %f\n", ydist );
printf( "{%f %f, %f %f, %f %f}\n", x[0][0], x[2][0], y[0][0], y[2][0], z[0][0], z[2][0] );
printf( "{%f, %f, %f}\n", x[0][0]*x[0][0]+x[2][0]*x[2][0], y[0][0]*y[0][0]+y[2][0]*y[2][0], z[0][0]*z[0][0]+z[2][0]*z[2][0] );
    // we know the distance into (or out of) the camera for the z axis,
    //  but we don't know which direction . . .
    FLOAT x_y = sqrt(1.0 - x[0][0]*x[0][0] - x[2][0]*x[2][0]);
    FLOAT y_y = sqrt(1.0 - y[0][0]*y[0][0] - y[2][0]*y[2][0]);
    FLOAT z_y = sqrt(1.0 - z[0][0]*z[0][0] - z[2][0]*z[2][0]);
printf( "{%f %f %f}\n", x_y, y_y, z_y );
    // Exhaustively flip the minus sign of the z axis until we find the right one . . .
    FLOAT bestErr = 9999.0;
    FLOAT xy_dot2 = x[0][0]*y[0][0] + x[2][0]*y[2][0];
    FLOAT yz_dot2 = y[0][0]*z[0][0] + y[2][0]*z[2][0];
    FLOAT zx_dot2 = z[0][0]*x[0][0] + z[2][0]*x[2][0];
    for (i=0;i<2;i++) {
        for (j=0;j<2;j++) {
            for(k=0;k<2;k++) {
            
                // Calculate the error term
                FLOAT xy_dot = xy_dot2 + x_y*y_y;
                FLOAT yz_dot = yz_dot2 + y_y*z_y;
                FLOAT zx_dot = zx_dot2 + z_y*x_y;
                FLOAT err = _ABS(xy_dot) + _ABS(yz_dot) + _ABS(zx_dot);
                
                // Calculate the handedness
                FLOAT cx,cy,cz;
                CrossProduct(cx,cy,cz,x[0][0],x_y,x[2][0],y[0][0],y_y,y[2][0]);
                FLOAT hand = cx*z[0][0] + cy*y_y + cz*z[2][0];
                printf("err %f hand %f\n", err, hand);
                
                // If we are the best right-handed frame so far
                if (err < bestErr) { x[1][0]=x_y; y[1][0]=y_y; z[1][0]=z_y; bestErr=err; }
				//if (i ==  1 && j == 1 && k == 1) { x[1][0]=x_y; y[1][0]=y_y; z[1][0]=z_y; bestErr=err; }
                z_y = -z_y;
            }
            y_y = -y_y;
        }
        x_y = -x_y;
    }
    printf("bestErr %f\n", bestErr);
/*
    for (i=0; i<nPoints; i++) {
        float x1 = x[0][0]*X[0][i] + y[0][0]*X[1][i] + z[0][0]*X[2][i];
        float y1 = x[1][0]*X[0][i] + y[1][0]*X[1][i] + z[1][0]*X[2][i];
        float z1 = x[2][0]*X[0][i] + y[2][0]*X[1][i] + z[2][0]*X[2][i];
        printf("x1z1 %f %f y1 %f\n", x1, z1, y1);
    }
*/
/*    
    //--------------------
    // Combine uhat and rhat to figure out the unit x-vector
    //--------------------
    FLOAT xhat[2][1]  = { {0.0}, {1.0} };
    FLOAT urhat[2][2] = {
        {uhat[0][0], uhat[1][0]},
        {rhat[0][0], rhat[1][0]} };
    FLOAT inv_urhat[2][2];
    FLOAT ab[2][1];
    INV(urhat,inv_urhat,2);
    MUL(inv_urhat,xhat,ab,2,2,1);
PRINT(ab,2,1);
    FLOAT a = ab[0][0], b = ab[1][0];

    //-------------------
    // calculate the xyz coordinate system
    //-------------------
    FLOAT y[3][1] = { {f[0][0]}, {f[1][0]}, {f[2][0]} };
    FLOAT x[3][1] = { {a*u[0][0] + b*r[0][0]}, {a*u[1][0] + b*r[1][0]}, {a*u[2][0] + b*r[2][0]} };
    FLOAT inv_xlen = 1.0 / sqrt( x[0][0]*x[0][0] + x[1][0]*x[1][0] + x[2][0]*x[2][0] );
    x[0][0]*=inv_xlen; x[1][0]*=inv_xlen; x[2][0]*=inv_xlen;
    FLOAT z[3][1];
    CrossProduct(z[0][0],z[1][0],z[2][0],x[0][0],x[1][0],x[2][0],y[0][0],y[1][0],y[2][0]);
*/
    // Store into the rotation matrix
    for (i=0; i<3; i++) { R[i][0] = x[i][0]; R[i][1] = y[i][0]; R[i][2] = z[i][0]; }
//PRINT(R,3,3);

    //-------------------
    // Calculate the translation of the centroid
    //-------------------
    trans[0]=tan(sbar[0]);  trans[1]=1.0;  trans[2]=tan(sbar[1]);
    FLOAT inv_translen = ydist / sqrt( trans[0]*trans[0] + trans[1]*trans[1] + trans[2]*trans[2] );
    trans[0]*=inv_translen; trans[1]*=inv_translen; trans[2]*=inv_translen;

    //-------------------
    // Add in the centroid point
    //-------------------
    trans[0] -= xbar[0]*R[0][0] + xbar[1]*R[0][1] + xbar[2]*R[0][2];
    trans[1] -= xbar[0]*R[1][0] + xbar[1]*R[1][1] + xbar[2]*R[1][2];
    trans[2] -= xbar[0]*R[2][0] + xbar[1]*R[2][1] + xbar[2]*R[2][2];
    FLOAT transdist = sqrt( trans[0]*trans[0] + trans[1]*trans[1] + trans[2]*trans[2] );

    //-------------------
    // Pack into the 4x4 transformation matrix
    //-------------------
    T[0][0]=R[0][0]; T[0][1]=R[0][1]; T[0][2]=R[0][2]; T[0][3]=trans[0];
    T[1][0]=R[1][0]; T[1][1]=R[1][1]; T[1][2]=R[1][2]; T[1][3]=trans[1];
    T[2][0]=R[2][0]; T[2][1]=R[2][1]; T[2][2]=R[2][2]; T[2][3]=trans[2];
    T[3][0]=0.0;     T[3][1]=0.0;     T[3][2]=0.0;     T[3][3]=1.0;

    //-------------------
    // Plot the output points
    //-------------------
    for (i=0; i<nPoints; i++) {
        float Tx = T[0][0]*X_in[0][i] + T[0][1]*X_in[1][i] + T[0][2]*X_in[2][i] + T[0][3];
        float Ty = T[1][0]*X_in[0][i] + T[1][1]*X_in[1][i] + T[1][2]*X_in[2][i] + T[1][3];
        float Tz = T[2][0]*X_in[0][i] + T[2][1]*X_in[1][i] + T[2][2]*X_in[2][i] + T[2][3];
        S_out[0][i] = atan2(Tx, Ty);   // horiz
        S_out[1][i] = atan2(Tz, Ty);   // vert
        //S_out[0][i] = Tx;
        //S_out[1][i] = Tz;
        printf("point %i Txyz %f %f %f in %f %f out %f %f morph %f %f\n", i, Tx,Ty,Tz, S_in[0][i], S_in[1][i], S_out[0][i], S_out[1][i], S_morph[0][i], S_morph[1][i]);
    }

//    printf("xbar %f %f %f\n", xbar[0], xbar[1], xbar[2]);
//    printf("trans %f %f %f dist: %f\n", trans[0], trans[1], trans[2], transdist);
}

void AffineSolve(
    float T[4][4],           // OUTPUT: transform
    float O[MAX_POINTS][4],  // INPUT:  points, offsets
    float N[MAX_POINTS][3],  // INPUT:  plane normals
    float D[MAX_POINTS],     // INPUT:  plane offsets
    int nPoints, int nIter,
    float stepSizeRot, float stepSizePos, float falloff, int constrain)
{
    int i,j,k,iter;
    //T[3][3] = 1.0f;
    
    printf("iter x y z error\n");
    
    float gradDot     = 1.0;
    float prevGradDot = 1.0;
    float de_dT[3][4];  // the gradient
    float conj[3][4];   // the conjugate
    float errorSq=0.0;
    for (iter=0; iter<nIter; iter++)
    {
        //----------------------------------
        // Calculate the gradient direction
        //----------------------------------
        errorSq = 0.0;
        memset(de_dT, 0, 3*4*sizeof(float));
        for (i=0; i<nPoints; i++)
        {
            // What is the plane deviation error
            float Ei = -D[i];
            for (j=0; j<3; j++) {
                float Tj_oi = 0.0f;
                for (k=0; k<4; k++) {
                    Tj_oi += T[j][k] * O[i][k];
                }
                Ei += N[i][j] * Tj_oi;
            }
//            printf("E[%d] %f\n", i, Ei);
        
            // Figure out contribution to the error
            for (j=0; j<3; j++) {
                for (k=0; k<4; k++) {
                    de_dT[j][k] += N[i][j] * O[i][k] * Ei;
                }
            }
            
            errorSq += Ei*Ei;
        }

//        printf("%d %f %f %f %f\n", iter, T[0][3], T[1][3], T[2][3], sqrt(errorSq));
//exit(1);
        // Constrain the gradient (such that dot products are zero)
        if (constrain)
        {
            float T0T1 = 0.0, T1T2 = 0.0, T2T0 = 0.0;
            for (k=0; k<3; k++) {
                T0T1 += T[0][k] * T[1][k];
                T1T2 += T[1][k] * T[2][k];
                T2T0 += T[2][k] * T[0][k];
            }
//            printf("T0T1 %f T1T2 %f T2T0 %f\n", T0T1, T1T2, T2T0);
            for (k=0; k<3; k++) {
                de_dT[0][k] += ORTHOG_PENALTY * 2.0 * T0T1 * T[1][k];
                de_dT[0][k] += ORTHOG_PENALTY * 2.0 * T2T0 * T[2][k];
                de_dT[1][k] += ORTHOG_PENALTY * 2.0 * T1T2 * T[2][k];
                de_dT[1][k] += ORTHOG_PENALTY * 2.0 * T0T1 * T[0][k];
                de_dT[2][k] += ORTHOG_PENALTY * 2.0 * T1T2 * T[1][k];
                de_dT[2][k] += ORTHOG_PENALTY * 2.0 * T2T0 * T[0][k];
            }
        }

        // Calculate the gradient dot product
        //  (used by conjugate gradient method)
        prevGradDot = gradDot;
        gradDot = 0.0;
        for (j=0; j<3; j++) {
            for (k=0; k<4; k++) {
                gradDot += de_dT[j][k] * de_dT[j][k];
            }
        }

//        printf("Iter %d error %f gradDot %f prevGradDot %f\n", iter, sqrt(errorSq), gradDot, prevGradDot);

        //----------------------------------
        // Calculate the conjugate direction
        //----------------------------------
//        if (iter==0) {
            // First iteration, just use the gradient
            for (j=0; j<3; j++) {
                for (k=0; k<4; k++) {
                    conj[j][k] = -de_dT[j][k];
                }
            }
/*        } else {
            // Calculate "beta" for Fletcher Reeves method
            float beta = gradDot / prevGradDot;
//printf("gradDot %f prevGradDot %f beta %f\n", gradDot, prevGradDot, beta);

            // Update the conjugate
            for (j=0; j<3; j++) {
                for (k=0; k<4; k++) {
                    conj[j][k] = beta*conj[j][k] - de_dT[j][k];
                }
            }            
        }
*/

//        PRINT_MAT(de_dT,4,4);
//        exit(1);

        //----------------------------------
        // How large is the gradient ?
        //----------------------------------
        
        double gradSizeRot = 0.0;
        double gradSizePos = 0.0;
        for (j=0; j<3; j++) {
            for (k=0; k<3; k++) {
                gradSizeRot += _ABS(conj[j][k]);
            }
            gradSizePos += _ABS(conj[j][k]);
        }
        if (gradSizeRot <= TOO_SMALL && gradSizePos <= TOO_SMALL) { break; }  // Quit, we've totally converged
        
        //----------------------------------
        // Descend in the gradient direction
        //----------------------------------
        if (gradSizeRot > TOO_SMALL) {
            float scaleRot = stepSizeRot / gradSizeRot;
            for (j=0; j<3; j++) {
                for (k=0; k<3; k++) {
                    T[j][k] += scaleRot * conj[j][k];
                }
            }
            stepSizeRot *= falloff;
        }
        
        if (gradSizePos > TOO_SMALL) {
            float scalePos = stepSizePos / gradSizePos;
            for (j=0; j<3; j++) {
                T[j][3] += scalePos * conj[j][3];
            }
            stepSizePos *= falloff;
        }
        
        // Constrain the gradient (such that scaling is one)
        if (constrain)
        {
            // Measure the scales
            float len[3] = {0.0, 0.0, 0.0};
            for (j=0; j<3; j++) {
                double lenSq = 0.0;
                for (k=0; k<3; k++) { lenSq += (double)T[j][k] * (double)T[j][k]; }
                len[j] = sqrt(lenSq);
            }
            
            // How far off is the scale?
            float xzLen = 0.5 * (len[0] + len[2]);
            if (xzLen > TOO_SMALL) {
                float inv_xzLen = 1.0 / xzLen;
                for (j=0; j<3; j++) {
                    T[3][j] *= inv_xzLen;
                }
            }
            
            // Rescale the thing
            for (j=0; j<3; j++)
            {
                if (len[j] > TOO_SMALL) {
                    float inv_len = 1.0 / len[j];
                    for (k=0; k<3; k++) { T[j][k] *= inv_len; }
                }
            }
        }
    }
    float dist = sqrt(T[0][3]*T[0][3] + T[1][3]*T[1][3] + T[2][3]*T[2][3]);
    printf("AffineSolve: pos: %f %f %f dist: %f\n", T[0][3], T[1][3], T[2][3], dist);
}

int main()
{
    int i,j,k,sen,axis;
        
    // Read the data files
	printf( "...\n" );
    ReadHmdPoints();
    ReadPtinfo();

    //-------------------------
    // Package the lighthouse data for "AffineSolve"
    //-------------------------

    // Data for the "iterative" affine solve formula
   // float Tcalc[4][4];
    float O[MAX_POINTS][4];
    float N[MAX_POINTS][3];
    float D[MAX_POINTS];
    int nPlanes = 0;

    for (sen=0; sen<NUM_HMD; sen++)
    {
        for (axis=0; axis<2; axis++)
        {
            if (hmd_angle[sen][axis] != -9999.0)
            {
                // Set the offset
                O[nPlanes][0] = hmd_pos[sen][0];
                O[nPlanes][1] = hmd_pos[sen][1];
                O[nPlanes][2] = hmd_pos[sen][2];
                O[nPlanes][3] = 1.0;
        
                // Calculate the plane equation
                if (axis == 0) {   // Horizontal
                    N[nPlanes][0] = -cos(hmd_angle[sen][axis]);
                    N[nPlanes][1] = -sin(hmd_angle[sen][axis]);
                    N[nPlanes][2] = 0.0;
                    D[nPlanes]    = 0.0;
                } else {           // Vertical
                    N[nPlanes][0] = 0.0;
                    N[nPlanes][1] = -sin(hmd_angle[sen][axis]);
                    N[nPlanes][2] =  cos(hmd_angle[sen][axis]);
                    D[nPlanes]    = 0.0;
                }

                printf("plane %d O %.3f %.3f %.3f %.3f  N %.3f %.3f %.3f  D %.3f\n",
                    nPlanes,
                    O[nPlanes][0], O[nPlanes][1], O[nPlanes][2], O[nPlanes][3], 
                    N[nPlanes][0], N[nPlanes][1], N[nPlanes][2], 
                    D[nPlanes]);
                nPlanes++;
            }
        }
    }

    
    printf("nPlanes %d\n", nPlanes);
        
    //}
    
    //PRINT_MAT(Tcalc,4,4);

    
    //--------------------------------------------------
    // Package the data for "OrthoSolve"
    //--------------------------------------------------

    // Data for the "fake" ortho solve formula
    float Tortho[4][4];         // OUTPUT: 4x4 transformation matrix
    FLOAT S_out[2][MAX_POINTS];  // INPUT:  array of screenspace points
    FLOAT S_in[2][MAX_POINTS];  // INPUT:  array of screenspace points
    FLOAT X_in[3][MAX_POINTS];  // INPUT:  array of offsets
    int nPoints=0;  

    // Transform into the "OrthoSolve" format
    for (sen=0; sen<NUM_HMD; sen++)
    {
        if (hmd_angle[sen][0] != -9999.0 && hmd_angle[sen][1] != -9999.0)
        {
            S_in[0][nPoints] = hmd_angle[sen][0];
            S_in[1][nPoints] = hmd_angle[sen][1];
            X_in[0][nPoints] = hmd_pos[sen][0];
            X_in[1][nPoints] = hmd_pos[sen][1];
            X_in[2][nPoints] = hmd_pos[sen][2];
            nPoints++;
        }
    }
    printf("OrthoSolve nPoints %d\n", nPoints);
    
    //--------------------------------------------------
    // Run the "OrthoSolve" and then the "AffineSolve"
    //--------------------------------------------------    
    
    int loop;
   // for (loop=0; loop<1000000; loop++)
    {
        // Run OrthoSolve
        OrthoSolve(
            Tortho,     // OUTPUT: 4x4 transformation matrix
            S_out,      // OUTPUT: array of output screenspace points
            S_in,       // INPUT:  array of screenspace points
            X_in,       // INPUT:  array of offsets
            nPoints);
    }

    // Run the calculation for Tcalc
    //int run;
    //for (run=0; run<100; run++) {
/*
    // Initialize Tcalc to the identity matrix
    memcpy(Tcalc, Tortho, 4*4*sizeof(float));
    //memset(Tcalc, 0, 4*4*sizeof(float));
    //for (i=0; i<4; i++) { Tcalc[i][i] = 1.0f; }

    // Solve it!
    AffineSolve(
        Tcalc,           // OUTPUT: transform
        O,  // INPUT:  points, offsets
        N,  // INPUT:  plane normals
        D,     // INPUT:  plane offsets
        nPlanes, NITER,
        STEP_SIZE_ROT, STEP_SIZE_POS, FALLOFF,
        1);
*/
    // insert code here...
    return 0;
}