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14 * $Source: /cvs/cvsroot/d2x/maths/vecmat.c,v $
17 * $Date: 2001-10-31 07:41:54 $
19 * C version of vecmat library
21 * $Log: not supported by cvs2svn $
22 * Revision 1.2 2001/01/31 15:18:04 bradleyb
23 * Makefile and conf.h fixes
25 * Revision 1.1.1.2 2001/01/19 03:33:42 bradleyb
26 * Import of d2x-0.0.9-pre1
28 * Revision 1.1.1.1 1999/06/14 22:13:42 donut
29 * Import of d1x 1.37 source.
31 * Revision 1.5 1995/10/30 11:08:16 allender
32 * fix check_vec to return if vector is the NULL vector
34 * Revision 1.4 1995/09/23 09:38:14 allender
35 * removed calls for PPC that are now handled in asm
37 * Revision 1.3 1995/08/31 15:50:24 allender
38 * fixing up of functions for PPC
40 * Revision 1.2 1995/07/05 16:40:21 allender
41 * some vecmat stuff might be using isqrt -- commented out
44 * Revision 1.1 1995/04/17 16:18:02 allender
48 * --- PC RCS Information ---
49 * Revision 1.1 1995/03/08 15:56:50 matt
60 static char rcsid[] = "$Id: vecmat.c,v 1.3 2001-10-31 07:41:54 bradleyb Exp $";
64 #include <math.h> // for sqrt
73 vms_vector vmd_zero_vector = {0,0,0};
74 vms_matrix vmd_identity_matrix = { { f1_0,0,0 },
78 //adds two vectors, fills in dest, returns ptr to dest
79 //ok for dest to equal either source, but should use vm_vec_add2() if so
80 vms_vector *vm_vec_add(vms_vector *dest,vms_vector *src0,vms_vector *src1)
82 dest->x = src0->x + src1->x;
83 dest->y = src0->y + src1->y;
84 dest->z = src0->z + src1->z;
90 //subs two vectors, fills in dest, returns ptr to dest
91 //ok for dest to equal either source, but should use vm_vec_sub2() if so
92 vms_vector *vm_vec_sub(vms_vector *dest,vms_vector *src0,vms_vector *src1)
94 dest->x = src0->x - src1->x;
95 dest->y = src0->y - src1->y;
96 dest->z = src0->z - src1->z;
101 //adds one vector to another. returns ptr to dest
102 //dest can equal source
103 vms_vector *vm_vec_add2(vms_vector *dest,vms_vector *src)
112 //subs one vector from another, returns ptr to dest
113 //dest can equal source
114 vms_vector *vm_vec_sub2(vms_vector *dest,vms_vector *src)
123 //averages two vectors. returns ptr to dest
124 //dest can equal either source
125 vms_vector *vm_vec_avg(vms_vector *dest,vms_vector *src0,vms_vector *src1)
127 dest->x = (src0->x + src1->x)/2;
128 dest->y = (src0->y + src1->y)/2;
129 dest->z = (src0->z + src1->z)/2;
135 //averages four vectors. returns ptr to dest
136 //dest can equal any source
137 vms_vector *vm_vec_avg4(vms_vector *dest,vms_vector *src0,vms_vector *src1,vms_vector *src2,vms_vector *src3)
139 dest->x = (src0->x + src1->x + src2->x + src3->x)/4;
140 dest->y = (src0->y + src1->y + src2->y + src3->y)/4;
141 dest->z = (src0->z + src1->z + src2->z + src3->z)/4;
147 //scales a vector in place. returns ptr to vector
148 vms_vector *vm_vec_scale(vms_vector *dest,fix s)
150 dest->x = fixmul(dest->x,s);
151 dest->y = fixmul(dest->y,s);
152 dest->z = fixmul(dest->z,s);
157 //scales and copies a vector. returns ptr to dest
158 vms_vector *vm_vec_copy_scale(vms_vector *dest,vms_vector *src,fix s)
160 dest->x = fixmul(src->x,s);
161 dest->y = fixmul(src->y,s);
162 dest->z = fixmul(src->z,s);
167 //scales a vector, adds it to another, and stores in a 3rd vector
168 //dest = src1 + k * src2
169 vms_vector *vm_vec_scale_add(vms_vector *dest,vms_vector *src1,vms_vector *src2,fix k)
171 dest->x = src1->x + fixmul(src2->x,k);
172 dest->y = src1->y + fixmul(src2->y,k);
173 dest->z = src1->z + fixmul(src2->z,k);
178 //scales a vector and adds it to another
180 vms_vector *vm_vec_scale_add2(vms_vector *dest,vms_vector *src,fix k)
182 dest->x += fixmul(src->x,k);
183 dest->y += fixmul(src->y,k);
184 dest->z += fixmul(src->z,k);
189 //scales a vector in place, taking n/d for scale. returns ptr to vector
191 vms_vector *vm_vec_scale2(vms_vector *dest,fix n,fix d)
193 #if 1 // DPH: Kludge: this was overflowing a lot, so I made it use the FPU.
195 // printf("scale n=%d d=%d\n",n,d);
196 nd = f2fl(n) / f2fl(d);
197 dest->x = fl2f( f2fl(dest->x) * nd);
198 dest->y = fl2f( f2fl(dest->y) * nd);
199 dest->z = fl2f( f2fl(dest->z) * nd);
201 dest->x = fixmuldiv(dest->x,n,d);
202 dest->y = fixmuldiv(dest->y,n,d);
203 dest->z = fixmuldiv(dest->z,n,d);
209 fix vm_vec_dotprod(vms_vector *v0,vms_vector *v1)
215 fixmulaccum(&q,v0->x,v1->x);
216 fixmulaccum(&q,v0->y,v1->y);
217 fixmulaccum(&q,v0->z,v1->z);
219 return fixquadadjust(&q);
222 fix vm_vec_dot3(fix x,fix y,fix z,vms_vector *v)
228 fixmulaccum(&q,x,v->x);
229 fixmulaccum(&q,y,v->y);
230 fixmulaccum(&q,z,v->z);
232 return fixquadadjust(&q);
235 //returns magnitude of a vector
236 fix vm_vec_mag(vms_vector *v)
242 fixmulaccum(&q,v->x,v->x);
243 fixmulaccum(&q,v->y,v->y);
244 fixmulaccum(&q,v->z,v->z);
246 return quad_sqrt(q.low,q.high);
249 //computes the distance between two points. (does sub and mag)
250 fix vm_vec_dist(vms_vector *v0,vms_vector *v1)
254 vm_vec_sub(&t,v0,v1);
256 return vm_vec_mag(&t);
260 //computes an approximation of the magnitude of the vector
261 //uses dist = largest + next_largest*3/8 + smallest*3/16
262 fix vm_vec_mag_quick(vms_vector *v)
282 bc = (b>>2) + (c>>3);
284 return a + bc + (bc>>1);
288 //computes an approximation of the distance between two points.
289 //uses dist = largest + next_largest*3/8 + smallest*3/16
290 fix vm_vec_dist_quick(vms_vector *v0,vms_vector *v1)
294 vm_vec_sub(&t,v0,v1);
296 return vm_vec_mag_quick(&t);
299 //normalize a vector. returns mag of source vec
300 fix vm_vec_copy_normalize(vms_vector *dest,vms_vector *src)
307 dest->x = fixdiv(src->x,m);
308 dest->y = fixdiv(src->y,m);
309 dest->z = fixdiv(src->z,m);
315 //normalize a vector. returns mag of source vec
316 fix vm_vec_normalize(vms_vector *v)
318 return vm_vec_copy_normalize(v,v);
322 //normalize a vector. returns mag of source vec. uses approx mag
323 fix vm_vec_copy_normalize_quick(vms_vector *dest,vms_vector *src)
327 m = vm_vec_mag_quick(src);
330 dest->x = fixdiv(src->x,m);
331 dest->y = fixdiv(src->y,m);
332 dest->z = fixdiv(src->z,m);
339 //these routines use an approximation for 1/sqrt
341 //returns approximation of 1/magnitude of a vector
342 fix vm_vec_imag(vms_vector *v)
348 fixmulaccum(&q,v->x,v->x);
349 fixmulaccum(&q,v->y,v->y);
350 fixmulaccum(&q,v->z,v->z);
353 return fix_isqrt(fixquadadjust(&q));
354 else if (q.high >= 0x800000) {
355 return (fix_isqrt(q.high) >> 8);
358 return (fix_isqrt((q.high<<8) + (q.low>>24)) >> 4);
361 //normalize a vector. returns 1/mag of source vec. uses approx 1/mag
362 fix vm_vec_copy_normalize_quick(vms_vector *dest,vms_vector *src)
366 im = vm_vec_imag(src);
368 dest->x = fixmul(src->x,im);
369 dest->y = fixmul(src->y,im);
370 dest->z = fixmul(src->z,im);
377 //normalize a vector. returns 1/mag of source vec. uses approx 1/mag
378 fix vm_vec_normalize_quick(vms_vector *v)
380 return vm_vec_copy_normalize_quick(v,v);
383 //return the normalized direction vector between two points
384 //dest = normalized(end - start). Returns 1/mag of direction vector
385 //NOTE: the order of the parameters matches the vector subtraction
386 fix vm_vec_normalized_dir_quick(vms_vector *dest,vms_vector *end,vms_vector *start)
388 vm_vec_sub(dest,end,start);
390 return vm_vec_normalize_quick(dest);
393 //return the normalized direction vector between two points
394 //dest = normalized(end - start). Returns mag of direction vector
395 //NOTE: the order of the parameters matches the vector subtraction
396 fix vm_vec_normalized_dir(vms_vector *dest,vms_vector *end,vms_vector *start)
398 vm_vec_sub(dest,end,start);
400 return vm_vec_normalize(dest);
403 //computes surface normal from three points. result is normalized
404 //returns ptr to dest
405 //dest CANNOT equal either source
406 vms_vector *vm_vec_normal(vms_vector *dest,vms_vector *p0,vms_vector *p1,vms_vector *p2)
408 vm_vec_perp(dest,p0,p1,p2);
410 vm_vec_normalize(dest);
415 //make sure a vector is reasonably sized to go into a cross product
416 void check_vec(vms_vector *v)
421 check = labs(v->x) | labs(v->y) | labs(v->z);
426 if (check & 0xfffc0000) { //too big
428 while (check & 0xfff00000) {
433 while (check & 0xfffc0000) {
442 else //maybe too small
443 if ((check & 0xffff8000) == 0) { //yep, too small
445 while ((check & 0xfffff000) == 0) {
450 while ((check & 0xffff8000) == 0) {
461 //computes cross product of two vectors.
462 //Note: this magnitude of the resultant vector is the
463 //product of the magnitudes of the two source vectors. This means it is
464 //quite easy for this routine to overflow and underflow. Be careful that
465 //your inputs are ok.
468 vms_vector *vm_vec_crossprod(vms_vector *dest,vms_vector *src0,vms_vector *src1)
471 Assert(dest!=src0 && dest!=src1);
473 d = (double)(src0->y) * (double)(src1->z);
474 d += (double)-(src0->z) * (double)(src1->y);
480 d = (double)(src0->z) * (double)(src1->x);
481 d += (double)-(src0->x) * (double)(src1->z);
487 d = (double)(src0->x) * (double)(src1->y);
488 d += (double)-(src0->y) * (double)(src1->x);
498 vms_vector *vm_vec_crossprod(vms_vector *dest,vms_vector *src0,vms_vector *src1)
502 Assert(dest!=src0 && dest!=src1);
505 fixmulaccum(&q,src0->y,src1->z);
506 fixmulaccum(&q,-src0->z,src1->y);
507 dest->x = fixquadadjust(&q);
510 fixmulaccum(&q,src0->z,src1->x);
511 fixmulaccum(&q,-src0->x,src1->z);
512 dest->y = fixquadadjust(&q);
515 fixmulaccum(&q,src0->x,src1->y);
516 fixmulaccum(&q,-src0->y,src1->x);
517 dest->z = fixquadadjust(&q);
525 //computes non-normalized surface normal from three points.
526 //returns ptr to dest
527 //dest CANNOT equal either source
528 vms_vector *vm_vec_perp(vms_vector *dest,vms_vector *p0,vms_vector *p1,vms_vector *p2)
532 vm_vec_sub(&t0,p1,p0);
533 vm_vec_sub(&t1,p2,p1);
538 return vm_vec_crossprod(dest,&t0,&t1);
542 //computes the delta angle between two vectors.
543 //vectors need not be normalized. if they are, call vm_vec_delta_ang_norm()
544 //the forward vector (third parameter) can be NULL, in which case the absolute
545 //value of the angle in returned. Otherwise the angle around that vector is
547 fixang vm_vec_delta_ang(vms_vector *v0,vms_vector *v1,vms_vector *fvec)
551 vm_vec_copy_normalize(&t0,v0);
552 vm_vec_copy_normalize(&t1,v1);
554 return vm_vec_delta_ang_norm(&t0,&t1,fvec);
557 //computes the delta angle between two normalized vectors.
558 fixang vm_vec_delta_ang_norm(vms_vector *v0,vms_vector *v1,vms_vector *fvec)
562 a = fix_acos(vm_vec_dot(v0,v1));
567 vm_vec_cross(&t,v0,v1);
569 if (vm_vec_dot(&t,fvec) < 0)
576 vms_matrix *sincos_2_matrix(vms_matrix *m,fix sinp,fix cosp,fix sinb,fix cosb,fix sinh,fix cosh)
578 fix sbsh,cbch,cbsh,sbch;
580 sbsh = fixmul(sinb,sinh);
581 cbch = fixmul(cosb,cosh);
582 cbsh = fixmul(cosb,sinh);
583 sbch = fixmul(sinb,cosh);
585 m->rvec.x = cbch + fixmul(sinp,sbsh); //m1
586 m->uvec.z = sbsh + fixmul(sinp,cbch); //m8
588 m->uvec.x = fixmul(sinp,cbsh) - sbch; //m2
589 m->rvec.z = fixmul(sinp,sbch) - cbsh; //m7
591 m->fvec.x = fixmul(sinh,cosp); //m3
592 m->rvec.y = fixmul(sinb,cosp); //m4
593 m->uvec.y = fixmul(cosb,cosp); //m5
594 m->fvec.z = fixmul(cosh,cosp); //m9
596 m->fvec.y = -sinp; //m6
602 //computes a matrix from a set of three angles. returns ptr to matrix
603 vms_matrix *vm_angles_2_matrix(vms_matrix *m,vms_angvec *a)
605 fix sinp,cosp,sinb,cosb,sinh,cosh;
607 fix_sincos(a->p,&sinp,&cosp);
608 fix_sincos(a->b,&sinb,&cosb);
609 fix_sincos(a->h,&sinh,&cosh);
611 return sincos_2_matrix(m,sinp,cosp,sinb,cosb,sinh,cosh);
615 //computes a matrix from a forward vector and an angle
616 vms_matrix *vm_vec_ang_2_matrix(vms_matrix *m,vms_vector *v,fixang a)
618 fix sinb,cosb,sinp,cosp,sinh,cosh;
620 fix_sincos(a,&sinb,&cosb);
623 cosp = fix_sqrt(f1_0 - fixmul(sinp,sinp));
625 sinh = fixdiv(v->x,cosp);
626 cosh = fixdiv(v->z,cosp);
628 return sincos_2_matrix(m,sinp,cosp,sinb,cosb,sinh,cosh);
632 //computes a matrix from one or more vectors. The forward vector is required,
633 //with the other two being optional. If both up & right vectors are passed,
634 //the up vector is used. If only the forward vector is passed, a bank of
636 //returns ptr to matrix
637 vms_matrix *vm_vector_2_matrix(vms_matrix *m,vms_vector *fvec,vms_vector *uvec,vms_vector *rvec)
639 vms_vector *xvec=&m->rvec,*yvec=&m->uvec,*zvec=&m->fvec;
641 Assert(fvec != NULL);
643 if (vm_vec_copy_normalize(zvec,fvec) == 0) {
644 Int3(); //forward vec should not be zero-length
650 if (rvec == NULL) { //just forward vec
655 if (zvec->x==0 && zvec->z==0) { //forward vec is straight up or down
658 m->uvec.z = (zvec->y<0)?f1_0:-f1_0;
660 m->rvec.y = m->rvec.z = m->uvec.x = m->uvec.y = 0;
662 else { //not straight up or down
668 vm_vec_normalize(xvec);
670 vm_vec_crossprod(yvec,zvec,xvec);
675 else { //use right vec
677 if (vm_vec_copy_normalize(xvec,rvec) == 0)
680 vm_vec_crossprod(yvec,zvec,xvec);
682 //normalize new perpendicular vector
683 if (vm_vec_normalize(yvec) == 0)
686 //now recompute right vector, in case it wasn't entirely perpendiclar
687 vm_vec_crossprod(xvec,yvec,zvec);
693 if (vm_vec_copy_normalize(yvec,uvec) == 0)
696 vm_vec_crossprod(xvec,yvec,zvec);
698 //normalize new perpendicular vector
699 if (vm_vec_normalize(xvec) == 0)
702 //now recompute up vector, in case it wasn't entirely perpendiclar
703 vm_vec_crossprod(yvec,zvec,xvec);
711 //quicker version of vm_vector_2_matrix() that takes normalized vectors
712 vms_matrix *vm_vector_2_matrix_norm(vms_matrix *m,vms_vector *fvec,vms_vector *uvec,vms_vector *rvec)
714 vms_vector *xvec=&m->rvec,*yvec=&m->uvec,*zvec=&m->fvec;
716 Assert(fvec != NULL);
720 if (rvec == NULL) { //just forward vec
725 if (zvec->x==0 && zvec->z==0) { //forward vec is straight up or down
728 m->uvec.z = (zvec->y<0)?f1_0:-f1_0;
730 m->rvec.y = m->rvec.z = m->uvec.x = m->uvec.y = 0;
732 else { //not straight up or down
738 vm_vec_normalize(xvec);
740 vm_vec_crossprod(yvec,zvec,xvec);
745 else { //use right vec
747 vm_vec_crossprod(yvec,zvec,xvec);
749 //normalize new perpendicular vector
750 if (vm_vec_normalize(yvec) == 0)
753 //now recompute right vector, in case it wasn't entirely perpendiclar
754 vm_vec_crossprod(xvec,yvec,zvec);
760 vm_vec_crossprod(xvec,yvec,zvec);
762 //normalize new perpendicular vector
763 if (vm_vec_normalize(xvec) == 0)
766 //now recompute up vector, in case it wasn't entirely perpendiclar
767 vm_vec_crossprod(yvec,zvec,xvec);
775 //rotates a vector through a matrix. returns ptr to dest vector
776 //dest CANNOT equal source
777 vms_vector *vm_vec_rotate(vms_vector *dest,vms_vector *src,vms_matrix *m)
781 dest->x = vm_vec_dot(src,&m->rvec);
782 dest->y = vm_vec_dot(src,&m->uvec);
783 dest->z = vm_vec_dot(src,&m->fvec);
789 //transpose a matrix in place. returns ptr to matrix
790 vms_matrix *vm_transpose_matrix(vms_matrix *m)
794 t = m->uvec.x; m->uvec.x = m->rvec.y; m->rvec.y = t;
795 t = m->fvec.x; m->fvec.x = m->rvec.z; m->rvec.z = t;
796 t = m->fvec.y; m->fvec.y = m->uvec.z; m->uvec.z = t;
801 //copy and transpose a matrix. returns ptr to matrix
802 //dest CANNOT equal source. use vm_transpose_matrix() if this is the case
803 vms_matrix *vm_copy_transpose_matrix(vms_matrix *dest,vms_matrix *src)
807 dest->rvec.x = src->rvec.x;
808 dest->rvec.y = src->uvec.x;
809 dest->rvec.z = src->fvec.x;
811 dest->uvec.x = src->rvec.y;
812 dest->uvec.y = src->uvec.y;
813 dest->uvec.z = src->fvec.y;
815 dest->fvec.x = src->rvec.z;
816 dest->fvec.y = src->uvec.z;
817 dest->fvec.z = src->fvec.z;
822 //mulitply 2 matrices, fill in dest. returns ptr to dest
823 //dest CANNOT equal either source
824 vms_matrix *vm_matrix_x_matrix(vms_matrix *dest,vms_matrix *src0,vms_matrix *src1)
826 Assert(dest!=src0 && dest!=src1);
828 dest->rvec.x = vm_vec_dot3(src0->rvec.x,src0->uvec.x,src0->fvec.x, &src1->rvec);
829 dest->uvec.x = vm_vec_dot3(src0->rvec.x,src0->uvec.x,src0->fvec.x, &src1->uvec);
830 dest->fvec.x = vm_vec_dot3(src0->rvec.x,src0->uvec.x,src0->fvec.x, &src1->fvec);
832 dest->rvec.y = vm_vec_dot3(src0->rvec.y,src0->uvec.y,src0->fvec.y, &src1->rvec);
833 dest->uvec.y = vm_vec_dot3(src0->rvec.y,src0->uvec.y,src0->fvec.y, &src1->uvec);
834 dest->fvec.y = vm_vec_dot3(src0->rvec.y,src0->uvec.y,src0->fvec.y, &src1->fvec);
836 dest->rvec.z = vm_vec_dot3(src0->rvec.z,src0->uvec.z,src0->fvec.z, &src1->rvec);
837 dest->uvec.z = vm_vec_dot3(src0->rvec.z,src0->uvec.z,src0->fvec.z, &src1->uvec);
838 dest->fvec.z = vm_vec_dot3(src0->rvec.z,src0->uvec.z,src0->fvec.z, &src1->fvec);
845 //extract angles from a matrix
846 vms_angvec *vm_extract_angles_matrix(vms_angvec *a,vms_matrix *m)
850 if (m->fvec.x==0 && m->fvec.z==0) //zero head
853 a->h = fix_atan2(m->fvec.z,m->fvec.x);
855 fix_sincos(a->h,&sinh,&cosh);
857 if (abs(sinh) > abs(cosh)) //sine is larger, so use it
858 cosp = fixdiv(m->fvec.x,sinh);
859 else //cosine is larger, so use it
860 cosp = fixdiv(m->fvec.z,cosh);
862 if (cosp==0 && m->fvec.y==0)
865 a->p = fix_atan2(cosp,-m->fvec.y);
868 if (cosp == 0) //the cosine of pitch is zero. we're pitched straight up. say no bank
875 sinb = fixdiv(m->rvec.y,cosp);
876 cosb = fixdiv(m->uvec.y,cosp);
878 if (sinb==0 && cosb==0)
881 a->b = fix_atan2(cosb,sinb);
889 //extract heading and pitch from a vector, assuming bank==0
890 vms_angvec *vm_extract_angles_vector_normalized(vms_angvec *a,vms_vector *v)
892 a->b = 0; //always zero bank
894 a->p = fix_asin(-v->y);
896 if (v->x==0 && v->z==0)
899 a->h = fix_atan2(v->z,v->x);
904 //extract heading and pitch from a vector, assuming bank==0
905 vms_angvec *vm_extract_angles_vector(vms_angvec *a,vms_vector *v)
909 if (vm_vec_copy_normalize(&t,v) != 0)
910 vm_extract_angles_vector_normalized(a,&t);
916 //compute the distance from a point to a plane. takes the normalized normal
917 //of the plane (ebx), a point on the plane (edi), and the point to check (esi).
918 //returns distance in eax
919 //distance is signed, so negative dist is on the back of the plane
920 fix vm_dist_to_plane(vms_vector *checkp,vms_vector *norm,vms_vector *planep)
924 vm_vec_sub(&t,checkp,planep);
926 return vm_vec_dot(&t,norm);
930 vms_vector *vm_vec_make(vms_vector *v,fix x,fix y,fix z) {
931 v->x=x; v->y=y; v->z=z;