1 /* $Id: vecmat.c,v 1.6 2004-05-12 07:31:37 btb Exp $ */
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17 * C version of vecmat library
20 * Revision 1.5 1995/10/30 11:08:16 allender
21 * fix check_vec to return if vector is the NULL vector
23 * Revision 1.4 1995/09/23 09:38:14 allender
24 * removed calls for PPC that are now handled in asm
26 * Revision 1.3 1995/08/31 15:50:24 allender
27 * fixing up of functions for PPC
29 * Revision 1.2 1995/07/05 16:40:21 allender
30 * some vecmat stuff might be using isqrt -- commented out
33 * Revision 1.1 1995/04/17 16:18:02 allender
37 * --- PC RCS Information ---
38 * Revision 1.1 1995/03/08 15:56:50 matt
49 static char rcsid[] = "$Id: vecmat.c,v 1.6 2004-05-12 07:31:37 btb Exp $";
53 #include <math.h> // for sqrt
62 vms_vector vmd_zero_vector = {0, 0, 0};
63 vms_matrix vmd_identity_matrix = { { f1_0, 0, 0 },
67 //adds two vectors, fills in dest, returns ptr to dest
68 //ok for dest to equal either source, but should use vm_vec_add2() if so
69 vms_vector *vm_vec_add(vms_vector *dest,vms_vector *src0,vms_vector *src1)
71 dest->x = src0->x + src1->x;
72 dest->y = src0->y + src1->y;
73 dest->z = src0->z + src1->z;
79 //subs two vectors, fills in dest, returns ptr to dest
80 //ok for dest to equal either source, but should use vm_vec_sub2() if so
81 vms_vector *vm_vec_sub(vms_vector *dest,vms_vector *src0,vms_vector *src1)
83 dest->x = src0->x - src1->x;
84 dest->y = src0->y - src1->y;
85 dest->z = src0->z - src1->z;
90 //adds one vector to another. returns ptr to dest
91 //dest can equal source
92 vms_vector *vm_vec_add2(vms_vector *dest,vms_vector *src)
101 //subs one vector from another, returns ptr to dest
102 //dest can equal source
103 vms_vector *vm_vec_sub2(vms_vector *dest,vms_vector *src)
112 //averages two vectors. returns ptr to dest
113 //dest can equal either source
114 vms_vector *vm_vec_avg(vms_vector *dest,vms_vector *src0,vms_vector *src1)
116 dest->x = (src0->x + src1->x)/2;
117 dest->y = (src0->y + src1->y)/2;
118 dest->z = (src0->z + src1->z)/2;
124 //averages four vectors. returns ptr to dest
125 //dest can equal any source
126 vms_vector *vm_vec_avg4(vms_vector *dest,vms_vector *src0,vms_vector *src1,vms_vector *src2,vms_vector *src3)
128 dest->x = (src0->x + src1->x + src2->x + src3->x)/4;
129 dest->y = (src0->y + src1->y + src2->y + src3->y)/4;
130 dest->z = (src0->z + src1->z + src2->z + src3->z)/4;
136 //scales a vector in place. returns ptr to vector
137 vms_vector *vm_vec_scale(vms_vector *dest,fix s)
139 dest->x = fixmul(dest->x,s);
140 dest->y = fixmul(dest->y,s);
141 dest->z = fixmul(dest->z,s);
146 //scales and copies a vector. returns ptr to dest
147 vms_vector *vm_vec_copy_scale(vms_vector *dest,vms_vector *src,fix s)
149 dest->x = fixmul(src->x,s);
150 dest->y = fixmul(src->y,s);
151 dest->z = fixmul(src->z,s);
156 //scales a vector, adds it to another, and stores in a 3rd vector
157 //dest = src1 + k * src2
158 vms_vector *vm_vec_scale_add(vms_vector *dest,vms_vector *src1,vms_vector *src2,fix k)
160 dest->x = src1->x + fixmul(src2->x,k);
161 dest->y = src1->y + fixmul(src2->y,k);
162 dest->z = src1->z + fixmul(src2->z,k);
167 //scales a vector and adds it to another
169 vms_vector *vm_vec_scale_add2(vms_vector *dest,vms_vector *src,fix k)
171 dest->x += fixmul(src->x,k);
172 dest->y += fixmul(src->y,k);
173 dest->z += fixmul(src->z,k);
178 //scales a vector in place, taking n/d for scale. returns ptr to vector
180 vms_vector *vm_vec_scale2(vms_vector *dest,fix n,fix d)
182 #if 1 // DPH: Kludge: this was overflowing a lot, so I made it use the FPU.
184 // printf("scale n=%d d=%d\n",n,d);
185 nd = f2fl(n) / f2fl(d);
186 dest->x = fl2f( f2fl(dest->x) * nd);
187 dest->y = fl2f( f2fl(dest->y) * nd);
188 dest->z = fl2f( f2fl(dest->z) * nd);
190 dest->x = fixmuldiv(dest->x,n,d);
191 dest->y = fixmuldiv(dest->y,n,d);
192 dest->z = fixmuldiv(dest->z,n,d);
198 fix vm_vec_dotprod(vms_vector *v0,vms_vector *v1)
204 fixmulaccum(&q,v0->x,v1->x);
205 fixmulaccum(&q,v0->y,v1->y);
206 fixmulaccum(&q,v0->z,v1->z);
208 return fixquadadjust(&q);
211 fix vm_vec_dot3(fix x,fix y,fix z,vms_vector *v)
217 fixmulaccum(&q,x,v->x);
218 fixmulaccum(&q,y,v->y);
219 fixmulaccum(&q,z,v->z);
221 return fixquadadjust(&q);
224 //returns magnitude of a vector
225 fix vm_vec_mag(vms_vector *v)
231 fixmulaccum(&q,v->x,v->x);
232 fixmulaccum(&q,v->y,v->y);
233 fixmulaccum(&q,v->z,v->z);
235 return quad_sqrt(q.low,q.high);
238 //computes the distance between two points. (does sub and mag)
239 fix vm_vec_dist(vms_vector *v0,vms_vector *v1)
243 vm_vec_sub(&t,v0,v1);
245 return vm_vec_mag(&t);
249 //computes an approximation of the magnitude of the vector
250 //uses dist = largest + next_largest*3/8 + smallest*3/16
251 fix vm_vec_mag_quick(vms_vector *v)
271 bc = (b>>2) + (c>>3);
273 return a + bc + (bc>>1);
277 //computes an approximation of the distance between two points.
278 //uses dist = largest + next_largest*3/8 + smallest*3/16
279 fix vm_vec_dist_quick(vms_vector *v0,vms_vector *v1)
283 vm_vec_sub(&t,v0,v1);
285 return vm_vec_mag_quick(&t);
288 //normalize a vector. returns mag of source vec
289 fix vm_vec_copy_normalize(vms_vector *dest,vms_vector *src)
296 dest->x = fixdiv(src->x,m);
297 dest->y = fixdiv(src->y,m);
298 dest->z = fixdiv(src->z,m);
304 //normalize a vector. returns mag of source vec
305 fix vm_vec_normalize(vms_vector *v)
307 return vm_vec_copy_normalize(v,v);
311 //normalize a vector. returns mag of source vec. uses approx mag
312 fix vm_vec_copy_normalize_quick(vms_vector *dest,vms_vector *src)
316 m = vm_vec_mag_quick(src);
319 dest->x = fixdiv(src->x,m);
320 dest->y = fixdiv(src->y,m);
321 dest->z = fixdiv(src->z,m);
328 //these routines use an approximation for 1/sqrt
330 //returns approximation of 1/magnitude of a vector
331 fix vm_vec_imag(vms_vector *v)
337 fixmulaccum(&q,v->x,v->x);
338 fixmulaccum(&q,v->y,v->y);
339 fixmulaccum(&q,v->z,v->z);
342 return fix_isqrt(fixquadadjust(&q));
343 else if (q.high >= 0x800000) {
344 return (fix_isqrt(q.high) >> 8);
347 return (fix_isqrt((q.high<<8) + (q.low>>24)) >> 4);
350 //normalize a vector. returns 1/mag of source vec. uses approx 1/mag
351 fix vm_vec_copy_normalize_quick(vms_vector *dest,vms_vector *src)
355 im = vm_vec_imag(src);
357 dest->x = fixmul(src->x,im);
358 dest->y = fixmul(src->y,im);
359 dest->z = fixmul(src->z,im);
366 //normalize a vector. returns 1/mag of source vec. uses approx 1/mag
367 fix vm_vec_normalize_quick(vms_vector *v)
369 return vm_vec_copy_normalize_quick(v,v);
372 //return the normalized direction vector between two points
373 //dest = normalized(end - start). Returns 1/mag of direction vector
374 //NOTE: the order of the parameters matches the vector subtraction
375 fix vm_vec_normalized_dir_quick(vms_vector *dest,vms_vector *end,vms_vector *start)
377 vm_vec_sub(dest,end,start);
379 return vm_vec_normalize_quick(dest);
382 //return the normalized direction vector between two points
383 //dest = normalized(end - start). Returns mag of direction vector
384 //NOTE: the order of the parameters matches the vector subtraction
385 fix vm_vec_normalized_dir(vms_vector *dest,vms_vector *end,vms_vector *start)
387 vm_vec_sub(dest,end,start);
389 return vm_vec_normalize(dest);
392 //computes surface normal from three points. result is normalized
393 //returns ptr to dest
394 //dest CANNOT equal either source
395 vms_vector *vm_vec_normal(vms_vector *dest,vms_vector *p0,vms_vector *p1,vms_vector *p2)
397 vm_vec_perp(dest,p0,p1,p2);
399 vm_vec_normalize(dest);
404 //make sure a vector is reasonably sized to go into a cross product
405 void check_vec(vms_vector *v)
410 check = labs(v->x) | labs(v->y) | labs(v->z);
415 if (check & 0xfffc0000) { //too big
417 while (check & 0xfff00000) {
422 while (check & 0xfffc0000) {
431 else //maybe too small
432 if ((check & 0xffff8000) == 0) { //yep, too small
434 while ((check & 0xfffff000) == 0) {
439 while ((check & 0xffff8000) == 0) {
450 //computes cross product of two vectors.
451 //Note: this magnitude of the resultant vector is the
452 //product of the magnitudes of the two source vectors. This means it is
453 //quite easy for this routine to overflow and underflow. Be careful that
454 //your inputs are ok.
457 vms_vector *vm_vec_crossprod(vms_vector *dest,vms_vector *src0,vms_vector *src1)
460 Assert(dest!=src0 && dest!=src1);
462 d = (double)(src0->y) * (double)(src1->z);
463 d += (double)-(src0->z) * (double)(src1->y);
469 d = (double)(src0->z) * (double)(src1->x);
470 d += (double)-(src0->x) * (double)(src1->z);
476 d = (double)(src0->x) * (double)(src1->y);
477 d += (double)-(src0->y) * (double)(src1->x);
487 vms_vector *vm_vec_crossprod(vms_vector *dest,vms_vector *src0,vms_vector *src1)
491 Assert(dest!=src0 && dest!=src1);
494 fixmulaccum(&q,src0->y,src1->z);
495 fixmulaccum(&q,-src0->z,src1->y);
496 dest->x = fixquadadjust(&q);
499 fixmulaccum(&q,src0->z,src1->x);
500 fixmulaccum(&q,-src0->x,src1->z);
501 dest->y = fixquadadjust(&q);
504 fixmulaccum(&q,src0->x,src1->y);
505 fixmulaccum(&q,-src0->y,src1->x);
506 dest->z = fixquadadjust(&q);
514 //computes non-normalized surface normal from three points.
515 //returns ptr to dest
516 //dest CANNOT equal either source
517 vms_vector *vm_vec_perp(vms_vector *dest,vms_vector *p0,vms_vector *p1,vms_vector *p2)
521 vm_vec_sub(&t0,p1,p0);
522 vm_vec_sub(&t1,p2,p1);
527 return vm_vec_crossprod(dest,&t0,&t1);
531 //computes the delta angle between two vectors.
532 //vectors need not be normalized. if they are, call vm_vec_delta_ang_norm()
533 //the forward vector (third parameter) can be NULL, in which case the absolute
534 //value of the angle in returned. Otherwise the angle around that vector is
536 fixang vm_vec_delta_ang(vms_vector *v0,vms_vector *v1,vms_vector *fvec)
540 vm_vec_copy_normalize(&t0,v0);
541 vm_vec_copy_normalize(&t1,v1);
543 return vm_vec_delta_ang_norm(&t0,&t1,fvec);
546 //computes the delta angle between two normalized vectors.
547 fixang vm_vec_delta_ang_norm(vms_vector *v0,vms_vector *v1,vms_vector *fvec)
551 a = fix_acos(vm_vec_dot(v0,v1));
556 vm_vec_cross(&t,v0,v1);
558 if (vm_vec_dot(&t,fvec) < 0)
565 vms_matrix *sincos_2_matrix(vms_matrix *m,fix sinp,fix cosp,fix sinb,fix cosb,fix sinh,fix cosh)
567 fix sbsh,cbch,cbsh,sbch;
569 sbsh = fixmul(sinb,sinh);
570 cbch = fixmul(cosb,cosh);
571 cbsh = fixmul(cosb,sinh);
572 sbch = fixmul(sinb,cosh);
574 m->rvec.x = cbch + fixmul(sinp,sbsh); //m1
575 m->uvec.z = sbsh + fixmul(sinp,cbch); //m8
577 m->uvec.x = fixmul(sinp,cbsh) - sbch; //m2
578 m->rvec.z = fixmul(sinp,sbch) - cbsh; //m7
580 m->fvec.x = fixmul(sinh,cosp); //m3
581 m->rvec.y = fixmul(sinb,cosp); //m4
582 m->uvec.y = fixmul(cosb,cosp); //m5
583 m->fvec.z = fixmul(cosh,cosp); //m9
585 m->fvec.y = -sinp; //m6
591 //computes a matrix from a set of three angles. returns ptr to matrix
592 vms_matrix *vm_angles_2_matrix(vms_matrix *m,vms_angvec *a)
594 fix sinp,cosp,sinb,cosb,sinh,cosh;
596 fix_sincos(a->p,&sinp,&cosp);
597 fix_sincos(a->b,&sinb,&cosb);
598 fix_sincos(a->h,&sinh,&cosh);
600 return sincos_2_matrix(m,sinp,cosp,sinb,cosb,sinh,cosh);
604 //computes a matrix from a forward vector and an angle
605 vms_matrix *vm_vec_ang_2_matrix(vms_matrix *m,vms_vector *v,fixang a)
607 fix sinb,cosb,sinp,cosp,sinh,cosh;
609 fix_sincos(a,&sinb,&cosb);
612 cosp = fix_sqrt(f1_0 - fixmul(sinp,sinp));
614 sinh = fixdiv(v->x,cosp);
615 cosh = fixdiv(v->z,cosp);
617 return sincos_2_matrix(m,sinp,cosp,sinb,cosb,sinh,cosh);
621 //computes a matrix from one or more vectors. The forward vector is required,
622 //with the other two being optional. If both up & right vectors are passed,
623 //the up vector is used. If only the forward vector is passed, a bank of
625 //returns ptr to matrix
626 vms_matrix *vm_vector_2_matrix(vms_matrix *m,vms_vector *fvec,vms_vector *uvec,vms_vector *rvec)
628 vms_vector *xvec=&m->rvec,*yvec=&m->uvec,*zvec=&m->fvec;
630 Assert(fvec != NULL);
632 if (vm_vec_copy_normalize(zvec,fvec) == 0) {
633 Int3(); //forward vec should not be zero-length
639 if (rvec == NULL) { //just forward vec
644 if (zvec->x==0 && zvec->z==0) { //forward vec is straight up or down
647 m->uvec.z = (zvec->y<0)?f1_0:-f1_0;
649 m->rvec.y = m->rvec.z = m->uvec.x = m->uvec.y = 0;
651 else { //not straight up or down
657 vm_vec_normalize(xvec);
659 vm_vec_crossprod(yvec,zvec,xvec);
664 else { //use right vec
666 if (vm_vec_copy_normalize(xvec,rvec) == 0)
669 vm_vec_crossprod(yvec,zvec,xvec);
671 //normalize new perpendicular vector
672 if (vm_vec_normalize(yvec) == 0)
675 //now recompute right vector, in case it wasn't entirely perpendiclar
676 vm_vec_crossprod(xvec,yvec,zvec);
682 if (vm_vec_copy_normalize(yvec,uvec) == 0)
685 vm_vec_crossprod(xvec,yvec,zvec);
687 //normalize new perpendicular vector
688 if (vm_vec_normalize(xvec) == 0)
691 //now recompute up vector, in case it wasn't entirely perpendiclar
692 vm_vec_crossprod(yvec,zvec,xvec);
700 //quicker version of vm_vector_2_matrix() that takes normalized vectors
701 vms_matrix *vm_vector_2_matrix_norm(vms_matrix *m,vms_vector *fvec,vms_vector *uvec,vms_vector *rvec)
703 vms_vector *xvec=&m->rvec,*yvec=&m->uvec,*zvec=&m->fvec;
705 Assert(fvec != NULL);
709 if (rvec == NULL) { //just forward vec
714 if (zvec->x==0 && zvec->z==0) { //forward vec is straight up or down
717 m->uvec.z = (zvec->y<0)?f1_0:-f1_0;
719 m->rvec.y = m->rvec.z = m->uvec.x = m->uvec.y = 0;
721 else { //not straight up or down
727 vm_vec_normalize(xvec);
729 vm_vec_crossprod(yvec,zvec,xvec);
734 else { //use right vec
736 vm_vec_crossprod(yvec,zvec,xvec);
738 //normalize new perpendicular vector
739 if (vm_vec_normalize(yvec) == 0)
742 //now recompute right vector, in case it wasn't entirely perpendiclar
743 vm_vec_crossprod(xvec,yvec,zvec);
749 vm_vec_crossprod(xvec,yvec,zvec);
751 //normalize new perpendicular vector
752 if (vm_vec_normalize(xvec) == 0)
755 //now recompute up vector, in case it wasn't entirely perpendiclar
756 vm_vec_crossprod(yvec,zvec,xvec);
764 //rotates a vector through a matrix. returns ptr to dest vector
765 //dest CANNOT equal source
766 vms_vector *vm_vec_rotate(vms_vector *dest,vms_vector *src,vms_matrix *m)
770 dest->x = vm_vec_dot(src,&m->rvec);
771 dest->y = vm_vec_dot(src,&m->uvec);
772 dest->z = vm_vec_dot(src,&m->fvec);
778 //transpose a matrix in place. returns ptr to matrix
779 vms_matrix *vm_transpose_matrix(vms_matrix *m)
783 t = m->uvec.x; m->uvec.x = m->rvec.y; m->rvec.y = t;
784 t = m->fvec.x; m->fvec.x = m->rvec.z; m->rvec.z = t;
785 t = m->fvec.y; m->fvec.y = m->uvec.z; m->uvec.z = t;
790 //copy and transpose a matrix. returns ptr to matrix
791 //dest CANNOT equal source. use vm_transpose_matrix() if this is the case
792 vms_matrix *vm_copy_transpose_matrix(vms_matrix *dest,vms_matrix *src)
796 dest->rvec.x = src->rvec.x;
797 dest->rvec.y = src->uvec.x;
798 dest->rvec.z = src->fvec.x;
800 dest->uvec.x = src->rvec.y;
801 dest->uvec.y = src->uvec.y;
802 dest->uvec.z = src->fvec.y;
804 dest->fvec.x = src->rvec.z;
805 dest->fvec.y = src->uvec.z;
806 dest->fvec.z = src->fvec.z;
811 //mulitply 2 matrices, fill in dest. returns ptr to dest
812 //dest CANNOT equal either source
813 vms_matrix *vm_matrix_x_matrix(vms_matrix *dest,vms_matrix *src0,vms_matrix *src1)
815 Assert(dest!=src0 && dest!=src1);
817 dest->rvec.x = vm_vec_dot3(src0->rvec.x,src0->uvec.x,src0->fvec.x, &src1->rvec);
818 dest->uvec.x = vm_vec_dot3(src0->rvec.x,src0->uvec.x,src0->fvec.x, &src1->uvec);
819 dest->fvec.x = vm_vec_dot3(src0->rvec.x,src0->uvec.x,src0->fvec.x, &src1->fvec);
821 dest->rvec.y = vm_vec_dot3(src0->rvec.y,src0->uvec.y,src0->fvec.y, &src1->rvec);
822 dest->uvec.y = vm_vec_dot3(src0->rvec.y,src0->uvec.y,src0->fvec.y, &src1->uvec);
823 dest->fvec.y = vm_vec_dot3(src0->rvec.y,src0->uvec.y,src0->fvec.y, &src1->fvec);
825 dest->rvec.z = vm_vec_dot3(src0->rvec.z,src0->uvec.z,src0->fvec.z, &src1->rvec);
826 dest->uvec.z = vm_vec_dot3(src0->rvec.z,src0->uvec.z,src0->fvec.z, &src1->uvec);
827 dest->fvec.z = vm_vec_dot3(src0->rvec.z,src0->uvec.z,src0->fvec.z, &src1->fvec);
834 //extract angles from a matrix
835 vms_angvec *vm_extract_angles_matrix(vms_angvec *a,vms_matrix *m)
839 if (m->fvec.x==0 && m->fvec.z==0) //zero head
842 a->h = fix_atan2(m->fvec.z,m->fvec.x);
844 fix_sincos(a->h,&sinh,&cosh);
846 if (abs(sinh) > abs(cosh)) //sine is larger, so use it
847 cosp = fixdiv(m->fvec.x,sinh);
848 else //cosine is larger, so use it
849 cosp = fixdiv(m->fvec.z,cosh);
851 if (cosp==0 && m->fvec.y==0)
854 a->p = fix_atan2(cosp,-m->fvec.y);
857 if (cosp == 0) //the cosine of pitch is zero. we're pitched straight up. say no bank
864 sinb = fixdiv(m->rvec.y,cosp);
865 cosb = fixdiv(m->uvec.y,cosp);
867 if (sinb==0 && cosb==0)
870 a->b = fix_atan2(cosb,sinb);
878 //extract heading and pitch from a vector, assuming bank==0
879 vms_angvec *vm_extract_angles_vector_normalized(vms_angvec *a,vms_vector *v)
881 a->b = 0; //always zero bank
883 a->p = fix_asin(-v->y);
885 if (v->x==0 && v->z==0)
888 a->h = fix_atan2(v->z,v->x);
893 //extract heading and pitch from a vector, assuming bank==0
894 vms_angvec *vm_extract_angles_vector(vms_angvec *a,vms_vector *v)
898 if (vm_vec_copy_normalize(&t,v) != 0)
899 vm_extract_angles_vector_normalized(a,&t);
905 //compute the distance from a point to a plane. takes the normalized normal
906 //of the plane (ebx), a point on the plane (edi), and the point to check (esi).
907 //returns distance in eax
908 //distance is signed, so negative dist is on the back of the plane
909 fix vm_dist_to_plane(vms_vector *checkp,vms_vector *norm,vms_vector *planep)
913 vm_vec_sub(&t,checkp,planep);
915 return vm_vec_dot(&t,norm);
919 vms_vector *vm_vec_make(vms_vector *v,fix x,fix y,fix z)
921 v->x=x; v->y=y; v->z=z;