1 /* $Id: vecmat.c,v 1.7 2004-08-28 23:17:45 schaffner Exp $ */
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17 * C version of vecmat library
26 static char rcsid[] = "$Id: vecmat.c,v 1.7 2004-08-28 23:17:45 schaffner Exp $";
30 #include <math.h> // for sqrt
39 vms_vector vmd_zero_vector = {0, 0, 0};
40 vms_matrix vmd_identity_matrix = { { f1_0, 0, 0 },
44 //adds two vectors, fills in dest, returns ptr to dest
45 //ok for dest to equal either source, but should use vm_vec_add2() if so
46 vms_vector *vm_vec_add(vms_vector *dest,vms_vector *src0,vms_vector *src1)
48 dest->x = src0->x + src1->x;
49 dest->y = src0->y + src1->y;
50 dest->z = src0->z + src1->z;
56 //subs two vectors, fills in dest, returns ptr to dest
57 //ok for dest to equal either source, but should use vm_vec_sub2() if so
58 vms_vector *vm_vec_sub(vms_vector *dest,vms_vector *src0,vms_vector *src1)
60 dest->x = src0->x - src1->x;
61 dest->y = src0->y - src1->y;
62 dest->z = src0->z - src1->z;
67 //adds one vector to another. returns ptr to dest
68 //dest can equal source
69 vms_vector *vm_vec_add2(vms_vector *dest,vms_vector *src)
78 //subs one vector from another, returns ptr to dest
79 //dest can equal source
80 vms_vector *vm_vec_sub2(vms_vector *dest,vms_vector *src)
89 //averages two vectors. returns ptr to dest
90 //dest can equal either source
91 vms_vector *vm_vec_avg(vms_vector *dest,vms_vector *src0,vms_vector *src1)
93 dest->x = (src0->x + src1->x)/2;
94 dest->y = (src0->y + src1->y)/2;
95 dest->z = (src0->z + src1->z)/2;
101 //averages four vectors. returns ptr to dest
102 //dest can equal any source
103 vms_vector *vm_vec_avg4(vms_vector *dest,vms_vector *src0,vms_vector *src1,vms_vector *src2,vms_vector *src3)
105 dest->x = (src0->x + src1->x + src2->x + src3->x)/4;
106 dest->y = (src0->y + src1->y + src2->y + src3->y)/4;
107 dest->z = (src0->z + src1->z + src2->z + src3->z)/4;
113 //scales a vector in place. returns ptr to vector
114 vms_vector *vm_vec_scale(vms_vector *dest,fix s)
116 dest->x = fixmul(dest->x,s);
117 dest->y = fixmul(dest->y,s);
118 dest->z = fixmul(dest->z,s);
123 //scales and copies a vector. returns ptr to dest
124 vms_vector *vm_vec_copy_scale(vms_vector *dest,vms_vector *src,fix s)
126 dest->x = fixmul(src->x,s);
127 dest->y = fixmul(src->y,s);
128 dest->z = fixmul(src->z,s);
133 //scales a vector, adds it to another, and stores in a 3rd vector
134 //dest = src1 + k * src2
135 vms_vector *vm_vec_scale_add(vms_vector *dest,vms_vector *src1,vms_vector *src2,fix k)
137 dest->x = src1->x + fixmul(src2->x,k);
138 dest->y = src1->y + fixmul(src2->y,k);
139 dest->z = src1->z + fixmul(src2->z,k);
144 //scales a vector and adds it to another
146 vms_vector *vm_vec_scale_add2(vms_vector *dest,vms_vector *src,fix k)
148 dest->x += fixmul(src->x,k);
149 dest->y += fixmul(src->y,k);
150 dest->z += fixmul(src->z,k);
155 //scales a vector in place, taking n/d for scale. returns ptr to vector
157 vms_vector *vm_vec_scale2(vms_vector *dest,fix n,fix d)
159 #if 1 // DPH: Kludge: this was overflowing a lot, so I made it use the FPU.
161 // printf("scale n=%d d=%d\n",n,d);
162 nd = f2fl(n) / f2fl(d);
163 dest->x = fl2f( f2fl(dest->x) * nd);
164 dest->y = fl2f( f2fl(dest->y) * nd);
165 dest->z = fl2f( f2fl(dest->z) * nd);
167 dest->x = fixmuldiv(dest->x,n,d);
168 dest->y = fixmuldiv(dest->y,n,d);
169 dest->z = fixmuldiv(dest->z,n,d);
175 fix vm_vec_dotprod(vms_vector *v0,vms_vector *v1)
181 fixmulaccum(&q,v0->x,v1->x);
182 fixmulaccum(&q,v0->y,v1->y);
183 fixmulaccum(&q,v0->z,v1->z);
185 return fixquadadjust(&q);
188 fix vm_vec_dot3(fix x,fix y,fix z,vms_vector *v)
194 fixmulaccum(&q,x,v->x);
195 fixmulaccum(&q,y,v->y);
196 fixmulaccum(&q,z,v->z);
198 return fixquadadjust(&q);
201 //returns magnitude of a vector
202 fix vm_vec_mag(vms_vector *v)
208 fixmulaccum(&q,v->x,v->x);
209 fixmulaccum(&q,v->y,v->y);
210 fixmulaccum(&q,v->z,v->z);
212 return quad_sqrt(q.low,q.high);
215 //computes the distance between two points. (does sub and mag)
216 fix vm_vec_dist(vms_vector *v0,vms_vector *v1)
220 vm_vec_sub(&t,v0,v1);
222 return vm_vec_mag(&t);
226 //computes an approximation of the magnitude of the vector
227 //uses dist = largest + next_largest*3/8 + smallest*3/16
228 fix vm_vec_mag_quick(vms_vector *v)
248 bc = (b>>2) + (c>>3);
250 return a + bc + (bc>>1);
254 //computes an approximation of the distance between two points.
255 //uses dist = largest + next_largest*3/8 + smallest*3/16
256 fix vm_vec_dist_quick(vms_vector *v0,vms_vector *v1)
260 vm_vec_sub(&t,v0,v1);
262 return vm_vec_mag_quick(&t);
265 //normalize a vector. returns mag of source vec
266 fix vm_vec_copy_normalize(vms_vector *dest,vms_vector *src)
273 dest->x = fixdiv(src->x,m);
274 dest->y = fixdiv(src->y,m);
275 dest->z = fixdiv(src->z,m);
281 //normalize a vector. returns mag of source vec
282 fix vm_vec_normalize(vms_vector *v)
284 return vm_vec_copy_normalize(v,v);
288 //normalize a vector. returns mag of source vec. uses approx mag
289 fix vm_vec_copy_normalize_quick(vms_vector *dest,vms_vector *src)
293 m = vm_vec_mag_quick(src);
296 dest->x = fixdiv(src->x,m);
297 dest->y = fixdiv(src->y,m);
298 dest->z = fixdiv(src->z,m);
305 //these routines use an approximation for 1/sqrt
307 //returns approximation of 1/magnitude of a vector
308 fix vm_vec_imag(vms_vector *v)
314 fixmulaccum(&q,v->x,v->x);
315 fixmulaccum(&q,v->y,v->y);
316 fixmulaccum(&q,v->z,v->z);
319 return fix_isqrt(fixquadadjust(&q));
320 else if (q.high >= 0x800000) {
321 return (fix_isqrt(q.high) >> 8);
324 return (fix_isqrt((q.high<<8) + (q.low>>24)) >> 4);
327 //normalize a vector. returns 1/mag of source vec. uses approx 1/mag
328 fix vm_vec_copy_normalize_quick(vms_vector *dest,vms_vector *src)
332 im = vm_vec_imag(src);
334 dest->x = fixmul(src->x,im);
335 dest->y = fixmul(src->y,im);
336 dest->z = fixmul(src->z,im);
343 //normalize a vector. returns 1/mag of source vec. uses approx 1/mag
344 fix vm_vec_normalize_quick(vms_vector *v)
346 return vm_vec_copy_normalize_quick(v,v);
349 //return the normalized direction vector between two points
350 //dest = normalized(end - start). Returns 1/mag of direction vector
351 //NOTE: the order of the parameters matches the vector subtraction
352 fix vm_vec_normalized_dir_quick(vms_vector *dest,vms_vector *end,vms_vector *start)
354 vm_vec_sub(dest,end,start);
356 return vm_vec_normalize_quick(dest);
359 //return the normalized direction vector between two points
360 //dest = normalized(end - start). Returns mag of direction vector
361 //NOTE: the order of the parameters matches the vector subtraction
362 fix vm_vec_normalized_dir(vms_vector *dest,vms_vector *end,vms_vector *start)
364 vm_vec_sub(dest,end,start);
366 return vm_vec_normalize(dest);
369 //computes surface normal from three points. result is normalized
370 //returns ptr to dest
371 //dest CANNOT equal either source
372 vms_vector *vm_vec_normal(vms_vector *dest,vms_vector *p0,vms_vector *p1,vms_vector *p2)
374 vm_vec_perp(dest,p0,p1,p2);
376 vm_vec_normalize(dest);
381 //make sure a vector is reasonably sized to go into a cross product
382 void check_vec(vms_vector *v)
387 check = labs(v->x) | labs(v->y) | labs(v->z);
392 if (check & 0xfffc0000) { //too big
394 while (check & 0xfff00000) {
399 while (check & 0xfffc0000) {
408 else //maybe too small
409 if ((check & 0xffff8000) == 0) { //yep, too small
411 while ((check & 0xfffff000) == 0) {
416 while ((check & 0xffff8000) == 0) {
427 //computes cross product of two vectors.
428 //Note: this magnitude of the resultant vector is the
429 //product of the magnitudes of the two source vectors. This means it is
430 //quite easy for this routine to overflow and underflow. Be careful that
431 //your inputs are ok.
434 vms_vector *vm_vec_crossprod(vms_vector *dest,vms_vector *src0,vms_vector *src1)
437 Assert(dest!=src0 && dest!=src1);
439 d = (double)(src0->y) * (double)(src1->z);
440 d += (double)-(src0->z) * (double)(src1->y);
446 d = (double)(src0->z) * (double)(src1->x);
447 d += (double)-(src0->x) * (double)(src1->z);
453 d = (double)(src0->x) * (double)(src1->y);
454 d += (double)-(src0->y) * (double)(src1->x);
464 vms_vector *vm_vec_crossprod(vms_vector *dest,vms_vector *src0,vms_vector *src1)
468 Assert(dest!=src0 && dest!=src1);
471 fixmulaccum(&q,src0->y,src1->z);
472 fixmulaccum(&q,-src0->z,src1->y);
473 dest->x = fixquadadjust(&q);
476 fixmulaccum(&q,src0->z,src1->x);
477 fixmulaccum(&q,-src0->x,src1->z);
478 dest->y = fixquadadjust(&q);
481 fixmulaccum(&q,src0->x,src1->y);
482 fixmulaccum(&q,-src0->y,src1->x);
483 dest->z = fixquadadjust(&q);
491 //computes non-normalized surface normal from three points.
492 //returns ptr to dest
493 //dest CANNOT equal either source
494 vms_vector *vm_vec_perp(vms_vector *dest,vms_vector *p0,vms_vector *p1,vms_vector *p2)
498 vm_vec_sub(&t0,p1,p0);
499 vm_vec_sub(&t1,p2,p1);
504 return vm_vec_crossprod(dest,&t0,&t1);
508 //computes the delta angle between two vectors.
509 //vectors need not be normalized. if they are, call vm_vec_delta_ang_norm()
510 //the forward vector (third parameter) can be NULL, in which case the absolute
511 //value of the angle in returned. Otherwise the angle around that vector is
513 fixang vm_vec_delta_ang(vms_vector *v0,vms_vector *v1,vms_vector *fvec)
517 vm_vec_copy_normalize(&t0,v0);
518 vm_vec_copy_normalize(&t1,v1);
520 return vm_vec_delta_ang_norm(&t0,&t1,fvec);
523 //computes the delta angle between two normalized vectors.
524 fixang vm_vec_delta_ang_norm(vms_vector *v0,vms_vector *v1,vms_vector *fvec)
528 a = fix_acos(vm_vec_dot(v0,v1));
533 vm_vec_cross(&t,v0,v1);
535 if (vm_vec_dot(&t,fvec) < 0)
542 vms_matrix *sincos_2_matrix(vms_matrix *m,fix sinp,fix cosp,fix sinb,fix cosb,fix sinh,fix cosh)
544 fix sbsh,cbch,cbsh,sbch;
546 sbsh = fixmul(sinb,sinh);
547 cbch = fixmul(cosb,cosh);
548 cbsh = fixmul(cosb,sinh);
549 sbch = fixmul(sinb,cosh);
551 m->rvec.x = cbch + fixmul(sinp,sbsh); //m1
552 m->uvec.z = sbsh + fixmul(sinp,cbch); //m8
554 m->uvec.x = fixmul(sinp,cbsh) - sbch; //m2
555 m->rvec.z = fixmul(sinp,sbch) - cbsh; //m7
557 m->fvec.x = fixmul(sinh,cosp); //m3
558 m->rvec.y = fixmul(sinb,cosp); //m4
559 m->uvec.y = fixmul(cosb,cosp); //m5
560 m->fvec.z = fixmul(cosh,cosp); //m9
562 m->fvec.y = -sinp; //m6
568 //computes a matrix from a set of three angles. returns ptr to matrix
569 vms_matrix *vm_angles_2_matrix(vms_matrix *m,vms_angvec *a)
571 fix sinp,cosp,sinb,cosb,sinh,cosh;
573 fix_sincos(a->p,&sinp,&cosp);
574 fix_sincos(a->b,&sinb,&cosb);
575 fix_sincos(a->h,&sinh,&cosh);
577 return sincos_2_matrix(m,sinp,cosp,sinb,cosb,sinh,cosh);
581 //computes a matrix from a forward vector and an angle
582 vms_matrix *vm_vec_ang_2_matrix(vms_matrix *m,vms_vector *v,fixang a)
584 fix sinb,cosb,sinp,cosp,sinh,cosh;
586 fix_sincos(a,&sinb,&cosb);
589 cosp = fix_sqrt(f1_0 - fixmul(sinp,sinp));
591 sinh = fixdiv(v->x,cosp);
592 cosh = fixdiv(v->z,cosp);
594 return sincos_2_matrix(m,sinp,cosp,sinb,cosb,sinh,cosh);
598 //computes a matrix from one or more vectors. The forward vector is required,
599 //with the other two being optional. If both up & right vectors are passed,
600 //the up vector is used. If only the forward vector is passed, a bank of
602 //returns ptr to matrix
603 vms_matrix *vm_vector_2_matrix(vms_matrix *m,vms_vector *fvec,vms_vector *uvec,vms_vector *rvec)
605 vms_vector *xvec=&m->rvec,*yvec=&m->uvec,*zvec=&m->fvec;
607 Assert(fvec != NULL);
609 if (vm_vec_copy_normalize(zvec,fvec) == 0) {
610 Int3(); //forward vec should not be zero-length
616 if (rvec == NULL) { //just forward vec
621 if (zvec->x==0 && zvec->z==0) { //forward vec is straight up or down
624 m->uvec.z = (zvec->y<0)?f1_0:-f1_0;
626 m->rvec.y = m->rvec.z = m->uvec.x = m->uvec.y = 0;
628 else { //not straight up or down
634 vm_vec_normalize(xvec);
636 vm_vec_crossprod(yvec,zvec,xvec);
641 else { //use right vec
643 if (vm_vec_copy_normalize(xvec,rvec) == 0)
646 vm_vec_crossprod(yvec,zvec,xvec);
648 //normalize new perpendicular vector
649 if (vm_vec_normalize(yvec) == 0)
652 //now recompute right vector, in case it wasn't entirely perpendiclar
653 vm_vec_crossprod(xvec,yvec,zvec);
659 if (vm_vec_copy_normalize(yvec,uvec) == 0)
662 vm_vec_crossprod(xvec,yvec,zvec);
664 //normalize new perpendicular vector
665 if (vm_vec_normalize(xvec) == 0)
668 //now recompute up vector, in case it wasn't entirely perpendiclar
669 vm_vec_crossprod(yvec,zvec,xvec);
677 //quicker version of vm_vector_2_matrix() that takes normalized vectors
678 vms_matrix *vm_vector_2_matrix_norm(vms_matrix *m,vms_vector *fvec,vms_vector *uvec,vms_vector *rvec)
680 vms_vector *xvec=&m->rvec,*yvec=&m->uvec,*zvec=&m->fvec;
682 Assert(fvec != NULL);
686 if (rvec == NULL) { //just forward vec
691 if (zvec->x==0 && zvec->z==0) { //forward vec is straight up or down
694 m->uvec.z = (zvec->y<0)?f1_0:-f1_0;
696 m->rvec.y = m->rvec.z = m->uvec.x = m->uvec.y = 0;
698 else { //not straight up or down
704 vm_vec_normalize(xvec);
706 vm_vec_crossprod(yvec,zvec,xvec);
711 else { //use right vec
713 vm_vec_crossprod(yvec,zvec,xvec);
715 //normalize new perpendicular vector
716 if (vm_vec_normalize(yvec) == 0)
719 //now recompute right vector, in case it wasn't entirely perpendiclar
720 vm_vec_crossprod(xvec,yvec,zvec);
726 vm_vec_crossprod(xvec,yvec,zvec);
728 //normalize new perpendicular vector
729 if (vm_vec_normalize(xvec) == 0)
732 //now recompute up vector, in case it wasn't entirely perpendiclar
733 vm_vec_crossprod(yvec,zvec,xvec);
741 //rotates a vector through a matrix. returns ptr to dest vector
742 //dest CANNOT equal source
743 vms_vector *vm_vec_rotate(vms_vector *dest,vms_vector *src,vms_matrix *m)
747 dest->x = vm_vec_dot(src,&m->rvec);
748 dest->y = vm_vec_dot(src,&m->uvec);
749 dest->z = vm_vec_dot(src,&m->fvec);
755 //transpose a matrix in place. returns ptr to matrix
756 vms_matrix *vm_transpose_matrix(vms_matrix *m)
760 t = m->uvec.x; m->uvec.x = m->rvec.y; m->rvec.y = t;
761 t = m->fvec.x; m->fvec.x = m->rvec.z; m->rvec.z = t;
762 t = m->fvec.y; m->fvec.y = m->uvec.z; m->uvec.z = t;
767 //copy and transpose a matrix. returns ptr to matrix
768 //dest CANNOT equal source. use vm_transpose_matrix() if this is the case
769 vms_matrix *vm_copy_transpose_matrix(vms_matrix *dest,vms_matrix *src)
773 dest->rvec.x = src->rvec.x;
774 dest->rvec.y = src->uvec.x;
775 dest->rvec.z = src->fvec.x;
777 dest->uvec.x = src->rvec.y;
778 dest->uvec.y = src->uvec.y;
779 dest->uvec.z = src->fvec.y;
781 dest->fvec.x = src->rvec.z;
782 dest->fvec.y = src->uvec.z;
783 dest->fvec.z = src->fvec.z;
788 //mulitply 2 matrices, fill in dest. returns ptr to dest
789 //dest CANNOT equal either source
790 vms_matrix *vm_matrix_x_matrix(vms_matrix *dest,vms_matrix *src0,vms_matrix *src1)
792 Assert(dest!=src0 && dest!=src1);
794 dest->rvec.x = vm_vec_dot3(src0->rvec.x,src0->uvec.x,src0->fvec.x, &src1->rvec);
795 dest->uvec.x = vm_vec_dot3(src0->rvec.x,src0->uvec.x,src0->fvec.x, &src1->uvec);
796 dest->fvec.x = vm_vec_dot3(src0->rvec.x,src0->uvec.x,src0->fvec.x, &src1->fvec);
798 dest->rvec.y = vm_vec_dot3(src0->rvec.y,src0->uvec.y,src0->fvec.y, &src1->rvec);
799 dest->uvec.y = vm_vec_dot3(src0->rvec.y,src0->uvec.y,src0->fvec.y, &src1->uvec);
800 dest->fvec.y = vm_vec_dot3(src0->rvec.y,src0->uvec.y,src0->fvec.y, &src1->fvec);
802 dest->rvec.z = vm_vec_dot3(src0->rvec.z,src0->uvec.z,src0->fvec.z, &src1->rvec);
803 dest->uvec.z = vm_vec_dot3(src0->rvec.z,src0->uvec.z,src0->fvec.z, &src1->uvec);
804 dest->fvec.z = vm_vec_dot3(src0->rvec.z,src0->uvec.z,src0->fvec.z, &src1->fvec);
811 //extract angles from a matrix
812 vms_angvec *vm_extract_angles_matrix(vms_angvec *a,vms_matrix *m)
816 if (m->fvec.x==0 && m->fvec.z==0) //zero head
819 a->h = fix_atan2(m->fvec.z,m->fvec.x);
821 fix_sincos(a->h,&sinh,&cosh);
823 if (abs(sinh) > abs(cosh)) //sine is larger, so use it
824 cosp = fixdiv(m->fvec.x,sinh);
825 else //cosine is larger, so use it
826 cosp = fixdiv(m->fvec.z,cosh);
828 if (cosp==0 && m->fvec.y==0)
831 a->p = fix_atan2(cosp,-m->fvec.y);
834 if (cosp == 0) //the cosine of pitch is zero. we're pitched straight up. say no bank
841 sinb = fixdiv(m->rvec.y,cosp);
842 cosb = fixdiv(m->uvec.y,cosp);
844 if (sinb==0 && cosb==0)
847 a->b = fix_atan2(cosb,sinb);
855 //extract heading and pitch from a vector, assuming bank==0
856 vms_angvec *vm_extract_angles_vector_normalized(vms_angvec *a,vms_vector *v)
858 a->b = 0; //always zero bank
860 a->p = fix_asin(-v->y);
862 if (v->x==0 && v->z==0)
865 a->h = fix_atan2(v->z,v->x);
870 //extract heading and pitch from a vector, assuming bank==0
871 vms_angvec *vm_extract_angles_vector(vms_angvec *a,vms_vector *v)
875 if (vm_vec_copy_normalize(&t,v) != 0)
876 vm_extract_angles_vector_normalized(a,&t);
882 //compute the distance from a point to a plane. takes the normalized normal
883 //of the plane (ebx), a point on the plane (edi), and the point to check (esi).
884 //returns distance in eax
885 //distance is signed, so negative dist is on the back of the plane
886 fix vm_dist_to_plane(vms_vector *checkp,vms_vector *norm,vms_vector *planep)
890 vm_vec_sub(&t,checkp,planep);
892 return vm_vec_dot(&t,norm);
896 vms_vector *vm_vec_make(vms_vector *v,fix x,fix y,fix z)
898 v->x=x; v->y=y; v->z=z;