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14 * $Source: /cvs/cvsroot/d2x/maths/vecmat.c,v $
15 * $Revision: 1.1.1.2 $
17 * $Date: 2001-01-19 03:33:42 $
19 * C version of vecmat library
21 * $Log: not supported by cvs2svn $
22 * Revision 1.1.1.1 1999/06/14 22:13:42 donut
23 * Import of d1x 1.37 source.
25 * Revision 1.5 1995/10/30 11:08:16 allender
26 * fix check_vec to return if vector is the NULL vector
28 * Revision 1.4 1995/09/23 09:38:14 allender
29 * removed calls for PPC that are now handled in asm
31 * Revision 1.3 1995/08/31 15:50:24 allender
32 * fixing up of functions for PPC
34 * Revision 1.2 1995/07/05 16:40:21 allender
35 * some vecmat stuff might be using isqrt -- commented out
38 * Revision 1.1 1995/04/17 16:18:02 allender
42 * --- PC RCS Information ---
43 * Revision 1.1 1995/03/08 15:56:50 matt
50 static char rcsid[] = "$Id: vecmat.c,v 1.1.1.2 2001-01-19 03:33:42 bradleyb Exp $";
55 #include <math.h> // for sqrt
64 // DPH: Kludge: this was overflowing a lot, so I made it use the FPU.
65 //scales a vector in place, taking n/d for scale. returns ptr to vector
67 vms_vector *vm_vec_scale2(vms_vector *dest,fix n,fix d)
70 // printf("scale n=%d d=%d\n",n,d);
71 nd = f2fl(n) / f2fl(d);
72 dest->x = fl2f( f2fl(dest->x) * nd);
73 dest->y = fl2f( f2fl(dest->y) * nd);
74 dest->z = fl2f( f2fl(dest->z) * nd);
75 /* dest->x = fixmuldiv(dest->x,n,d);
76 dest->y = fixmuldiv(dest->y,n,d);
77 dest->z = fixmuldiv(dest->z,n,d);*/
83 vms_vector vmd_zero_vector = {0,0,0};
84 vms_matrix vmd_identity_matrix = { { f1_0,0,0 },
88 //adds two vectors, fills in dest, returns ptr to dest
89 //ok for dest to equal either source, but should use vm_vec_add2() if so
90 vms_vector *vm_vec_add(vms_vector *dest,vms_vector *src0,vms_vector *src1)
92 dest->x = src0->x + src1->x;
93 dest->y = src0->y + src1->y;
94 dest->z = src0->z + src1->z;
100 //subs two vectors, fills in dest, returns ptr to dest
101 //ok for dest to equal either source, but should use vm_vec_sub2() if so
102 vms_vector *vm_vec_sub(vms_vector *dest,vms_vector *src0,vms_vector *src1)
104 dest->x = src0->x - src1->x;
105 dest->y = src0->y - src1->y;
106 dest->z = src0->z - src1->z;
111 //adds one vector to another. returns ptr to dest
112 //dest can equal source
113 vms_vector *vm_vec_add2(vms_vector *dest,vms_vector *src)
122 //subs one vector from another, returns ptr to dest
123 //dest can equal source
124 vms_vector *vm_vec_sub2(vms_vector *dest,vms_vector *src)
133 //averages two vectors. returns ptr to dest
134 //dest can equal either source
135 vms_vector *vm_vec_avg(vms_vector *dest,vms_vector *src0,vms_vector *src1)
137 dest->x = (src0->x + src1->x)/2;
138 dest->y = (src0->y + src1->y)/2;
139 dest->z = (src0->z + src1->z)/2;
145 //averages four vectors. returns ptr to dest
146 //dest can equal any source
147 vms_vector *vm_vec_avg4(vms_vector *dest,vms_vector *src0,vms_vector *src1,vms_vector *src2,vms_vector *src3)
149 dest->x = (src0->x + src1->x + src2->x + src3->x)/4;
150 dest->y = (src0->y + src1->y + src2->y + src3->y)/4;
151 dest->z = (src0->z + src1->z + src2->z + src3->z)/4;
157 //scales a vector in place. returns ptr to vector
158 vms_vector *vm_vec_scale(vms_vector *dest,fix s)
160 dest->x = fixmul(dest->x,s);
161 dest->y = fixmul(dest->y,s);
162 dest->z = fixmul(dest->z,s);
167 //scales and copies a vector. returns ptr to dest
168 vms_vector *vm_vec_copy_scale(vms_vector *dest,vms_vector *src,fix s)
170 dest->x = fixmul(src->x,s);
171 dest->y = fixmul(src->y,s);
172 dest->z = fixmul(src->z,s);
177 //scales a vector, adds it to another, and stores in a 3rd vector
178 //dest = src1 + k * src2
179 vms_vector *vm_vec_scale_add(vms_vector *dest,vms_vector *src1,vms_vector *src2,fix k)
181 dest->x = src1->x + fixmul(src2->x,k);
182 dest->y = src1->y + fixmul(src2->y,k);
183 dest->z = src1->z + fixmul(src2->z,k);
188 //scales a vector and adds it to another
190 vms_vector *vm_vec_scale_add2(vms_vector *dest,vms_vector *src,fix k)
192 dest->x += fixmul(src->x,k);
193 dest->y += fixmul(src->y,k);
194 dest->z += fixmul(src->z,k);
199 //scales a vector in place, taking n/d for scale. returns ptr to vector
201 /*vms_vector *vm_vec_scale2(vms_vector *dest,fix n,fix d)
203 dest->x = fixmuldiv(dest->x,n,d);
204 dest->y = fixmuldiv(dest->y,n,d);
205 dest->z = fixmuldiv(dest->z,n,d);
210 fix vm_vec_dotprod(vms_vector *v0,vms_vector *v1)
216 fixmulaccum(&q,v0->x,v1->x);
217 fixmulaccum(&q,v0->y,v1->y);
218 fixmulaccum(&q,v0->z,v1->z);
220 return fixquadadjust(&q);
223 fix vm_vec_dot3(fix x,fix y,fix z,vms_vector *v)
229 fixmulaccum(&q,x,v->x);
230 fixmulaccum(&q,y,v->y);
231 fixmulaccum(&q,z,v->z);
233 return fixquadadjust(&q);
236 //returns magnitude of a vector
237 fix vm_vec_mag(vms_vector *v)
243 fixmulaccum(&q,v->x,v->x);
244 fixmulaccum(&q,v->y,v->y);
245 fixmulaccum(&q,v->z,v->z);
247 return quad_sqrt(q.low,q.high);
250 //computes the distance between two points. (does sub and mag)
251 fix vm_vec_dist(vms_vector *v0,vms_vector *v1)
255 vm_vec_sub(&t,v0,v1);
257 return vm_vec_mag(&t);
261 //computes an approximation of the magnitude of the vector
262 //uses dist = largest + next_largest*3/8 + smallest*3/16
263 fix vm_vec_mag_quick(vms_vector *v)
283 bc = (b>>2) + (c>>3);
285 return a + bc + (bc>>1);
289 //computes an approximation of the distance between two points.
290 //uses dist = largest + next_largest*3/8 + smallest*3/16
291 fix vm_vec_dist_quick(vms_vector *v0,vms_vector *v1)
295 vm_vec_sub(&t,v0,v1);
297 return vm_vec_mag_quick(&t);
300 //normalize a vector. returns mag of source vec
301 fix vm_vec_copy_normalize(vms_vector *dest,vms_vector *src)
308 dest->x = fixdiv(src->x,m);
309 dest->y = fixdiv(src->y,m);
310 dest->z = fixdiv(src->z,m);
316 //normalize a vector. returns mag of source vec
317 fix vm_vec_normalize(vms_vector *v)
319 return vm_vec_copy_normalize(v,v);
323 //normalize a vector. returns mag of source vec. uses approx mag
324 fix vm_vec_copy_normalize_quick(vms_vector *dest,vms_vector *src)
328 m = vm_vec_mag_quick(src);
331 dest->x = fixdiv(src->x,m);
332 dest->y = fixdiv(src->y,m);
333 dest->z = fixdiv(src->z,m);
340 //these routines use an approximation for 1/sqrt
342 //returns approximation of 1/magnitude of a vector
343 fix vm_vec_imag(vms_vector *v)
349 fixmulaccum(&q,v->x,v->x);
350 fixmulaccum(&q,v->y,v->y);
351 fixmulaccum(&q,v->z,v->z);
354 return fix_isqrt(fixquadadjust(&q));
355 else if (q.high >= 0x800000) {
356 return (fix_isqrt(q.high) >> 8);
359 return (fix_isqrt((q.high<<8) + (q.low>>24)) >> 4);
362 //normalize a vector. returns 1/mag of source vec. uses approx 1/mag
363 fix vm_vec_copy_normalize_quick(vms_vector *dest,vms_vector *src)
367 im = vm_vec_imag(src);
369 dest->x = fixmul(src->x,im);
370 dest->y = fixmul(src->y,im);
371 dest->z = fixmul(src->z,im);
378 //normalize a vector. returns 1/mag of source vec. uses approx 1/mag
379 fix vm_vec_normalize_quick(vms_vector *v)
381 return vm_vec_copy_normalize_quick(v,v);
384 //return the normalized direction vector between two points
385 //dest = normalized(end - start). Returns 1/mag of direction vector
386 //NOTE: the order of the parameters matches the vector subtraction
387 fix vm_vec_normalized_dir_quick(vms_vector *dest,vms_vector *end,vms_vector *start)
389 vm_vec_sub(dest,end,start);
391 return vm_vec_normalize_quick(dest);
394 //return the normalized direction vector between two points
395 //dest = normalized(end - start). Returns mag of direction vector
396 //NOTE: the order of the parameters matches the vector subtraction
397 fix vm_vec_normalized_dir(vms_vector *dest,vms_vector *end,vms_vector *start)
399 vm_vec_sub(dest,end,start);
401 return vm_vec_normalize(dest);
404 //computes surface normal from three points. result is normalized
405 //returns ptr to dest
406 //dest CANNOT equal either source
407 vms_vector *vm_vec_normal(vms_vector *dest,vms_vector *p0,vms_vector *p1,vms_vector *p2)
409 vm_vec_perp(dest,p0,p1,p2);
411 vm_vec_normalize(dest);
416 //make sure a vector is reasonably sized to go into a cross product
417 void check_vec(vms_vector *v)
422 check = labs(v->x) | labs(v->y) | labs(v->z);
427 if (check & 0xfffc0000) { //too big
429 while (check & 0xfff00000) {
434 while (check & 0xfffc0000) {
443 else //maybe too small
444 if ((check & 0xffff8000) == 0) { //yep, too small
446 while ((check & 0xfffff000) == 0) {
451 while ((check & 0xffff8000) == 0) {
462 //computes cross product of two vectors.
463 //Note: this magnitude of the resultant vector is the
464 //product of the magnitudes of the two source vectors. This means it is
465 //quite easy for this routine to overflow and underflow. Be careful that
466 //your inputs are ok.
469 vms_vector *vm_vec_crossprod(vms_vector *dest,vms_vector *src0,vms_vector *src1)
472 Assert(dest!=src0 && dest!=src1);
474 d = (double)(src0->y) * (double)(src1->z);
475 d += (double)-(src0->z) * (double)(src1->y);
481 d = (double)(src0->z) * (double)(src1->x);
482 d += (double)-(src0->x) * (double)(src1->z);
488 d = (double)(src0->x) * (double)(src1->y);
489 d += (double)-(src0->y) * (double)(src1->x);
499 vms_vector *vm_vec_crossprod(vms_vector *dest,vms_vector *src0,vms_vector *src1)
503 Assert(dest!=src0 && dest!=src1);
506 fixmulaccum(&q,src0->y,src1->z);
507 fixmulaccum(&q,-src0->z,src1->y);
508 dest->x = fixquadadjust(&q);
511 fixmulaccum(&q,src0->z,src1->x);
512 fixmulaccum(&q,-src0->x,src1->z);
513 dest->y = fixquadadjust(&q);
516 fixmulaccum(&q,src0->x,src1->y);
517 fixmulaccum(&q,-src0->y,src1->x);
518 dest->z = fixquadadjust(&q);
526 //computes non-normalized surface normal from three points.
527 //returns ptr to dest
528 //dest CANNOT equal either source
529 vms_vector *vm_vec_perp(vms_vector *dest,vms_vector *p0,vms_vector *p1,vms_vector *p2)
533 vm_vec_sub(&t0,p1,p0);
534 vm_vec_sub(&t1,p2,p1);
539 return vm_vec_crossprod(dest,&t0,&t1);
543 //computes the delta angle between two vectors.
544 //vectors need not be normalized. if they are, call vm_vec_delta_ang_norm()
545 //the forward vector (third parameter) can be NULL, in which case the absolute
546 //value of the angle in returned. Otherwise the angle around that vector is
548 fixang vm_vec_delta_ang(vms_vector *v0,vms_vector *v1,vms_vector *fvec)
552 vm_vec_copy_normalize(&t0,v0);
553 vm_vec_copy_normalize(&t1,v1);
555 return vm_vec_delta_ang_norm(&t0,&t1,fvec);
558 //computes the delta angle between two normalized vectors.
559 fixang vm_vec_delta_ang_norm(vms_vector *v0,vms_vector *v1,vms_vector *fvec)
563 a = fix_acos(vm_vec_dot(v0,v1));
568 vm_vec_cross(&t,v0,v1);
570 if (vm_vec_dot(&t,fvec) < 0)
577 vms_matrix *sincos_2_matrix(vms_matrix *m,fix sinp,fix cosp,fix sinb,fix cosb,fix sinh,fix cosh)
579 fix sbsh,cbch,cbsh,sbch;
581 sbsh = fixmul(sinb,sinh);
582 cbch = fixmul(cosb,cosh);
583 cbsh = fixmul(cosb,sinh);
584 sbch = fixmul(sinb,cosh);
586 m->rvec.x = cbch + fixmul(sinp,sbsh); //m1
587 m->uvec.z = sbsh + fixmul(sinp,cbch); //m8
589 m->uvec.x = fixmul(sinp,cbsh) - sbch; //m2
590 m->rvec.z = fixmul(sinp,sbch) - cbsh; //m7
592 m->fvec.x = fixmul(sinh,cosp); //m3
593 m->rvec.y = fixmul(sinb,cosp); //m4
594 m->uvec.y = fixmul(cosb,cosp); //m5
595 m->fvec.z = fixmul(cosh,cosp); //m9
597 m->fvec.y = -sinp; //m6
603 //computes a matrix from a set of three angles. returns ptr to matrix
604 vms_matrix *vm_angles_2_matrix(vms_matrix *m,vms_angvec *a)
606 fix sinp,cosp,sinb,cosb,sinh,cosh;
608 fix_sincos(a->p,&sinp,&cosp);
609 fix_sincos(a->b,&sinb,&cosb);
610 fix_sincos(a->h,&sinh,&cosh);
612 return sincos_2_matrix(m,sinp,cosp,sinb,cosb,sinh,cosh);
616 //computes a matrix from a forward vector and an angle
617 vms_matrix *vm_vec_ang_2_matrix(vms_matrix *m,vms_vector *v,fixang a)
619 fix sinb,cosb,sinp,cosp,sinh,cosh;
621 fix_sincos(a,&sinb,&cosb);
624 cosp = fix_sqrt(f1_0 - fixmul(sinp,sinp));
626 sinh = fixdiv(v->x,cosp);
627 cosh = fixdiv(v->z,cosp);
629 return sincos_2_matrix(m,sinp,cosp,sinb,cosb,sinh,cosh);
633 //computes a matrix from one or more vectors. The forward vector is required,
634 //with the other two being optional. If both up & right vectors are passed,
635 //the up vector is used. If only the forward vector is passed, a bank of
637 //returns ptr to matrix
638 vms_matrix *vm_vector_2_matrix(vms_matrix *m,vms_vector *fvec,vms_vector *uvec,vms_vector *rvec)
640 vms_vector *xvec=&m->rvec,*yvec=&m->uvec,*zvec=&m->fvec;
642 Assert(fvec != NULL);
644 if (vm_vec_copy_normalize(zvec,fvec) == 0) {
645 Int3(); //forward vec should not be zero-length
651 if (rvec == NULL) { //just forward vec
656 if (zvec->x==0 && zvec->z==0) { //forward vec is straight up or down
659 m->uvec.z = (zvec->y<0)?f1_0:-f1_0;
661 m->rvec.y = m->rvec.z = m->uvec.x = m->uvec.y = 0;
663 else { //not straight up or down
669 vm_vec_normalize(xvec);
671 vm_vec_crossprod(yvec,zvec,xvec);
676 else { //use right vec
678 if (vm_vec_copy_normalize(xvec,rvec) == 0)
681 vm_vec_crossprod(yvec,zvec,xvec);
683 //normalize new perpendicular vector
684 if (vm_vec_normalize(yvec) == 0)
687 //now recompute right vector, in case it wasn't entirely perpendiclar
688 vm_vec_crossprod(xvec,yvec,zvec);
694 if (vm_vec_copy_normalize(yvec,uvec) == 0)
697 vm_vec_crossprod(xvec,yvec,zvec);
699 //normalize new perpendicular vector
700 if (vm_vec_normalize(xvec) == 0)
703 //now recompute up vector, in case it wasn't entirely perpendiclar
704 vm_vec_crossprod(yvec,zvec,xvec);
712 //quicker version of vm_vector_2_matrix() that takes normalized vectors
713 vms_matrix *vm_vector_2_matrix_norm(vms_matrix *m,vms_vector *fvec,vms_vector *uvec,vms_vector *rvec)
715 vms_vector *xvec=&m->rvec,*yvec=&m->uvec,*zvec=&m->fvec;
717 Assert(fvec != NULL);
721 if (rvec == NULL) { //just forward vec
726 if (zvec->x==0 && zvec->z==0) { //forward vec is straight up or down
729 m->uvec.z = (zvec->y<0)?f1_0:-f1_0;
731 m->rvec.y = m->rvec.z = m->uvec.x = m->uvec.y = 0;
733 else { //not straight up or down
739 vm_vec_normalize(xvec);
741 vm_vec_crossprod(yvec,zvec,xvec);
746 else { //use right vec
748 vm_vec_crossprod(yvec,zvec,xvec);
750 //normalize new perpendicular vector
751 if (vm_vec_normalize(yvec) == 0)
754 //now recompute right vector, in case it wasn't entirely perpendiclar
755 vm_vec_crossprod(xvec,yvec,zvec);
761 vm_vec_crossprod(xvec,yvec,zvec);
763 //normalize new perpendicular vector
764 if (vm_vec_normalize(xvec) == 0)
767 //now recompute up vector, in case it wasn't entirely perpendiclar
768 vm_vec_crossprod(yvec,zvec,xvec);
776 //rotates a vector through a matrix. returns ptr to dest vector
777 //dest CANNOT equal source
778 vms_vector *vm_vec_rotate(vms_vector *dest,vms_vector *src,vms_matrix *m)
782 dest->x = vm_vec_dot(src,&m->rvec);
783 dest->y = vm_vec_dot(src,&m->uvec);
784 dest->z = vm_vec_dot(src,&m->fvec);
790 //transpose a matrix in place. returns ptr to matrix
791 vms_matrix *vm_transpose_matrix(vms_matrix *m)
795 t = m->uvec.x; m->uvec.x = m->rvec.y; m->rvec.y = t;
796 t = m->fvec.x; m->fvec.x = m->rvec.z; m->rvec.z = t;
797 t = m->fvec.y; m->fvec.y = m->uvec.z; m->uvec.z = t;
802 //copy and transpose a matrix. returns ptr to matrix
803 //dest CANNOT equal source. use vm_transpose_matrix() if this is the case
804 vms_matrix *vm_copy_transpose_matrix(vms_matrix *dest,vms_matrix *src)
808 dest->rvec.x = src->rvec.x;
809 dest->rvec.y = src->uvec.x;
810 dest->rvec.z = src->fvec.x;
812 dest->uvec.x = src->rvec.y;
813 dest->uvec.y = src->uvec.y;
814 dest->uvec.z = src->fvec.y;
816 dest->fvec.x = src->rvec.z;
817 dest->fvec.y = src->uvec.z;
818 dest->fvec.z = src->fvec.z;
823 //mulitply 2 matrices, fill in dest. returns ptr to dest
824 //dest CANNOT equal either source
825 vms_matrix *vm_matrix_x_matrix(vms_matrix *dest,vms_matrix *src0,vms_matrix *src1)
827 Assert(dest!=src0 && dest!=src1);
829 dest->rvec.x = vm_vec_dot3(src0->rvec.x,src0->uvec.x,src0->fvec.x, &src1->rvec);
830 dest->uvec.x = vm_vec_dot3(src0->rvec.x,src0->uvec.x,src0->fvec.x, &src1->uvec);
831 dest->fvec.x = vm_vec_dot3(src0->rvec.x,src0->uvec.x,src0->fvec.x, &src1->fvec);
833 dest->rvec.y = vm_vec_dot3(src0->rvec.y,src0->uvec.y,src0->fvec.y, &src1->rvec);
834 dest->uvec.y = vm_vec_dot3(src0->rvec.y,src0->uvec.y,src0->fvec.y, &src1->uvec);
835 dest->fvec.y = vm_vec_dot3(src0->rvec.y,src0->uvec.y,src0->fvec.y, &src1->fvec);
837 dest->rvec.z = vm_vec_dot3(src0->rvec.z,src0->uvec.z,src0->fvec.z, &src1->rvec);
838 dest->uvec.z = vm_vec_dot3(src0->rvec.z,src0->uvec.z,src0->fvec.z, &src1->uvec);
839 dest->fvec.z = vm_vec_dot3(src0->rvec.z,src0->uvec.z,src0->fvec.z, &src1->fvec);
846 //extract angles from a matrix
847 vms_angvec *vm_extract_angles_matrix(vms_angvec *a,vms_matrix *m)
851 if (m->fvec.x==0 && m->fvec.z==0) //zero head
854 a->h = fix_atan2(m->fvec.z,m->fvec.x);
856 fix_sincos(a->h,&sinh,&cosh);
858 if (abs(sinh) > abs(cosh)) //sine is larger, so use it
859 cosp = fixdiv(m->fvec.x,sinh);
860 else //cosine is larger, so use it
861 cosp = fixdiv(m->fvec.z,cosh);
863 if (cosp==0 && m->fvec.y==0)
866 a->p = fix_atan2(cosp,-m->fvec.y);
869 if (cosp == 0) //the cosine of pitch is zero. we're pitched straight up. say no bank
876 sinb = fixdiv(m->rvec.y,cosp);
877 cosb = fixdiv(m->uvec.y,cosp);
879 if (sinb==0 && cosb==0)
882 a->b = fix_atan2(cosb,sinb);
890 //extract heading and pitch from a vector, assuming bank==0
891 vms_angvec *vm_extract_angles_vector_normalized(vms_angvec *a,vms_vector *v)
893 a->b = 0; //always zero bank
895 a->p = fix_asin(-v->y);
897 if (v->x==0 && v->z==0)
900 a->h = fix_atan2(v->z,v->x);
905 //extract heading and pitch from a vector, assuming bank==0
906 vms_angvec *vm_extract_angles_vector(vms_angvec *a,vms_vector *v)
910 if (vm_vec_copy_normalize(&t,v) != 0)
911 vm_extract_angles_vector_normalized(a,&t);
917 //compute the distance from a point to a plane. takes the normalized normal
918 //of the plane (ebx), a point on the plane (edi), and the point to check (esi).
919 //returns distance in eax
920 //distance is signed, so negative dist is on the back of the plane
921 fix vm_dist_to_plane(vms_vector *checkp,vms_vector *norm,vms_vector *planep)
925 vm_vec_sub(&t,checkp,planep);
927 return vm_vec_dot(&t,norm);
931 vms_vector *vm_vec_make(vms_vector *v,fix x,fix y,fix z) {
932 v->x=x; v->y=y; v->z=z;