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14 * $Source: /cvs/cvsroot/d2x/maths/vecmat.c,v $
17 * $Date: 2002-10-28 19:49:15 $
19 * C version of vecmat library
21 * $Log: not supported by cvs2svn $
22 * Revision 1.3 2001/10/31 07:41:54 bradleyb
25 * Revision 1.2 2001/01/31 15:18:04 bradleyb
26 * Makefile and conf.h fixes
28 * Revision 1.1.1.2 2001/01/19 03:33:42 bradleyb
29 * Import of d2x-0.0.9-pre1
31 * Revision 1.1.1.1 1999/06/14 22:13:42 donut
32 * Import of d1x 1.37 source.
34 * Revision 1.5 1995/10/30 11:08:16 allender
35 * fix check_vec to return if vector is the NULL vector
37 * Revision 1.4 1995/09/23 09:38:14 allender
38 * removed calls for PPC that are now handled in asm
40 * Revision 1.3 1995/08/31 15:50:24 allender
41 * fixing up of functions for PPC
43 * Revision 1.2 1995/07/05 16:40:21 allender
44 * some vecmat stuff might be using isqrt -- commented out
47 * Revision 1.1 1995/04/17 16:18:02 allender
51 * --- PC RCS Information ---
52 * Revision 1.1 1995/03/08 15:56:50 matt
63 static char rcsid[] = "$Id: vecmat.c,v 1.4 2002-10-28 19:49:15 btb Exp $";
67 #include <math.h> // for sqrt
76 vms_vector vmd_zero_vector = {0,0,0};
77 vms_matrix vmd_identity_matrix = { { f1_0,0,0 },
81 //adds two vectors, fills in dest, returns ptr to dest
82 //ok for dest to equal either source, but should use vm_vec_add2() if so
83 vms_vector *vm_vec_add(vms_vector *dest,vms_vector *src0,vms_vector *src1)
85 dest->x = src0->x + src1->x;
86 dest->y = src0->y + src1->y;
87 dest->z = src0->z + src1->z;
93 //subs two vectors, fills in dest, returns ptr to dest
94 //ok for dest to equal either source, but should use vm_vec_sub2() if so
95 vms_vector *vm_vec_sub(vms_vector *dest,vms_vector *src0,vms_vector *src1)
97 dest->x = src0->x - src1->x;
98 dest->y = src0->y - src1->y;
99 dest->z = src0->z - src1->z;
104 //adds one vector to another. returns ptr to dest
105 //dest can equal source
106 vms_vector *vm_vec_add2(vms_vector *dest,vms_vector *src)
115 //subs one vector from another, returns ptr to dest
116 //dest can equal source
117 vms_vector *vm_vec_sub2(vms_vector *dest,vms_vector *src)
126 //averages two vectors. returns ptr to dest
127 //dest can equal either source
128 vms_vector *vm_vec_avg(vms_vector *dest,vms_vector *src0,vms_vector *src1)
130 dest->x = (src0->x + src1->x)/2;
131 dest->y = (src0->y + src1->y)/2;
132 dest->z = (src0->z + src1->z)/2;
138 //averages four vectors. returns ptr to dest
139 //dest can equal any source
140 vms_vector *vm_vec_avg4(vms_vector *dest,vms_vector *src0,vms_vector *src1,vms_vector *src2,vms_vector *src3)
142 dest->x = (src0->x + src1->x + src2->x + src3->x)/4;
143 dest->y = (src0->y + src1->y + src2->y + src3->y)/4;
144 dest->z = (src0->z + src1->z + src2->z + src3->z)/4;
150 //scales a vector in place. returns ptr to vector
151 vms_vector *vm_vec_scale(vms_vector *dest,fix s)
153 dest->x = fixmul(dest->x,s);
154 dest->y = fixmul(dest->y,s);
155 dest->z = fixmul(dest->z,s);
160 //scales and copies a vector. returns ptr to dest
161 vms_vector *vm_vec_copy_scale(vms_vector *dest,vms_vector *src,fix s)
163 dest->x = fixmul(src->x,s);
164 dest->y = fixmul(src->y,s);
165 dest->z = fixmul(src->z,s);
170 //scales a vector, adds it to another, and stores in a 3rd vector
171 //dest = src1 + k * src2
172 vms_vector *vm_vec_scale_add(vms_vector *dest,vms_vector *src1,vms_vector *src2,fix k)
174 dest->x = src1->x + fixmul(src2->x,k);
175 dest->y = src1->y + fixmul(src2->y,k);
176 dest->z = src1->z + fixmul(src2->z,k);
181 //scales a vector and adds it to another
183 vms_vector *vm_vec_scale_add2(vms_vector *dest,vms_vector *src,fix k)
185 dest->x += fixmul(src->x,k);
186 dest->y += fixmul(src->y,k);
187 dest->z += fixmul(src->z,k);
192 //scales a vector in place, taking n/d for scale. returns ptr to vector
194 vms_vector *vm_vec_scale2(vms_vector *dest,fix n,fix d)
196 #if 1 // DPH: Kludge: this was overflowing a lot, so I made it use the FPU.
198 // printf("scale n=%d d=%d\n",n,d);
199 nd = f2fl(n) / f2fl(d);
200 dest->x = fl2f( f2fl(dest->x) * nd);
201 dest->y = fl2f( f2fl(dest->y) * nd);
202 dest->z = fl2f( f2fl(dest->z) * nd);
204 dest->x = fixmuldiv(dest->x,n,d);
205 dest->y = fixmuldiv(dest->y,n,d);
206 dest->z = fixmuldiv(dest->z,n,d);
212 fix vm_vec_dotprod(vms_vector *v0,vms_vector *v1)
218 fixmulaccum(&q,v0->x,v1->x);
219 fixmulaccum(&q,v0->y,v1->y);
220 fixmulaccum(&q,v0->z,v1->z);
222 return fixquadadjust(&q);
225 fix vm_vec_dot3(fix x,fix y,fix z,vms_vector *v)
231 fixmulaccum(&q,x,v->x);
232 fixmulaccum(&q,y,v->y);
233 fixmulaccum(&q,z,v->z);
235 return fixquadadjust(&q);
238 //returns magnitude of a vector
239 fix vm_vec_mag(vms_vector *v)
245 fixmulaccum(&q,v->x,v->x);
246 fixmulaccum(&q,v->y,v->y);
247 fixmulaccum(&q,v->z,v->z);
249 return quad_sqrt(q.low,q.high);
252 //computes the distance between two points. (does sub and mag)
253 fix vm_vec_dist(vms_vector *v0,vms_vector *v1)
257 vm_vec_sub(&t,v0,v1);
259 return vm_vec_mag(&t);
263 //computes an approximation of the magnitude of the vector
264 //uses dist = largest + next_largest*3/8 + smallest*3/16
265 fix vm_vec_mag_quick(vms_vector *v)
285 bc = (b>>2) + (c>>3);
287 return a + bc + (bc>>1);
291 //computes an approximation of the distance between two points.
292 //uses dist = largest + next_largest*3/8 + smallest*3/16
293 fix vm_vec_dist_quick(vms_vector *v0,vms_vector *v1)
297 vm_vec_sub(&t,v0,v1);
299 return vm_vec_mag_quick(&t);
302 //normalize a vector. returns mag of source vec
303 fix vm_vec_copy_normalize(vms_vector *dest,vms_vector *src)
310 dest->x = fixdiv(src->x,m);
311 dest->y = fixdiv(src->y,m);
312 dest->z = fixdiv(src->z,m);
318 //normalize a vector. returns mag of source vec
319 fix vm_vec_normalize(vms_vector *v)
321 return vm_vec_copy_normalize(v,v);
325 //normalize a vector. returns mag of source vec. uses approx mag
326 fix vm_vec_copy_normalize_quick(vms_vector *dest,vms_vector *src)
330 m = vm_vec_mag_quick(src);
333 dest->x = fixdiv(src->x,m);
334 dest->y = fixdiv(src->y,m);
335 dest->z = fixdiv(src->z,m);
342 //these routines use an approximation for 1/sqrt
344 //returns approximation of 1/magnitude of a vector
345 fix vm_vec_imag(vms_vector *v)
351 fixmulaccum(&q,v->x,v->x);
352 fixmulaccum(&q,v->y,v->y);
353 fixmulaccum(&q,v->z,v->z);
356 return fix_isqrt(fixquadadjust(&q));
357 else if (q.high >= 0x800000) {
358 return (fix_isqrt(q.high) >> 8);
361 return (fix_isqrt((q.high<<8) + (q.low>>24)) >> 4);
364 //normalize a vector. returns 1/mag of source vec. uses approx 1/mag
365 fix vm_vec_copy_normalize_quick(vms_vector *dest,vms_vector *src)
369 im = vm_vec_imag(src);
371 dest->x = fixmul(src->x,im);
372 dest->y = fixmul(src->y,im);
373 dest->z = fixmul(src->z,im);
380 //normalize a vector. returns 1/mag of source vec. uses approx 1/mag
381 fix vm_vec_normalize_quick(vms_vector *v)
383 return vm_vec_copy_normalize_quick(v,v);
386 //return the normalized direction vector between two points
387 //dest = normalized(end - start). Returns 1/mag of direction vector
388 //NOTE: the order of the parameters matches the vector subtraction
389 fix vm_vec_normalized_dir_quick(vms_vector *dest,vms_vector *end,vms_vector *start)
391 vm_vec_sub(dest,end,start);
393 return vm_vec_normalize_quick(dest);
396 //return the normalized direction vector between two points
397 //dest = normalized(end - start). Returns mag of direction vector
398 //NOTE: the order of the parameters matches the vector subtraction
399 fix vm_vec_normalized_dir(vms_vector *dest,vms_vector *end,vms_vector *start)
401 vm_vec_sub(dest,end,start);
403 return vm_vec_normalize(dest);
406 //computes surface normal from three points. result is normalized
407 //returns ptr to dest
408 //dest CANNOT equal either source
409 vms_vector *vm_vec_normal(vms_vector *dest,vms_vector *p0,vms_vector *p1,vms_vector *p2)
411 vm_vec_perp(dest,p0,p1,p2);
413 vm_vec_normalize(dest);
418 //make sure a vector is reasonably sized to go into a cross product
419 void check_vec(vms_vector *v)
424 check = labs(v->x) | labs(v->y) | labs(v->z);
429 if (check & 0xfffc0000) { //too big
431 while (check & 0xfff00000) {
436 while (check & 0xfffc0000) {
445 else //maybe too small
446 if ((check & 0xffff8000) == 0) { //yep, too small
448 while ((check & 0xfffff000) == 0) {
453 while ((check & 0xffff8000) == 0) {
464 //computes cross product of two vectors.
465 //Note: this magnitude of the resultant vector is the
466 //product of the magnitudes of the two source vectors. This means it is
467 //quite easy for this routine to overflow and underflow. Be careful that
468 //your inputs are ok.
471 vms_vector *vm_vec_crossprod(vms_vector *dest,vms_vector *src0,vms_vector *src1)
474 Assert(dest!=src0 && dest!=src1);
476 d = (double)(src0->y) * (double)(src1->z);
477 d += (double)-(src0->z) * (double)(src1->y);
483 d = (double)(src0->z) * (double)(src1->x);
484 d += (double)-(src0->x) * (double)(src1->z);
490 d = (double)(src0->x) * (double)(src1->y);
491 d += (double)-(src0->y) * (double)(src1->x);
501 vms_vector *vm_vec_crossprod(vms_vector *dest,vms_vector *src0,vms_vector *src1)
505 Assert(dest!=src0 && dest!=src1);
508 fixmulaccum(&q,src0->y,src1->z);
509 fixmulaccum(&q,-src0->z,src1->y);
510 dest->x = fixquadadjust(&q);
513 fixmulaccum(&q,src0->z,src1->x);
514 fixmulaccum(&q,-src0->x,src1->z);
515 dest->y = fixquadadjust(&q);
518 fixmulaccum(&q,src0->x,src1->y);
519 fixmulaccum(&q,-src0->y,src1->x);
520 dest->z = fixquadadjust(&q);
528 //computes non-normalized surface normal from three points.
529 //returns ptr to dest
530 //dest CANNOT equal either source
531 vms_vector *vm_vec_perp(vms_vector *dest,vms_vector *p0,vms_vector *p1,vms_vector *p2)
535 vm_vec_sub(&t0,p1,p0);
536 vm_vec_sub(&t1,p2,p1);
541 return vm_vec_crossprod(dest,&t0,&t1);
545 //computes the delta angle between two vectors.
546 //vectors need not be normalized. if they are, call vm_vec_delta_ang_norm()
547 //the forward vector (third parameter) can be NULL, in which case the absolute
548 //value of the angle in returned. Otherwise the angle around that vector is
550 fixang vm_vec_delta_ang(vms_vector *v0,vms_vector *v1,vms_vector *fvec)
554 vm_vec_copy_normalize(&t0,v0);
555 vm_vec_copy_normalize(&t1,v1);
557 return vm_vec_delta_ang_norm(&t0,&t1,fvec);
560 //computes the delta angle between two normalized vectors.
561 fixang vm_vec_delta_ang_norm(vms_vector *v0,vms_vector *v1,vms_vector *fvec)
565 a = fix_acos(vm_vec_dot(v0,v1));
570 vm_vec_cross(&t,v0,v1);
572 if (vm_vec_dot(&t,fvec) < 0)
579 vms_matrix *sincos_2_matrix(vms_matrix *m,fix sinp,fix cosp,fix sinb,fix cosb,fix sinh,fix cosh)
581 fix sbsh,cbch,cbsh,sbch;
583 sbsh = fixmul(sinb,sinh);
584 cbch = fixmul(cosb,cosh);
585 cbsh = fixmul(cosb,sinh);
586 sbch = fixmul(sinb,cosh);
588 m->rvec.x = cbch + fixmul(sinp,sbsh); //m1
589 m->uvec.z = sbsh + fixmul(sinp,cbch); //m8
591 m->uvec.x = fixmul(sinp,cbsh) - sbch; //m2
592 m->rvec.z = fixmul(sinp,sbch) - cbsh; //m7
594 m->fvec.x = fixmul(sinh,cosp); //m3
595 m->rvec.y = fixmul(sinb,cosp); //m4
596 m->uvec.y = fixmul(cosb,cosp); //m5
597 m->fvec.z = fixmul(cosh,cosp); //m9
599 m->fvec.y = -sinp; //m6
605 //computes a matrix from a set of three angles. returns ptr to matrix
606 vms_matrix *vm_angles_2_matrix(vms_matrix *m,vms_angvec *a)
608 fix sinp,cosp,sinb,cosb,sinh,cosh;
610 fix_sincos(a->p,&sinp,&cosp);
611 fix_sincos(a->b,&sinb,&cosb);
612 fix_sincos(a->h,&sinh,&cosh);
614 return sincos_2_matrix(m,sinp,cosp,sinb,cosb,sinh,cosh);
618 //computes a matrix from a forward vector and an angle
619 vms_matrix *vm_vec_ang_2_matrix(vms_matrix *m,vms_vector *v,fixang a)
621 fix sinb,cosb,sinp,cosp,sinh,cosh;
623 fix_sincos(a,&sinb,&cosb);
626 cosp = fix_sqrt(f1_0 - fixmul(sinp,sinp));
628 sinh = fixdiv(v->x,cosp);
629 cosh = fixdiv(v->z,cosp);
631 return sincos_2_matrix(m,sinp,cosp,sinb,cosb,sinh,cosh);
635 //computes a matrix from one or more vectors. The forward vector is required,
636 //with the other two being optional. If both up & right vectors are passed,
637 //the up vector is used. If only the forward vector is passed, a bank of
639 //returns ptr to matrix
640 vms_matrix *vm_vector_2_matrix(vms_matrix *m,vms_vector *fvec,vms_vector *uvec,vms_vector *rvec)
642 vms_vector *xvec=&m->rvec,*yvec=&m->uvec,*zvec=&m->fvec;
644 Assert(fvec != NULL);
646 if (vm_vec_copy_normalize(zvec,fvec) == 0) {
647 Int3(); //forward vec should not be zero-length
653 if (rvec == NULL) { //just forward vec
658 if (zvec->x==0 && zvec->z==0) { //forward vec is straight up or down
661 m->uvec.z = (zvec->y<0)?f1_0:-f1_0;
663 m->rvec.y = m->rvec.z = m->uvec.x = m->uvec.y = 0;
665 else { //not straight up or down
671 vm_vec_normalize(xvec);
673 vm_vec_crossprod(yvec,zvec,xvec);
678 else { //use right vec
680 if (vm_vec_copy_normalize(xvec,rvec) == 0)
683 vm_vec_crossprod(yvec,zvec,xvec);
685 //normalize new perpendicular vector
686 if (vm_vec_normalize(yvec) == 0)
689 //now recompute right vector, in case it wasn't entirely perpendiclar
690 vm_vec_crossprod(xvec,yvec,zvec);
696 if (vm_vec_copy_normalize(yvec,uvec) == 0)
699 vm_vec_crossprod(xvec,yvec,zvec);
701 //normalize new perpendicular vector
702 if (vm_vec_normalize(xvec) == 0)
705 //now recompute up vector, in case it wasn't entirely perpendiclar
706 vm_vec_crossprod(yvec,zvec,xvec);
714 //quicker version of vm_vector_2_matrix() that takes normalized vectors
715 vms_matrix *vm_vector_2_matrix_norm(vms_matrix *m,vms_vector *fvec,vms_vector *uvec,vms_vector *rvec)
717 vms_vector *xvec=&m->rvec,*yvec=&m->uvec,*zvec=&m->fvec;
719 Assert(fvec != NULL);
723 if (rvec == NULL) { //just forward vec
728 if (zvec->x==0 && zvec->z==0) { //forward vec is straight up or down
731 m->uvec.z = (zvec->y<0)?f1_0:-f1_0;
733 m->rvec.y = m->rvec.z = m->uvec.x = m->uvec.y = 0;
735 else { //not straight up or down
741 vm_vec_normalize(xvec);
743 vm_vec_crossprod(yvec,zvec,xvec);
748 else { //use right vec
750 vm_vec_crossprod(yvec,zvec,xvec);
752 //normalize new perpendicular vector
753 if (vm_vec_normalize(yvec) == 0)
756 //now recompute right vector, in case it wasn't entirely perpendiclar
757 vm_vec_crossprod(xvec,yvec,zvec);
763 vm_vec_crossprod(xvec,yvec,zvec);
765 //normalize new perpendicular vector
766 if (vm_vec_normalize(xvec) == 0)
769 //now recompute up vector, in case it wasn't entirely perpendiclar
770 vm_vec_crossprod(yvec,zvec,xvec);
778 //rotates a vector through a matrix. returns ptr to dest vector
779 //dest CANNOT equal source
780 vms_vector *vm_vec_rotate(vms_vector *dest,vms_vector *src,vms_matrix *m)
784 dest->x = vm_vec_dot(src,&m->rvec);
785 dest->y = vm_vec_dot(src,&m->uvec);
786 dest->z = vm_vec_dot(src,&m->fvec);
792 //transpose a matrix in place. returns ptr to matrix
793 vms_matrix *vm_transpose_matrix(vms_matrix *m)
797 t = m->uvec.x; m->uvec.x = m->rvec.y; m->rvec.y = t;
798 t = m->fvec.x; m->fvec.x = m->rvec.z; m->rvec.z = t;
799 t = m->fvec.y; m->fvec.y = m->uvec.z; m->uvec.z = t;
804 //copy and transpose a matrix. returns ptr to matrix
805 //dest CANNOT equal source. use vm_transpose_matrix() if this is the case
806 vms_matrix *vm_copy_transpose_matrix(vms_matrix *dest,vms_matrix *src)
810 dest->rvec.x = src->rvec.x;
811 dest->rvec.y = src->uvec.x;
812 dest->rvec.z = src->fvec.x;
814 dest->uvec.x = src->rvec.y;
815 dest->uvec.y = src->uvec.y;
816 dest->uvec.z = src->fvec.y;
818 dest->fvec.x = src->rvec.z;
819 dest->fvec.y = src->uvec.z;
820 dest->fvec.z = src->fvec.z;
825 //mulitply 2 matrices, fill in dest. returns ptr to dest
826 //dest CANNOT equal either source
827 vms_matrix *vm_matrix_x_matrix(vms_matrix *dest,vms_matrix *src0,vms_matrix *src1)
829 Assert(dest!=src0 && dest!=src1);
831 dest->rvec.x = vm_vec_dot3(src0->rvec.x,src0->uvec.x,src0->fvec.x, &src1->rvec);
832 dest->uvec.x = vm_vec_dot3(src0->rvec.x,src0->uvec.x,src0->fvec.x, &src1->uvec);
833 dest->fvec.x = vm_vec_dot3(src0->rvec.x,src0->uvec.x,src0->fvec.x, &src1->fvec);
835 dest->rvec.y = vm_vec_dot3(src0->rvec.y,src0->uvec.y,src0->fvec.y, &src1->rvec);
836 dest->uvec.y = vm_vec_dot3(src0->rvec.y,src0->uvec.y,src0->fvec.y, &src1->uvec);
837 dest->fvec.y = vm_vec_dot3(src0->rvec.y,src0->uvec.y,src0->fvec.y, &src1->fvec);
839 dest->rvec.z = vm_vec_dot3(src0->rvec.z,src0->uvec.z,src0->fvec.z, &src1->rvec);
840 dest->uvec.z = vm_vec_dot3(src0->rvec.z,src0->uvec.z,src0->fvec.z, &src1->uvec);
841 dest->fvec.z = vm_vec_dot3(src0->rvec.z,src0->uvec.z,src0->fvec.z, &src1->fvec);
848 //extract angles from a matrix
849 vms_angvec *vm_extract_angles_matrix(vms_angvec *a,vms_matrix *m)
853 if (m->fvec.x==0 && m->fvec.z==0) //zero head
856 a->h = fix_atan2(m->fvec.z,m->fvec.x);
858 fix_sincos(a->h,&sinh,&cosh);
860 if (abs(sinh) > abs(cosh)) //sine is larger, so use it
861 cosp = fixdiv(m->fvec.x,sinh);
862 else //cosine is larger, so use it
863 cosp = fixdiv(m->fvec.z,cosh);
865 if (cosp==0 && m->fvec.y==0)
868 a->p = fix_atan2(cosp,-m->fvec.y);
871 if (cosp == 0) //the cosine of pitch is zero. we're pitched straight up. say no bank
878 sinb = fixdiv(m->rvec.y,cosp);
879 cosb = fixdiv(m->uvec.y,cosp);
881 if (sinb==0 && cosb==0)
884 a->b = fix_atan2(cosb,sinb);
892 //extract heading and pitch from a vector, assuming bank==0
893 vms_angvec *vm_extract_angles_vector_normalized(vms_angvec *a,vms_vector *v)
895 a->b = 0; //always zero bank
897 a->p = fix_asin(-v->y);
899 if (v->x==0 && v->z==0)
902 a->h = fix_atan2(v->z,v->x);
907 //extract heading and pitch from a vector, assuming bank==0
908 vms_angvec *vm_extract_angles_vector(vms_angvec *a,vms_vector *v)
912 if (vm_vec_copy_normalize(&t,v) != 0)
913 vm_extract_angles_vector_normalized(a,&t);
919 //compute the distance from a point to a plane. takes the normalized normal
920 //of the plane (ebx), a point on the plane (edi), and the point to check (esi).
921 //returns distance in eax
922 //distance is signed, so negative dist is on the back of the plane
923 fix vm_dist_to_plane(vms_vector *checkp,vms_vector *norm,vms_vector *planep)
927 vm_vec_sub(&t,checkp,planep);
929 return vm_vec_dot(&t,norm);
933 vms_vector *vm_vec_make(vms_vector *v,fix x,fix y,fix z) {
934 v->x=x; v->y=y; v->z=z;