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16 * C version of vecmat library
25 #include <math.h> // for sqrt
33 vms_vector vmd_zero_vector = {0, 0, 0};
34 vms_matrix vmd_identity_matrix = { { f1_0, 0, 0 },
38 //adds two vectors, fills in dest, returns ptr to dest
39 //ok for dest to equal either source, but should use vm_vec_add2() if so
40 vms_vector *vm_vec_add(vms_vector *dest,vms_vector *src0,vms_vector *src1)
42 dest->x = src0->x + src1->x;
43 dest->y = src0->y + src1->y;
44 dest->z = src0->z + src1->z;
50 //subs two vectors, fills in dest, returns ptr to dest
51 //ok for dest to equal either source, but should use vm_vec_sub2() if so
52 vms_vector *vm_vec_sub(vms_vector *dest,vms_vector *src0,vms_vector *src1)
54 dest->x = src0->x - src1->x;
55 dest->y = src0->y - src1->y;
56 dest->z = src0->z - src1->z;
61 //adds one vector to another. returns ptr to dest
62 //dest can equal source
63 vms_vector *vm_vec_add2(vms_vector *dest,vms_vector *src)
72 //subs one vector from another, returns ptr to dest
73 //dest can equal source
74 vms_vector *vm_vec_sub2(vms_vector *dest,vms_vector *src)
83 //averages two vectors. returns ptr to dest
84 //dest can equal either source
85 vms_vector *vm_vec_avg(vms_vector *dest,vms_vector *src0,vms_vector *src1)
87 dest->x = (src0->x + src1->x)/2;
88 dest->y = (src0->y + src1->y)/2;
89 dest->z = (src0->z + src1->z)/2;
95 //averages four vectors. returns ptr to dest
96 //dest can equal any source
97 vms_vector *vm_vec_avg4(vms_vector *dest,vms_vector *src0,vms_vector *src1,vms_vector *src2,vms_vector *src3)
99 dest->x = (src0->x + src1->x + src2->x + src3->x)/4;
100 dest->y = (src0->y + src1->y + src2->y + src3->y)/4;
101 dest->z = (src0->z + src1->z + src2->z + src3->z)/4;
107 //scales a vector in place. returns ptr to vector
108 vms_vector *vm_vec_scale(vms_vector *dest,fix s)
110 dest->x = fixmul(dest->x,s);
111 dest->y = fixmul(dest->y,s);
112 dest->z = fixmul(dest->z,s);
117 //scales and copies a vector. returns ptr to dest
118 vms_vector *vm_vec_copy_scale(vms_vector *dest,vms_vector *src,fix s)
120 dest->x = fixmul(src->x,s);
121 dest->y = fixmul(src->y,s);
122 dest->z = fixmul(src->z,s);
127 //scales a vector, adds it to another, and stores in a 3rd vector
128 //dest = src1 + k * src2
129 vms_vector *vm_vec_scale_add(vms_vector *dest,vms_vector *src1,vms_vector *src2,fix k)
131 dest->x = src1->x + fixmul(src2->x,k);
132 dest->y = src1->y + fixmul(src2->y,k);
133 dest->z = src1->z + fixmul(src2->z,k);
138 //scales a vector and adds it to another
140 vms_vector *vm_vec_scale_add2(vms_vector *dest,vms_vector *src,fix k)
142 dest->x += fixmul(src->x,k);
143 dest->y += fixmul(src->y,k);
144 dest->z += fixmul(src->z,k);
149 //scales a vector in place, taking n/d for scale. returns ptr to vector
151 vms_vector *vm_vec_scale2(vms_vector *dest,fix n,fix d)
153 #if 1 // DPH: Kludge: this was overflowing a lot, so I made it use the FPU.
155 // printf("scale n=%d d=%d\n",n,d);
156 nd = f2fl(n) / f2fl(d);
157 dest->x = fl2f( f2fl(dest->x) * nd);
158 dest->y = fl2f( f2fl(dest->y) * nd);
159 dest->z = fl2f( f2fl(dest->z) * nd);
161 dest->x = fixmuldiv(dest->x,n,d);
162 dest->y = fixmuldiv(dest->y,n,d);
163 dest->z = fixmuldiv(dest->z,n,d);
169 fix vm_vec_dotprod(vms_vector *v0,vms_vector *v1)
175 fixmulaccum(&q,v0->x,v1->x);
176 fixmulaccum(&q,v0->y,v1->y);
177 fixmulaccum(&q,v0->z,v1->z);
179 return fixquadadjust(&q);
182 fix vm_vec_dot3(fix x,fix y,fix z,vms_vector *v)
188 fixmulaccum(&q,x,v->x);
189 fixmulaccum(&q,y,v->y);
190 fixmulaccum(&q,z,v->z);
192 return fixquadadjust(&q);
195 //returns magnitude of a vector
196 fix vm_vec_mag(vms_vector *v)
202 fixmulaccum(&q,v->x,v->x);
203 fixmulaccum(&q,v->y,v->y);
204 fixmulaccum(&q,v->z,v->z);
206 return quad_sqrt(q.low,q.high);
209 //computes the distance between two points. (does sub and mag)
210 fix vm_vec_dist(vms_vector *v0,vms_vector *v1)
214 vm_vec_sub(&t,v0,v1);
216 return vm_vec_mag(&t);
220 //computes an approximation of the magnitude of the vector
221 //uses dist = largest + next_largest*3/8 + smallest*3/16
222 fix vm_vec_mag_quick(vms_vector *v)
242 bc = (b>>2) + (c>>3);
244 return a + bc + (bc>>1);
248 //computes an approximation of the distance between two points.
249 //uses dist = largest + next_largest*3/8 + smallest*3/16
250 fix vm_vec_dist_quick(vms_vector *v0,vms_vector *v1)
254 vm_vec_sub(&t,v0,v1);
256 return vm_vec_mag_quick(&t);
259 //normalize a vector. returns mag of source vec
260 fix vm_vec_copy_normalize(vms_vector *dest,vms_vector *src)
267 dest->x = fixdiv(src->x,m);
268 dest->y = fixdiv(src->y,m);
269 dest->z = fixdiv(src->z,m);
275 //normalize a vector. returns mag of source vec
276 fix vm_vec_normalize(vms_vector *v)
278 return vm_vec_copy_normalize(v,v);
282 //normalize a vector. returns mag of source vec. uses approx mag
283 fix vm_vec_copy_normalize_quick(vms_vector *dest,vms_vector *src)
287 m = vm_vec_mag_quick(src);
290 dest->x = fixdiv(src->x,m);
291 dest->y = fixdiv(src->y,m);
292 dest->z = fixdiv(src->z,m);
299 //these routines use an approximation for 1/sqrt
301 //returns approximation of 1/magnitude of a vector
302 fix vm_vec_imag(vms_vector *v)
308 fixmulaccum(&q,v->x,v->x);
309 fixmulaccum(&q,v->y,v->y);
310 fixmulaccum(&q,v->z,v->z);
313 return fix_isqrt(fixquadadjust(&q));
314 else if (q.high >= 0x800000) {
315 return (fix_isqrt(q.high) >> 8);
318 return (fix_isqrt((q.high<<8) + (q.low>>24)) >> 4);
321 //normalize a vector. returns 1/mag of source vec. uses approx 1/mag
322 fix vm_vec_copy_normalize_quick(vms_vector *dest,vms_vector *src)
326 im = vm_vec_imag(src);
328 dest->x = fixmul(src->x,im);
329 dest->y = fixmul(src->y,im);
330 dest->z = fixmul(src->z,im);
337 //normalize a vector. returns 1/mag of source vec. uses approx 1/mag
338 fix vm_vec_normalize_quick(vms_vector *v)
340 return vm_vec_copy_normalize_quick(v,v);
343 //return the normalized direction vector between two points
344 //dest = normalized(end - start). Returns 1/mag of direction vector
345 //NOTE: the order of the parameters matches the vector subtraction
346 fix vm_vec_normalized_dir_quick(vms_vector *dest,vms_vector *end,vms_vector *start)
348 vm_vec_sub(dest,end,start);
350 return vm_vec_normalize_quick(dest);
353 //return the normalized direction vector between two points
354 //dest = normalized(end - start). Returns mag of direction vector
355 //NOTE: the order of the parameters matches the vector subtraction
356 fix vm_vec_normalized_dir(vms_vector *dest,vms_vector *end,vms_vector *start)
358 vm_vec_sub(dest,end,start);
360 return vm_vec_normalize(dest);
363 //computes surface normal from three points. result is normalized
364 //returns ptr to dest
365 //dest CANNOT equal either source
366 vms_vector *vm_vec_normal(vms_vector *dest,vms_vector *p0,vms_vector *p1,vms_vector *p2)
368 vm_vec_perp(dest,p0,p1,p2);
370 vm_vec_normalize(dest);
375 //make sure a vector is reasonably sized to go into a cross product
376 void check_vec(vms_vector *v)
381 check = (fix)labs(v->x) | (fix)labs(v->y) | (fix)labs(v->z);
386 if (check & 0xfffc0000) { //too big
388 while (check & 0xfff00000) {
393 while (check & 0xfffc0000) {
402 else //maybe too small
403 if ((check & 0xffff8000) == 0) { //yep, too small
405 while ((check & 0xfffff000) == 0) {
410 while ((check & 0xffff8000) == 0) {
421 //computes cross product of two vectors.
422 //Note: this magnitude of the resultant vector is the
423 //product of the magnitudes of the two source vectors. This means it is
424 //quite easy for this routine to overflow and underflow. Be careful that
425 //your inputs are ok.
428 vms_vector *vm_vec_crossprod(vms_vector *dest,vms_vector *src0,vms_vector *src1)
431 Assert(dest!=src0 && dest!=src1);
433 d = (double)(src0->y) * (double)(src1->z);
434 d += (double)-(src0->z) * (double)(src1->y);
440 d = (double)(src0->z) * (double)(src1->x);
441 d += (double)-(src0->x) * (double)(src1->z);
447 d = (double)(src0->x) * (double)(src1->y);
448 d += (double)-(src0->y) * (double)(src1->x);
458 vms_vector *vm_vec_crossprod(vms_vector *dest,vms_vector *src0,vms_vector *src1)
462 Assert(dest!=src0 && dest!=src1);
465 fixmulaccum(&q,src0->y,src1->z);
466 fixmulaccum(&q,-src0->z,src1->y);
467 dest->x = fixquadadjust(&q);
470 fixmulaccum(&q,src0->z,src1->x);
471 fixmulaccum(&q,-src0->x,src1->z);
472 dest->y = fixquadadjust(&q);
475 fixmulaccum(&q,src0->x,src1->y);
476 fixmulaccum(&q,-src0->y,src1->x);
477 dest->z = fixquadadjust(&q);
485 //computes non-normalized surface normal from three points.
486 //returns ptr to dest
487 //dest CANNOT equal either source
488 vms_vector *vm_vec_perp(vms_vector *dest,vms_vector *p0,vms_vector *p1,vms_vector *p2)
492 vm_vec_sub(&t0,p1,p0);
493 vm_vec_sub(&t1,p2,p1);
498 return vm_vec_crossprod(dest,&t0,&t1);
502 //computes the delta angle between two vectors.
503 //vectors need not be normalized. if they are, call vm_vec_delta_ang_norm()
504 //the forward vector (third parameter) can be NULL, in which case the absolute
505 //value of the angle in returned. Otherwise the angle around that vector is
507 fixang vm_vec_delta_ang(vms_vector *v0,vms_vector *v1,vms_vector *fvec)
511 vm_vec_copy_normalize(&t0,v0);
512 vm_vec_copy_normalize(&t1,v1);
514 return vm_vec_delta_ang_norm(&t0,&t1,fvec);
517 //computes the delta angle between two normalized vectors.
518 fixang vm_vec_delta_ang_norm(vms_vector *v0,vms_vector *v1,vms_vector *fvec)
522 a = fix_acos(vm_vec_dot(v0,v1));
527 vm_vec_cross(&t,v0,v1);
529 if (vm_vec_dot(&t,fvec) < 0)
536 vms_matrix *sincos_2_matrix(vms_matrix *m,fix sinp,fix cosp,fix sinb,fix cosb,fix sinh,fix cosh)
538 fix sbsh,cbch,cbsh,sbch;
540 sbsh = fixmul(sinb,sinh);
541 cbch = fixmul(cosb,cosh);
542 cbsh = fixmul(cosb,sinh);
543 sbch = fixmul(sinb,cosh);
545 m->rvec.x = cbch + fixmul(sinp,sbsh); //m1
546 m->uvec.z = sbsh + fixmul(sinp,cbch); //m8
548 m->uvec.x = fixmul(sinp,cbsh) - sbch; //m2
549 m->rvec.z = fixmul(sinp,sbch) - cbsh; //m7
551 m->fvec.x = fixmul(sinh,cosp); //m3
552 m->rvec.y = fixmul(sinb,cosp); //m4
553 m->uvec.y = fixmul(cosb,cosp); //m5
554 m->fvec.z = fixmul(cosh,cosp); //m9
556 m->fvec.y = -sinp; //m6
562 //computes a matrix from a set of three angles. returns ptr to matrix
563 vms_matrix *vm_angles_2_matrix(vms_matrix *m,vms_angvec *a)
565 fix sinp,cosp,sinb,cosb,sinh,cosh;
567 fix_sincos(a->p,&sinp,&cosp);
568 fix_sincos(a->b,&sinb,&cosb);
569 fix_sincos(a->h,&sinh,&cosh);
571 return sincos_2_matrix(m,sinp,cosp,sinb,cosb,sinh,cosh);
575 //computes a matrix from a forward vector and an angle
576 vms_matrix *vm_vec_ang_2_matrix(vms_matrix *m,vms_vector *v,fixang a)
578 fix sinb,cosb,sinp,cosp,sinh,cosh;
580 fix_sincos(a,&sinb,&cosb);
583 cosp = fix_sqrt(f1_0 - fixmul(sinp,sinp));
585 sinh = fixdiv(v->x,cosp);
586 cosh = fixdiv(v->z,cosp);
588 return sincos_2_matrix(m,sinp,cosp,sinb,cosb,sinh,cosh);
592 //computes a matrix from one or more vectors. The forward vector is required,
593 //with the other two being optional. If both up & right vectors are passed,
594 //the up vector is used. If only the forward vector is passed, a bank of
596 //returns ptr to matrix
597 vms_matrix *vm_vector_2_matrix(vms_matrix *m,vms_vector *fvec,vms_vector *uvec,vms_vector *rvec)
599 vms_vector *xvec=&m->rvec,*yvec=&m->uvec,*zvec=&m->fvec;
601 Assert(fvec != NULL);
603 if (vm_vec_copy_normalize(zvec,fvec) == 0) {
604 Int3(); //forward vec should not be zero-length
610 if (rvec == NULL) { //just forward vec
615 if (zvec->x==0 && zvec->z==0) { //forward vec is straight up or down
618 m->uvec.z = (zvec->y<0)?f1_0:-f1_0;
620 m->rvec.y = m->rvec.z = m->uvec.x = m->uvec.y = 0;
622 else { //not straight up or down
628 vm_vec_normalize(xvec);
630 vm_vec_crossprod(yvec,zvec,xvec);
635 else { //use right vec
637 if (vm_vec_copy_normalize(xvec,rvec) == 0)
640 vm_vec_crossprod(yvec,zvec,xvec);
642 //normalize new perpendicular vector
643 if (vm_vec_normalize(yvec) == 0)
646 //now recompute right vector, in case it wasn't entirely perpendiclar
647 vm_vec_crossprod(xvec,yvec,zvec);
653 if (vm_vec_copy_normalize(yvec,uvec) == 0)
656 vm_vec_crossprod(xvec,yvec,zvec);
658 //normalize new perpendicular vector
659 if (vm_vec_normalize(xvec) == 0)
662 //now recompute up vector, in case it wasn't entirely perpendiclar
663 vm_vec_crossprod(yvec,zvec,xvec);
671 //quicker version of vm_vector_2_matrix() that takes normalized vectors
672 vms_matrix *vm_vector_2_matrix_norm(vms_matrix *m,vms_vector *fvec,vms_vector *uvec,vms_vector *rvec)
674 vms_vector *xvec=&m->rvec,*yvec=&m->uvec,*zvec=&m->fvec;
676 Assert(fvec != NULL);
680 if (rvec == NULL) { //just forward vec
685 if (zvec->x==0 && zvec->z==0) { //forward vec is straight up or down
688 m->uvec.z = (zvec->y<0)?f1_0:-f1_0;
690 m->rvec.y = m->rvec.z = m->uvec.x = m->uvec.y = 0;
692 else { //not straight up or down
698 vm_vec_normalize(xvec);
700 vm_vec_crossprod(yvec,zvec,xvec);
705 else { //use right vec
707 vm_vec_crossprod(yvec,zvec,xvec);
709 //normalize new perpendicular vector
710 if (vm_vec_normalize(yvec) == 0)
713 //now recompute right vector, in case it wasn't entirely perpendiclar
714 vm_vec_crossprod(xvec,yvec,zvec);
720 vm_vec_crossprod(xvec,yvec,zvec);
722 //normalize new perpendicular vector
723 if (vm_vec_normalize(xvec) == 0)
726 //now recompute up vector, in case it wasn't entirely perpendiclar
727 vm_vec_crossprod(yvec,zvec,xvec);
735 //rotates a vector through a matrix. returns ptr to dest vector
736 //dest CANNOT equal source
737 vms_vector *vm_vec_rotate(vms_vector *dest,vms_vector *src,vms_matrix *m)
741 dest->x = vm_vec_dot(src,&m->rvec);
742 dest->y = vm_vec_dot(src,&m->uvec);
743 dest->z = vm_vec_dot(src,&m->fvec);
749 //transpose a matrix in place. returns ptr to matrix
750 vms_matrix *vm_transpose_matrix(vms_matrix *m)
754 t = m->uvec.x; m->uvec.x = m->rvec.y; m->rvec.y = t;
755 t = m->fvec.x; m->fvec.x = m->rvec.z; m->rvec.z = t;
756 t = m->fvec.y; m->fvec.y = m->uvec.z; m->uvec.z = t;
761 //copy and transpose a matrix. returns ptr to matrix
762 //dest CANNOT equal source. use vm_transpose_matrix() if this is the case
763 vms_matrix *vm_copy_transpose_matrix(vms_matrix *dest,vms_matrix *src)
767 dest->rvec.x = src->rvec.x;
768 dest->rvec.y = src->uvec.x;
769 dest->rvec.z = src->fvec.x;
771 dest->uvec.x = src->rvec.y;
772 dest->uvec.y = src->uvec.y;
773 dest->uvec.z = src->fvec.y;
775 dest->fvec.x = src->rvec.z;
776 dest->fvec.y = src->uvec.z;
777 dest->fvec.z = src->fvec.z;
782 //mulitply 2 matrices, fill in dest. returns ptr to dest
783 //dest CANNOT equal either source
784 vms_matrix *vm_matrix_x_matrix(vms_matrix *dest,vms_matrix *src0,vms_matrix *src1)
786 Assert(dest!=src0 && dest!=src1);
788 dest->rvec.x = vm_vec_dot3(src0->rvec.x,src0->uvec.x,src0->fvec.x, &src1->rvec);
789 dest->uvec.x = vm_vec_dot3(src0->rvec.x,src0->uvec.x,src0->fvec.x, &src1->uvec);
790 dest->fvec.x = vm_vec_dot3(src0->rvec.x,src0->uvec.x,src0->fvec.x, &src1->fvec);
792 dest->rvec.y = vm_vec_dot3(src0->rvec.y,src0->uvec.y,src0->fvec.y, &src1->rvec);
793 dest->uvec.y = vm_vec_dot3(src0->rvec.y,src0->uvec.y,src0->fvec.y, &src1->uvec);
794 dest->fvec.y = vm_vec_dot3(src0->rvec.y,src0->uvec.y,src0->fvec.y, &src1->fvec);
796 dest->rvec.z = vm_vec_dot3(src0->rvec.z,src0->uvec.z,src0->fvec.z, &src1->rvec);
797 dest->uvec.z = vm_vec_dot3(src0->rvec.z,src0->uvec.z,src0->fvec.z, &src1->uvec);
798 dest->fvec.z = vm_vec_dot3(src0->rvec.z,src0->uvec.z,src0->fvec.z, &src1->fvec);
805 //extract angles from a matrix
806 vms_angvec *vm_extract_angles_matrix(vms_angvec *a,vms_matrix *m)
810 if (m->fvec.x==0 && m->fvec.z==0) //zero head
813 a->h = fix_atan2(m->fvec.z,m->fvec.x);
815 fix_sincos(a->h,&sinh,&cosh);
817 if (abs(sinh) > abs(cosh)) //sine is larger, so use it
818 cosp = fixdiv(m->fvec.x,sinh);
819 else //cosine is larger, so use it
820 cosp = fixdiv(m->fvec.z,cosh);
822 if (cosp==0 && m->fvec.y==0)
825 a->p = fix_atan2(cosp,-m->fvec.y);
828 if (cosp == 0) //the cosine of pitch is zero. we're pitched straight up. say no bank
835 sinb = fixdiv(m->rvec.y,cosp);
836 cosb = fixdiv(m->uvec.y,cosp);
838 if (sinb==0 && cosb==0)
841 a->b = fix_atan2(cosb,sinb);
849 //extract heading and pitch from a vector, assuming bank==0
850 vms_angvec *vm_extract_angles_vector_normalized(vms_angvec *a,vms_vector *v)
852 a->b = 0; //always zero bank
854 a->p = fix_asin(-v->y);
856 if (v->x==0 && v->z==0)
859 a->h = fix_atan2(v->z,v->x);
864 //extract heading and pitch from a vector, assuming bank==0
865 vms_angvec *vm_extract_angles_vector(vms_angvec *a,vms_vector *v)
869 if (vm_vec_copy_normalize(&t,v) != 0)
870 vm_extract_angles_vector_normalized(a,&t);
876 //compute the distance from a point to a plane. takes the normalized normal
877 //of the plane (ebx), a point on the plane (edi), and the point to check (esi).
878 //returns distance in eax
879 //distance is signed, so negative dist is on the back of the plane
880 fix vm_dist_to_plane(vms_vector *checkp,vms_vector *norm,vms_vector *planep)
884 vm_vec_sub(&t,checkp,planep);
886 return vm_vec_dot(&t,norm);
890 vms_vector *vm_vec_make(vms_vector *v,fix x,fix y,fix z)
892 v->x=x; v->y=y; v->z=z;