vmath.c

这是一个相当棒的Linux下的台球游戏

/* vmath.c
**
**    some vector mathematics and structures (float or double)
**    Copyright (C) 2001  Florian Berger
**    Email:  [e-mail],  [e-mail]
**
**    This program is free software; you can redistribute it and/or modify
**    it under the terms of the GNU General Public License Version 2 as
**    published by the Free Software Foundation;
**
**    This program is distributed in the hope that it will be useful,
**    but WITHOUT ANY WARRANTY; without even the implied warranty of
**    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
**    GNU General Public License for more details.
**
**    You should have received a copy of the GNU General Public License
**    along with this program; if not, write to the Free Software
**    Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
**
*/

#include <stdlib.h> // exit(1)
#include <stdio.h>
#include <string.h>
#include <math.h>
#include "vmath.h"



void outline_copy(struct Outline os, struct Outline * od)
{
    int i;
    if( od->shnr != os.shnr ) {
        if (od->shnr!=0) free(od->sh);
        od->sh = (struct Shape *)malloc( os.shnr*sizeof(struct Shape) );
        for(i=0;i<os.shnr;i++){
            od->sh[0].pnr=0;
        }
    }
    od->shnr = os.shnr;
    for(i=0;i<os.shnr;i++){
        shape_copy( os.sh[i], &(od->sh[i]) );
    }
}


void shape_copy( struct Shape shs, struct Shape *shd )
{int i;
   if( shd->pnr != shs.pnr ) {
      if (shd->pnr!=0) free(shd->p);
      shd->p = (struct Vect *)malloc( shs.pnr*sizeof(struct Vect) );
   }
   shd->pnr = shs.pnr;
   for(i=0;i<shs.pnr;i++) shd->p[i]=shs.p[i];
}



void shape_flip( struct Shape *sh )
{
    int i;
    struct Vect dummy;

    for(i=0;i<sh->pnr/2;i++){
        dummy=sh->p[i];
        sh->p[i]=sh->p[sh->pnr-1-i];
        sh->p[sh->pnr-1-i]=dummy;
    }
}



void shape_trans( struct Shape *s, struct Vect t )
{int i;
   for(i=0;i<s->pnr;i++){
      s->p[i].x+=t.x;
      s->p[i].y+=t.y;
      s->p[i].z+=t.z;
   }
}



struct Vect vec_cross( struct Vect v1, struct Vect v2 )
{struct Vect vr;
   vr.x = v1.y * v2.z - v2.y * v1.z;
   vr.y = v1.z * v2.x - v2.z * v1.x;
   vr.z = v1.x * v2.y - v2.x * v1.y;
   return vr;
}


VMfloat vec_mul( struct Vect v1, struct Vect v2 )
{ return( v1.x*v2.x + v1.y*v2.y + v1.z*v2.z ); }


struct Vect vec_diff( struct Vect v1, struct Vect v2 )
{struct Vect vr;
   vr.x = v1.x - v2.x;
   vr.y = v1.y - v2.y;
   vr.z = v1.z - v2.z;
   return vr;
}


struct Vect vec_add( struct Vect v1, struct Vect v2 )
{struct Vect vr;
   vr.x = v1.x + v2.x;
   vr.y = v1.y + v2.y;
   vr.z = v1.z + v2.z;
   return vr;
}


struct Vect vec_scale( struct Vect v1, VMfloat scale )
{struct Vect vr;
   vr.x = v1.x * scale;
   vr.y = v1.y * scale;
   vr.z = v1.z * scale;
   return vr;
}


struct Vect vec_rotate( struct Vect v1, struct Vect ang )
{
    struct Vect vr;
    vr=v1;
    rot_ax( vec_unit(ang), &vr, 1, vec_abs(ang) );
    return(vr);
}


VMfloat vec_abs( struct Vect v )
{ return( sqrt( v.x*v.x + v.y*v.y + v.z*v.z ) ); }


VMfloat vec_abssq( struct Vect v )
{ return( v.x*v.x + v.y*v.y + v.z*v.z ); }


struct Vect vec_unit( struct Vect v )
{struct Vect vr;
 VMfloat l;
   l=vec_abs(v);
   if(fabs(l)>1.0E-50){
       vr.x=v.x/l;
       vr.y=v.y/l;
       vr.z=v.z/l;
   } else {
       vr.x=0.0;
       vr.y=0.0;
       vr.z=0.0;
   }
   return vr;
}



int vec_equal( struct Vect v1, struct Vect v2 )
{
   return ( v1.x==v2.x && v1.y==v2.y && v1.z==v2.z );
}



int vec_nearly_equal( struct Vect v1, struct Vect v2, VMfloat tolerance )
{
    return ( fabs(v1.x-v2.x)<tolerance &&
             fabs(v1.y-v2.y)<tolerance &&
             fabs(v1.z-v2.z)<tolerance );
}



struct Vect vec_xyz( VMfloat x, VMfloat y, VMfloat z )
{ struct Vect vr;
   vr.x=x; vr.y=y; vr.z=z;
   return vr;
}


struct Vect  vec_ex(){ return(vec_xyz(1.0,0.0,0.0)); }
struct Vect  vec_ey(){ return(vec_xyz(0.0,1.0,0.0)); }
struct Vect  vec_ez(){ return(vec_xyz(0.0,0.0,1.0)); }
struct Vect  vec_null(){ return(vec_xyz(0.0,0.0,0.0)); }



void shape_rot_ax( struct Vect ax, struct Shape *s, struct Vect m, VMfloat phi,
	     struct Vect nax, VMfloat sc_x, VMfloat sc_y, VMfloat sc_z )
{ struct Vect bx,by,bz; // base
  struct Vect dp,dp2;
  VMfloat sinphi,cosphi;
  int i;

//   printf("rotax  ");
//   printf("ax=%lf,%lf,%lf  ", ax.x, ax.y, ax.z);
//   printf("phi=%lf  ", phi);
   
   if ( phi !=0.0 && vec_abs(ax)>0.0 ){
   
      bz = vec_unit( ax );
      bx = vec_unit( nax );
      by = vec_cross(bz,bx);
   
      sinphi=sin(phi);
      cosphi=cos(phi);
   
      for( i=0; i<s->pnr; i++ ){
         s->p[i] = vec_diff( s->p[i], m );
         // transform into axis-system
         dp.x = vec_mul( s->p[i], bx ) * sc_x;
         dp.y = vec_mul( s->p[i], by ) * sc_y;
         dp.z = vec_mul( s->p[i], bz ) * sc_z;
   
         dp2.x = dp.x*cosphi - dp.y*sinphi;
         dp2.y = dp.y*cosphi + dp.x*sinphi;
         dp2.z = dp.z;
      
         // retransform back
         s->p[i].x = dp2.x * bx.x + dp2.y * by.x + dp2.z * bz.x;
         s->p[i].y = dp2.x * bx.y + dp2.y * by.y + dp2.z * bz.y;
         s->p[i].z = dp2.x * bx.z + dp2.y * by.z + dp2.z * bz.z;
         s->p[i] = vec_add( s->p[i], m );
      }
      
   }
//   printf("rotaxed\n");
   
}


void rot_ax( struct Vect ax, struct Vect *v, int nr, VMfloat phi )
{ struct Vect bx,by,bz; // base
  struct Vect dp,dp2, nax;
  VMfloat sinphi,cosphi;
  int i;

//   printf("rotax  ");
//   printf("ax=%lf,%lf,%lf  ", ax.x, ax.y, ax.z);
//   printf("phi=%lf  ", phi);
   
   if ( phi !=0.0 && vec_abs(ax)>0.0 ){

      bz = vec_unit( ax );
      if( fabs(bz.x) <= fabs(bz.y) && fabs(bz.x) <= fabs(bz.z) ) nax=vec_xyz(1.0,0.0,0.0);
      if( fabs(bz.y) <= fabs(bz.z) && fabs(bz.y) <= fabs(bz.x) ) nax=vec_xyz(0.0,1.0,0.0);
      if( fabs(bz.z) <= fabs(bz.x) && fabs(bz.z) <= fabs(bz.y) ) nax=vec_xyz(0.0,0.0,1.0);
      bx = vec_unit( vec_diff( nax, vec_scale(bz,vec_mul(nax,bz)) ) );
      by = vec_cross(bz,bx);
   
      sinphi=sin(phi);
      cosphi=cos(phi);
   
      for( i=0; i<nr; i++ ){
//         v[i] = vec_diff( v[i], m );
         // transform into axis-system
         dp.x = vec_mul( v[i], bx );
         dp.y = vec_mul( v[i], by );
         dp.z = vec_mul( v[i], bz );
   
         dp2.x = dp.x*cosphi - dp.y*sinphi;
         dp2.y = dp.y*cosphi + dp.x*sinphi;
         dp2.z = dp.z;
      
         // retransform back
         v[i].x = dp2.x * bx.x + dp2.y * by.x + dp2.z * bz.x;
         v[i].y = dp2.x * bx.y + dp2.y * by.y + dp2.z * bz.y;
         v[i].z = dp2.x * bx.z + dp2.y * by.z + dp2.z * bz.z;
      }
      
   }
   
}


struct Vect  meshpt_nr( struct Point * plist, int index )
{
    int i;
    struct Point * act;

    for( i=0,act=plist ; i<index && act!=0 ; i++,act=act->next );

    if( act==0 ){
        fprintf(stderr,"meshpt_nr: error: index overflow (%d)\n",index);
    }

    return act->pos;
}


int remove_idle_points( struct Shape * sh, struct Shape * shd )
/* returns # of points removed */
{
    int i, in, id, removenr;

    id=0;
    for( i=0 ; i<sh->pnr ; i++ ){
//        fprintf(stderr,"%d\n",i);
        in=i+1; if( in >= sh->pnr ) in=0;
        if( !vec_nearly_equal( sh->p[in], sh->p[i], 1E-1 ) ){
            shd->p[id] = sh->p[i];
            id++;
        } else {
            fprintf(stderr,"removed point #%d\n",i);
        }
    }
    removenr = sh->pnr -id;
    shd->pnr=id;
    return ( removenr );
}


VMfloat vec_angle( struct Vect v1, struct Vect v2 )
/* returns positive angle between 0 and M_PI */
{
    return( acos(vec_mul( vec_unit(v1), vec_unit(v2) )) );
}


struct Vect vec_proj( struct Vect v1, struct Vect v2 )
{
    static VMfloat v2ls;

    v2ls = v2.x*v2.x + v2.y*v2.y + v2.z*v2.z;
    if( v2ls > 0.0 ){
        return( vec_scale( v2, vec_mul(v1,v2)/v2ls ) );
    } else {
        return( v1 );
    }
}

struct Vect vec_ncomp( struct Vect v1, struct Vect v2 )
{
    return( vec_diff(v1,vec_proj(v1,v2)) );
}


VMfloat vec_ndist ( struct Vect v, struct Vect v1, struct Vect v2 )
/* normal distance of v to line(v1,v2) */
{
    return( vec_abs(vec_ncomp(vec_diff(v,v1),vec_diff(v2,v1))) );
}


struct Vect vec_surf_proj( struct Vect center, struct Vect point, struct Vect n, struct Vect npos )
{
    double ndist_c, ndist_p;
    npos = vec_proj(npos,n);
    ndist_c=vec_mul(center,n)-vec_mul(npos,n);
    ndist_p=vec_mul(point,n)-vec_mul(npos,n);
    center = vec_ncomp(center,n);
    point = vec_ncomp(point,n);
    return vec_add( npos,
                    vec_add( center,
                             vec_scale(vec_diff(point,center),ndist_c/(ndist_c-ndist_p))
                           )
                    );
}


struct Vect matr4_rdot( struct Matrix4 m, struct Vect v )
{
    struct Vect rvec;
    rvec.x=v.x*m.m[0]+v.y*m.m[4]+v.z*m.m[ 8]+m.m[12];
    rvec.y=v.x*m.m[1]+v.y*m.m[5]+v.z*m.m[ 9]+m.m[13];
    rvec.z=v.x*m.m[2]+v.y*m.m[6]+v.z*m.m[10]+m.m[14];
    return rvec;
}


struct Matrix4 matr4_mul(struct Matrix4 m1, struct Matrix4 m2)
{
/*    m1   m5   m
      m2   m6
      m3   m7
      ...  ...
      */
    int i,j,k;
    struct Matrix4 m;
    for(i=0;i<4;i++){
        for(j=0;j<4;j++){
            m.m[i*4+j]=0.0;
            for(k=0;k<4;k++){
                m.m[i*4+j] += m1.m[i*4+k] + m2.m[k*4+j];
            }
        }
    }
    return m;
}


VMfloat shape_area( struct Shape sh )
{
    int i,in;
    VMfloat a;

    a=0.0;
    for(i=0;i<sh.pnr;i++){
        in=(i+1)%sh.pnr;
        a += (sh.p[i].x-sh.p[in].x)*(sh.p[in].y+sh.p[i].y)/2.0;
    }

    return a;
}


struct Vect tri_center( struct Vect v1, struct Vect v2, struct Vect v3 )
{
    return( vec_xyz( (v1.x+v2.x+v3.x)/3.0,
                     (v1.y+v2.y+v3.y)/3.0,
                     (v1.z+v2.z+v3.z)/3.0 ) );
}


VMfloat tri_area_xy( struct Vect v1, struct Vect v2, struct Vect v3 )
/* area of triangle ( +/- for ccw/cw ) */
{
    return( ( (v1.x-v2.x)*(v1.y+v2.y) +
              (v2.x-v3.x)*(v2.y+v3.y) +
              (v3.x-v1.x)*(v3.y+v1.y) ) / 2.0 );
}


VMfloat tri_vol_xy( struct Vect v1, struct Vect v2, struct Vect v3 )
/* calc the volume of the space under (-z) the triangle (v1,v2,v3) */
{
    return( tri_center(v1,v2,v3).z * tri_area_xy(v1,v2,v3) );
}