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C/C++ Source or Header  |  1995-06-22  |  9.7 KB  |  260 lines
  1. /** 3DGPL *************************************************\
  2.  *  ()                                                    *
  3.  *  3-D transformations of coordinates using floats.      *
  4.  *                                                        *
  5.  *  Defines:                                              *
  6.  *   T_init_math             Creating sin/cos tables;     *
  7.  *                                                        *
  8.  *   T_translation           Shifting of coordinates;     *
  9.  *   T_scaling               Scaling coordinates;         *
  10.  *                                                        *
  11.  *   T_set_world_rotation    Viewer's rotation;           *
  12.  *   T_world_rotation        Transforming coordinates;    *
  13.  *   T_set_self_rotation     Object rotation;             *
  14.  *   T_self_rotation         Transforming coordinates;    *
  15.  *                                                        *
  16.  *   T_perspective           Transform to perspective.    *
  17.  *                                                        *
  18.  *  (6/1995) By Sergei Savchenko. (savs@cs.mcgill.ca).    *
  19.  *  Copyright (c) 1995 Sergei Savchenko.                  *
  20.  *  THIS SOURCE CODE CAN'T BE USED FOR COMERCIAL PURPOSES *
  21.  *  WITHOUT AUTHORISATION                                 *
  22. \**********************************************************/
  23.  
  24. #include <math.h>                           /* sin & cos */
  25. #include "../hardware/hardware.h"           /* fast copy routines */
  26. #include "../trans/trans.h"                 /* 3D mathematics */
  27.  
  28. #define T_RADS                  40.7436642  /* pseudo-grads into rads */
  29.  
  30. float T_wx1,T_wx2,T_wx3,T_wy1,T_wy2,T_wy3,T_wz1,T_wz2,T_wz3;
  31. float T_sx1,T_sx2,T_sx3,T_sy1,T_sy2,T_sy3,T_sz1,T_sz2,T_sz3;
  32. float T_sin[256],T_cos[256];                /* precalculated */
  33.  
  34. /**********************************************************\
  35.  *  Initializing tables.                                  *
  36. \**********************************************************/
  37.  
  38. void T_init_math(void)
  39. {
  40.  int i;
  41.  
  42.  for(i=0;i<256;i++)
  43.  {
  44.   T_sin[i]=sin(i/T_RADS);
  45.   T_cos[i]=cos(i/T_RADS);
  46.  }
  47. } 
  48.  
  49. /**********************************************************\
  50.  *  Translation of coordinates.                           *
  51. \**********************************************************/
  52.  
  53. void T_translation(register int *from,register int *to,int length,
  54.            int addx,int addy,int addz
  55.           )
  56. {
  57.  register int i;
  58.  
  59.  for(i=0;i<length;i++)
  60.  {
  61.   (*to++)=(*from++)+addx;
  62.   (*to++)=(*from++)+addy;
  63.   (*to++)=(*from++)+addz;                   /* translation */
  64.  }
  65. }
  66.  
  67. /**********************************************************\
  68.  *  Scaling coordinates. (takes in float parameters).     *
  69. \**********************************************************/
  70.  
  71. void T_scaling(register int *from,register int *to,int length,
  72.            int mulx,int muly,int mulz
  73.           )
  74. {
  75.  register int i;
  76.  
  77.  for(i=0;i<length;i++)
  78.  {
  79.   (*to++)=(int)(*from++)*mulx;
  80.   (*to++)=(int)(*from++)*muly;
  81.   (*to++)=(int)(*from++)*mulz;
  82.  }                                          /* scaling */
  83. }
  84.  
  85. /**********************************************************\
  86.  *  Constructing rotation matrix. (gam-bet-alp), rotation *
  87.  *  then pitch then roll sequence. gam-rotation, bet-pitch*
  88.  *                                 alp-roll.              *
  89.  *                                                        *
  90.  *          Y^    Z           x'=z*sin(gam)+x*cos(gam)    *  
  91.  *           |   /            y'=y                        *
  92.  *           |  / alp         z'=z*cos(gam)-x*sin(gam)    * 
  93.  *          /|<---+                                       *
  94.  *         | |/   |           x"=x'                       *
  95.  *  -------|-+-----------> X  y"=y'*cos(bet)-z'*sin(bet)  *
  96.  *     bet | |   __           z"=y'*sin(bet)+z'*cos(bet)  *
  97.  *         V/|   /| gam                                   *
  98.  *         /----+             x"'=y"*sin(alp)+x"*cos(alp) *
  99.  *        /  |                y"'=y"*cos(alp)-x"*sin(alp) *
  100.  *       /   |                z"'=z"                      *
  101.  *           |                                            *
  102. \**********************************************************/
  103.  
  104. void T_set_world_rotation(int alp,int bet,int gam)
  105. {
  106.  float cosalp,sinalp,cosbet,sinbet,cosgam,singam;
  107.  
  108.  cosalp=T_cos[alp];
  109.  sinalp=T_sin[alp];
  110.  cosbet=T_cos[bet];
  111.  sinbet=T_sin[bet];
  112.  cosgam=T_cos[gam];
  113.  singam=T_sin[gam];                         /* initializing */
  114.  
  115.  T_wx1=singam*sinbet*sinalp + cosgam*cosalp;
  116.  T_wy1=cosbet*sinalp;
  117.  T_wz1=singam*cosalp - cosgam*sinbet*sinalp;
  118.  
  119.  T_wx2=singam*sinbet*cosalp - cosgam*sinalp;
  120.  T_wy2=cosbet*cosalp;
  121.  T_wz2=-cosgam*sinbet*cosalp - singam*sinalp;
  122.  
  123.  T_wx3=-singam*cosbet;
  124.  T_wy3=sinbet;
  125.  T_wz3=cosgam*cosbet;                       /* calculating the matrix */
  126. }
  127.  
  128. /**********************************************************\
  129.  *  Rotating coordinates.                                 *
  130.  *                                        |wx1 wx2 wx3|   *
  131.  *  T'=T[W]  where:  [x' y' z'] = [x y z]*|wy1 wy2 wy3|   *
  132.  *                                        |wz1 wz2 wz3|   *
  133. \**********************************************************/
  134.  
  135. void T_world_rotation(int *from,register int *to,int length)
  136. {
  137.  register int i;
  138.  register int xt,yt,zt;
  139.  
  140.  for(i=0;i<length;i++)
  141.  {
  142.   xt=*from++;
  143.   yt=*from++;
  144.   zt=*from++;
  145.  
  146.   *to++=(int)(T_wx1*xt+T_wy1*yt+T_wz1*zt);
  147.   *to++=(int)(T_wx2*xt+T_wy2*yt+T_wz2*zt);
  148.   *to++=(int)(T_wx3*xt+T_wy3*yt+T_wz3*zt); 
  149.  }
  150. }
  151.  
  152. /**********************************************************\
  153.  *  Constructing rotation matrix. (alp-bet-gam), roll     * 
  154.  *  then pitch then rotation sequence. gam-rotation,      *
  155.  *                                     bet-pitch, alp-roll*
  156.  *                                                        *
  157.  *          Y^    Z           x'=y*sin(alp)+x*cos(alp)    *   
  158.  *           |   /            y'=y*cos(alp)-x*sin(alp)    *
  159.  *           |  / alp         z'=z                        *
  160.  *          /|<---+                                       *
  161.  *         | |/   |           x"=x'                       *
  162.  *  -------|-+-----------> X  y"=y'*cos(bet)-z'*sin(bet)  *
  163.  *     bet | |   __           z"=y'*sin(bet)+z'*cos(bet)  *
  164.  *         V/|   /| gam                                   *
  165.  *         /----+             x"'=z"*sin(gam)+x"*cos(gam) *
  166.  *        /  |                y"'=y"                      *
  167.  *       /   |                z"'=z"*cos(gam)-x"*sin(gam) *
  168.  *           |                                            *
  169. \**********************************************************/
  170.  
  171. void T_set_self_rotation(int alp,int bet,int gam)
  172. {
  173.  float cosalp,sinalp,cosbet,sinbet,cosgam,singam;
  174.  
  175.  cosalp=T_cos[alp];
  176.  sinalp=T_sin[alp];
  177.  cosbet=T_cos[bet];
  178.  sinbet=T_sin[bet];
  179.  cosgam=T_cos[gam];
  180.  singam=T_sin[gam];                         /* initializing */
  181.  
  182.  T_sx1=cosalp*cosgam-sinalp*sinbet*singam;
  183.  T_sy1=sinalp*cosgam+cosalp*sinbet*singam;
  184.  T_sz1=cosbet*singam;
  185.  
  186.  T_sx2=-sinalp*cosbet;
  187.  T_sy2=cosalp*cosbet;
  188.  T_sz2=-sinbet;
  189.  
  190.  T_sx3=-cosalp*singam-sinalp*sinbet*cosgam;
  191.  T_sy3=cosalp*sinbet*cosgam-sinalp*singam;
  192.  T_sz3=cosbet*cosgam;                       /* calculating the matrix */
  193. }
  194.  
  195. /**********************************************************\
  196.  *  Rotating coordinates.                                 *
  197.  *                                        |sx1 sx2 sx3|   *
  198.  *  T'=T[S]  where:  [x' y' z'] = [x y z]*|sy1 sy2 sy3|   *
  199.  *                                        |sz1 sz2 sz3|   *
  200. \**********************************************************/
  201.  
  202. void T_self_rotation(int *from,register int *to,int length)
  203. {
  204.  register int i;
  205.  register int xt,yt,zt;
  206.  
  207.  for(i=0;i<length;i++)
  208.  {
  209.   xt=*from++;
  210.   yt=*from++;
  211.   zt=*from++;
  212.  
  213.   *to++=(int)(T_sx1*xt+T_sy1*yt+T_sz1*zt);
  214.   *to++=(int)(T_sx2*xt+T_sy2*yt+T_sz2*zt);
  215.   *to++=(int)(T_sx3*xt+T_sy3*yt+T_sz3*zt); 
  216.  }
  217. }
  218.  
  219. /**********************************************************\
  220.  *  Transforming to perspective, coordinates passed ase   *
  221.  *                        supposed to be both volume, and *  
  222.  *                *       Z-clipped, otherwise division   *
  223.  *               /|X      by 0 or overflow can occur.     *
  224.  *              / |                                       *
  225.  *             /  |                                       *
  226.  *            *   |                                       *
  227.  *           /|X' |       X'      X                       *
  228.  *          / |   |    ------- = ---                      *
  229.  *         /  |   |     focus     Z                       *
  230.  *        *---+---+                                       *
  231.  *        0   ^   Z    X'= X*focus/Z                      *
  232.  *            |                                           *
  233.  *          focus                                         *
  234.  *                                                        *
  235.  *  ADDITIONAL FUNCTIONS: 1) changing formats:            *
  236.  *  ---------------------                                 *
  237.  *    source:       x, y ,z,a1,...,aN where N==dimension-3*
  238.  *    destanation:  x',y',  a1,...,aN                     *
  239.  *                                                        *
  240.  *  2) performs translation to the screen centre.         *
  241. \**********************************************************/
  242.  
  243. void T_perspective(register int *from,register int *to,
  244.            int dimension,int length
  245.           )
  246. {
  247.  register int i;
  248.  
  249.  dimension-=3;                              /* other then X,Y */
  250.  
  251.  for(i=0;i<length;i++,from+=dimension,to+=dimension) 
  252.  {                                          /* Z is not being changed */
  253.   to[0]=((((long)from[0])<<T_LOG_FOCUS)/from[2])+HW_SCREEN_X_CENTRE;
  254.   to[1]=((((long)from[1])<<T_LOG_FOCUS)/from[2])+HW_SCREEN_Y_CENTRE;
  255.   HW_copy_int(from+=3,to+=2,dimension);
  256.  }
  257. }
  258.  
  259. /**********************************************************/
  260.