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t3d.c

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/*
** ---------------------------------------------------------------
** t3d.c  -  Package to manage 3D matrix transformations.
**
** ---------------------------------------------------------------
*/

/*
** ---------------------------------------------------------------
** Global variables and symbols:
*/
#include <math.h>
#include "t3d.h"

/*
** ---------------------------------------------------------------
** Local definitions and variables:
*/
#ifndef rad
#define rad(a)  ((a)*0.01745329252)
#endif

typedef struct {
  double x, y, z;
 } Vector;

typedef double Matrix3d[4][4];

static Matrix3d mt =
 {
  { 1.0, 0.0, 0.0, 0.0 } ,
  { 0.0, 1.0, 0.0, 0.0 } ,
  { 0.0, 0.0, 1.0, 0.0 } ,
  { 0.0, 0.0, 0.0, 1.0 }
 };

/*
** ---------------------------------------------------------------
** Local functions:
*/

/*========================  t3dVecUnit  ========================*/
static void t3dVecUnit( Vector *a, Vector *b )
{
 double len = sqrt(a->x*a->x + a->y*a->y + a->z*a->z);

 if( len != 0.0 )
 {
  b->x = a->x / len;
  b->y = a->y / len;
  b->z = a->z / len;
 }
}

/*========================  t3dVecCross  =======================*/
static void t3dVecCross( Vector *a, Vector *b, Vector *c )
{
 c->x = a->y * b->z - a->z * b->y;
 c->y = a->z * b->x - a->x * b->z;
 c->z = a->x * b->y - a->y * b->x;
}

/*=======================  t3dAccumulate  ======================*/
static void t3dAccumulate( Matrix3d new_mt )
{
 double   t0, t1, t2;

 t0       =  mt[0][0]*new_mt[0][0] + mt[1][0]*new_mt[0][1] 
           + mt[2][0]*new_mt[0][2] + mt[3][0]*new_mt[0][3];
 t1       =  mt[0][0]*new_mt[1][0] + mt[1][0]*new_mt[1][1] 
           + mt[2][0]*new_mt[1][2] + mt[3][0]*new_mt[1][3];
 t2       =  mt[0][0]*new_mt[2][0] + mt[1][0]*new_mt[2][1] 
           + mt[2][0]*new_mt[2][2] + mt[3][0]*new_mt[2][3];
 mt[3][0] =  mt[0][0]*new_mt[3][0] + mt[1][0]*new_mt[3][1] 
           + mt[2][0]*new_mt[3][2] + mt[3][0]*new_mt[3][3];
 mt[2][0] =  t2;
 mt[1][0] =  t1;
 mt[0][0] =  t0;

 t0       =  mt[0][1]*new_mt[0][0] + mt[1][1]*new_mt[0][1] 
           + mt[2][1]*new_mt[0][2] + mt[3][1]*new_mt[0][3];
 t1       =  mt[0][1]*new_mt[1][0] + mt[1][1]*new_mt[1][1] 
           + mt[2][1]*new_mt[1][2] + mt[3][1]*new_mt[1][3];
 t2       =  mt[0][1]*new_mt[2][0] + mt[1][1]*new_mt[2][1] 
           + mt[2][1]*new_mt[2][2] + mt[3][1]*new_mt[2][3];
 mt[3][1] =  mt[0][1]*new_mt[3][0] + mt[1][1]*new_mt[3][1] 
           + mt[2][1]*new_mt[3][2] + mt[3][1]*new_mt[3][3];
 mt[2][1] =  t2;
 mt[1][1] =  t1;
 mt[0][1] =  t0;

 t0       =  mt[0][2]*new_mt[0][0] + mt[1][2]*new_mt[0][1] 
           + mt[2][2]*new_mt[0][2] + mt[3][2]*new_mt[0][3];
 t1       =  mt[0][2]*new_mt[1][0] + mt[1][2]*new_mt[1][1] 
           + mt[2][2]*new_mt[1][2] + mt[3][2]*new_mt[1][3];
 t2       =  mt[0][2]*new_mt[2][0] + mt[1][2]*new_mt[2][1] 
           + mt[2][2]*new_mt[2][2] + mt[3][2]*new_mt[2][3];
 mt[3][2] =  mt[0][2]*new_mt[3][0] + mt[1][2]*new_mt[3][1] 
           + mt[2][2]*new_mt[3][2] + mt[3][2]*new_mt[3][3];
 mt[2][2] =  t2;
 mt[1][2] =  t1;
 mt[0][2] =  t0;

 t0       =  mt[0][3]*new_mt[0][0] + mt[1][3]*new_mt[0][1] 
           + mt[2][3]*new_mt[0][2] + mt[3][3]*new_mt[0][3];
 t1       =  mt[0][3]*new_mt[1][0] + mt[1][3]*new_mt[1][1] 
           + mt[2][3]*new_mt[1][2] + mt[3][3]*new_mt[1][3];
 t2       =  mt[0][3]*new_mt[2][0] + mt[1][3]*new_mt[2][1] 
           + mt[2][3]*new_mt[2][2] + mt[3][3]*new_mt[2][3];
 mt[3][3] =  mt[0][3]*new_mt[3][0] + mt[1][3]*new_mt[3][1] 
           + mt[2][3]*new_mt[3][2] + mt[3][3]*new_mt[3][3];
 mt[2][3] =  t2;
 mt[1][3] =  t1;
 mt[0][3] =  t0;
}


/*
** ---------------------------------------------------------------
** Public functions:
*/

/*======================  t3dTransform  ========================*/

void t3dTransform( double *x, double *y, double *z )
{
 double r, s, t, h;

  r = mt[0][0]*(*x)+mt[0][1]*(*y)+mt[0][2]*(*z)+mt[0][3];
  s = mt[1][0]*(*x)+mt[1][1]*(*y)+mt[1][2]*(*z)+mt[1][3];
  t = mt[2][0]*(*x)+mt[2][1]*(*y)+mt[2][2]*(*z)+mt[2][3];
  h = mt[3][0]*(*x)+mt[3][1]*(*y)+mt[3][2]*(*z)+mt[3][3];
 *x = r/h;
 *y = s/h;
 *z = t/h;
}

/*======================  t3dIdentity  ========================= */

void t3dIdentity( void )
{
 mt[0][0] = 1.0; mt[0][1] = 0.0; mt[0][2] = 0.0; mt[0][3] = 0.0;
 mt[1][0] = 0.0; mt[1][1] = 1.0; mt[1][2] = 0.0; mt[1][3] = 0.0;
 mt[2][0] = 0.0; mt[2][1] = 0.0; mt[2][2] = 1.0; mt[2][3] = 0.0;
 mt[3][0] = 0.0; mt[3][1] = 0.0; mt[3][2] = 0.0; mt[3][3] = 1.0;
}

/*=========================  t3dScale  =========================*/

void t3dScale( double sx, double sy, double sz )
{
 Matrix3d scale;

/*** COMPLETE HERE: 47 ***/

 t3dAccumulate( scale );
}

/*=======================  t3dTranslate  =======================*/

void t3dTranslate( double tx, double ty, double tz )
{
 Matrix3d transl;

/*** COMPLETE HERE: 48 ***/

 t3dAccumulate( transl );
}

/*======================  t3dRotateBasis  ======================*/

void t3dRotateBasis( double ux, double uy, double uz, 
                     double vx, double vy, double vz,
                     double wx, double wy, double wz )
{
 Matrix3d rot;

/*** COMPLETE HERE: 49 ***/

 t3dAccumulate( rot );
}

/*=========================  t3dCamera  ========================*/

void t3dCamera( double eyex, double eyey, double eyez, 
                double refx, double refy, double refz,
                double vupx, double vupy, double vupz )
{
 Vector  view, upvec;   /* view vector and view upper vector */
 Vector  u, v, w;       /* eye system unit vectors           */

/* Define view vector (from ref to eye) and view up vector.
 */
/*** COMPLETE HERE: 50 ***/

/* Find the eye system unit vectors.
 */
/*** COMPLETE HERE: 51 ***/

/* Concatenate a translation of basis from origin to eye point.
 */
 t3dTranslate( -eyex, -eyey, -eyez );

/* Concatenate a rotation of basis from world to eye system.
 */
 t3dRotateBasis( u.x, u.y, u.z, v.x, v.y, v.z, w.x, w.y, w.z );
}

/*======================  t3dPerspective  ======================*/

void t3dPerspective( double d, double front, double back )
{
 double   alpha, beta;        /* perspective parameters */
 Matrix3d persp;

/*** COMPLETE HERE: 52 ***/

 t3dAccumulate( persp );
}

/*=====================  t3dNormalizeView  =====================*/

void t3dNormalizeView( double left, double right, 
                       double bottom, double top, 
                       double front, double back )
{
 double tx, ty, tz;           /* translation factors */
 double sx, sy, sz;           /* scaling factors     */

/* Concatenate a translation of basis from origin to center
 * of view volume.
 */
/*** COMPLETE HERE: 53 ***/
 t3dTranslate( -tx, -ty, -tz );

/* Concatenate a scaling transformation that scales the view 
 * volume to a cube ranging from -1 to +1 in the 3 directions, 
 * also reverting the z-axis direction.
 */
/*** COMPLETE HERE: 54 ***/
 t3dScale( sx, sy, -sz );
}

** COMPLETE HERE: 53 ***/
 t3dTranslate( -tx, -ty, -tz );

/* Concatenate a scaling transformation that scales the view 
 * volume to a cube ranging from -1 to +1 in the 3 directions, 
 * also reverting the z-axis direction.
 */
/*** COMPLETE HERE: 54 ***/
 t3dScale( sx, sy, -sz );
}

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