/* Copyright (C) 2001-2006 Artifex Software, Inc.
   All Rights Reserved.
  
   This software is provided AS-IS with no warranty, either express or
   implied.

   This software is distributed under license and may not be copied, modified
   or distributed except as expressly authorized under the terms of that
   license.  Refer to licensing information at http://www.artifex.com/
   or contact Artifex Software, Inc.,  7 Mt. Lassen Drive - Suite A-134,
   San Rafael, CA  94903, U.S.A., +1(415)492-9861, for further information.
*/

/* $Id: gxdda.h 8522 2008-02-12 20:30:17Z leonardo $ */
/* Definitions for DDAs */
/* Requires gxfixed.h */

#ifndef gxdda_INCLUDED
#  define gxdda_INCLUDED

/*
 * We use the familiar Bresenham DDA algorithm for several purposes:
 *      - tracking the edges when filling trapezoids;
 *      - tracking the current pixel corner coordinates when rasterizing
 *      skewed or rotated images;
 *      - converting curves to sequences of lines (this is a 3rd-order
 *      DDA, the others are 1st-order);
 *      - perhaps someday for drawing single-pixel lines.
 * In the case of trapezoids, lines, and curves, we need to use
 * the DDA to find the integer X values at integer+0.5 values of Y;
 * in the case of images, we use DDAs to compute the (fixed)
 * X and Y values at (integer) source pixel corners.
 *
 * The purpose of the DDA is to compute the exact values Q(i) = floor(i*D/N)
 * for increasing integers i, 0 <= i <= N.  D is considered to be an
 * integer, although it may actually be a fixed.  For the algorithm,
 * we maintain i*D/N as Q + (N-R)/N where Q and R are integers, 0 < R <= N,
 * with the following auxiliary values:
 *      dQ = floor(D/N)
 *      dR = D mod N (0 <= dR < N)
 *      NdR = N - dR
 * Then at each iteration we do:
 *      Q += dQ;
 *      if ( R > dR ) R -= dR; else ++Q, R += NdR;
 * These formulas work regardless of the sign of D, and never let R go
 * out of range.
 */
/* In the following structure definitions, ntype must be an unsigned type. */
#define dda_state_struct(sname, dtype, ntype)\
  struct sname { dtype Q; ntype R; }
#define dda_step_struct(sname, dtype, ntype)\
  struct sname { dtype dQ; ntype dR, NdR; }

/* DDA with int Q and uint N */
typedef struct gx_dda_int_s {
    dda_state_struct(ia_, int, uint) state;
    dda_step_struct(ie_, int, uint) step;
} gx_dda_int_t;

/* DDA with fixed Q and (unsigned) integer N */
typedef 
dda_state_struct(_a, fixed, uint) gx_dda_state_fixed;
     typedef dda_step_struct(_e, fixed, uint) gx_dda_step_fixed;
     typedef struct gx_dda_fixed_s {
	 gx_dda_state_fixed state;
	 gx_dda_step_fixed step;
     } gx_dda_fixed;
/*
 * Define a pair of DDAs for iterating along an arbitrary line.
 */
     typedef struct gx_dda_fixed_point_s {
	 gx_dda_fixed x, y;
     } gx_dda_fixed_point;
/*
 * Initialize a DDA.  The sign test is needed only because C doesn't
 * provide reliable definitions of / and % for integers (!!!).
 */
#define dda_init_state(dstate, init, N)\
  (dstate).Q = (init), (dstate).R = (N)
#define dda_init_step(dstep, D, N)\
  if ( (N) == 0 )\
    (dstep).dQ = 0, (dstep).dR = 0;\
  else if ( (D) < 0 )\
   { (dstep).dQ = -(int)((uint)-(D) / (N));\
     if ( ((dstep).dR = -(D) % (N)) != 0 )\
       --(dstep).dQ, (dstep).dR = (N) - (dstep).dR;\
   }\
  else\
   { (dstep).dQ = (D) / (N); (dstep).dR = (D) % (N); }\
  (dstep).NdR = (N) - (dstep).dR
#define dda_init(dda, init, D, N)\
  dda_init_state((dda).state, init, N);\
  dda_init_step((dda).step, D, N)
/*
 * Compute the sum of two DDA steps with the same D and N.
 * Note that since dR + NdR = N, this quantity must be the same in both
 * fromstep and tostep.
 */
#define dda_step_add(tostep, fromstep)\
  (tostep).dQ +=\
    ((tostep).dR < (fromstep).NdR ?\
     ((tostep).dR += (fromstep).dR, (tostep).NdR -= (fromstep).dR,\
      (fromstep).dQ) :\
     ((tostep).dR -= (fromstep).NdR, (tostep).NdR += (fromstep).NdR,\
      (fromstep).dQ + 1))
/*
 * Return the current value in a DDA.
 */
#define dda_state_current(dstate) (dstate).Q
#define dda_current(dda) dda_state_current((dda).state)
#define dda_current_fixed2int(dda)\
  fixed2int_var(dda_state_current((dda).state))
/*
 * Increment a DDA to the next point.
 * Returns the updated current value.
 */
#define dda_state_next(dstate, dstep)\
  (dstate).Q +=\
    ((dstate).R > (dstep).dR ?\
     ((dstate).R -= (dstep).dR, (dstep).dQ) :\
     ((dstate).R += (dstep).NdR, (dstep).dQ + 1))
#define dda_next(dda) dda_state_next((dda).state, (dda).step)
/*
 * Back up a DDA to the previous point.
 * Returns the updated current value.
 */
#define dda_state_previous(dstate, dstep)\
  (dstate).Q -=\
    ((dstate).R <= (dstep).NdR ?\
     ((dstate).R += (dstep).dR, (dstep).dQ) :\
     ((dstate).R -= (dstep).NdR, (dstep).dQ + 1))
#define dda_previous(dda) dda_state_previous((dda).state, (dda).step)
/*
 * Advance a DDA by an arbitrary number of steps.
 * This implementation is very inefficient; we'll improve it if needed.
 */
#define dda_state_advance(dstate, dstep, nsteps)\
  BEGIN\
    uint n_ = (nsteps);\
    (dstate).Q += (dstep).dQ * (nsteps);\
    while ( n_-- )\
      if ( (dstate).R > (dstep).dR ) (dstate).R -= (dstep).dR;\
      else (dstate).R += (dstep).NdR, (dstate).Q++;\
  END
#define dda_advance(dda, nsteps)\
  dda_state_advance((dda).state, (dda).step, nsteps)
/*
 * Translate the position of a DDA by a given amount.
 */
#define dda_state_translate(dstate, delta)\
  ((dstate).Q += (delta))
#define dda_translate(dda, delta)\
  dda_state_translate((dda).state, delta)
  
#endif /* gxdda_INCLUDED */
