small3dlib/s3l.h

#ifndef S3L_H
#define S3L_H

#include <stdint.h>

typedef int16_t S3L_UNIT;
#define S3L_FRACTIONS_PER_UNIT 1024
typedef int16_t S3L_COORD;

typedef struct
{
  S3L_COORD x;           ///< Screen X coordinate.
  S3L_COORD y;           ///< Screen Y coordinate.

  S3L_UNIT barycentricA; /**< Barycentric coord A. Together with B and C coords
                              these serve to locate the pixel on a triangle and
                              interpolate values between it's three points. The
                              sum of the three coordinates will always be
                              exactly S3L_FRACTIONS_PER_UNIT. */
  S3L_UNIT barycentricB; ///< Baryc. coord B, same semantics as barycentricA.
  S3L_UNIT barycentricC; ///< Baryc. coord C, same semantics as barycentricA.
} S3L_PixelInfo;

typedef struct
{
  int16_t steps;
  int16_t err;
  int16_t x;
  int16_t y;

  int16_t *majorCoord;
  int16_t *minorCoord;
  int16_t majorIncrement;
  int16_t minorIncrement;
  int16_t majorDiff;
  int16_t minorDiff; 
} S3L_BresenhamState;

static inline int16_t S3L_abs(int16_t value)
{
  return value >= 0 ? value : -1 * value;
}

static inline int16_t S3L_min(int16_t v1, int16_t v2)
{
  return v1 >= v2 ? v2 : v1;
}

static inline int16_t S3L_max(int16_t v1, int16_t v2)
{
  return v1 >= v2 ? v1 : v2;
}

/**
  Interpolated between two values, v1 and v2, in the same ratio as t is to
  tMax. Does NOT prevent zero division.
*/

static inline int16_t S3L_interpolate(int16_t v1, int16_t v2, int16_t t,
  int16_t tMax)
{
  return v1 + ((v2 - v1) * t) / tMax;
}

/**
  Same as S3L_interpolate but with v1 = 0. Should be faster.
*/

static inline int16_t S3L_interpolateFrom0(int16_t v2, int16_t t, int16_t tMax)
{
  return (v2 * t) / tMax;
}

void S3L_bresenhamInit(S3L_BresenhamState *state, int16_t x0, int16_t y0, int16_t x1, int16_t y1)
{
  int16_t dx = x1 - x0;
  int16_t dy = y1 - y0;

  int16_t absDx = S3L_abs(dx);
  int16_t absDy = S3L_abs(dy);

  if (absDx >= absDy)
  {
    state->majorCoord = &(state->x);
    state->minorCoord = &(state->y);

    state->minorDiff = 2 * absDy;
    state->majorDiff = 2 * absDx;
    state->err = 2 * dy - dx;
  
    state->majorIncrement = dx >= 0 ? 1 : -1;
    state->minorIncrement = dy >= 0 ? 1 : -1;

    state->steps = absDx;
  }
  else
  {
    state->majorCoord = &(state->y);
    state->minorCoord = &(state->x);

    state->minorDiff = 2 * absDx;
    state->majorDiff = 2 * absDy;
    state->err = 2 * dx - dy;

    state->majorIncrement = dy >= 0 ? 1 : -1;
    state->minorIncrement = dx >= 0 ? 1 : -1;

    state->steps = absDy;
  }

  state->x = x0;
  state->y = y0;
}

int S3L_bresenhamStep(S3L_BresenhamState *state)
{
  state->steps--;

  (*state->majorCoord) += state->majorIncrement;

  if (state->err > 0)
  {
    (*state->minorCoord) += state->minorIncrement;
    state->err -= state->majorDiff;
  }

  state->err += state->minorDiff;

  return state->steps >= 0;
}

void S3L_drawTriangle(int16_t x0, int16_t y0, int16_t x1, int16_t y1, int16_t x2, int16_t y2)
{
  S3L_COORD
    tPointX, tPointY,    // top triangle point coords
    lPointX, lPointY,    // left triangle point coords
    rPointX, rPointY;    // right triangle point coords

  // Sort the points.

  #define handleLR(a,b)\
    if (x##a <= x##b)\
    {\
      lPointX = x##a; lPointY = y##a;\
      rPointX = x##b; rPointY = y##b;\
    }\
    else\
    {\
      lPointX = x##b; lPointY = y##b;\
      rPointX = x##a; rPointY = y##a;\
    }

  if (y0 <= y1)
  {
    if (y0 <= y2)
    {
      tPointX = x0;
      tPointY = y0;
      handleLR(1,2)
    }
    else
    {
      tPointX = x2;
      tPointY = y2;
      handleLR(0,1)
    }
  }
  else
  {
    if (y1 <= y2)
    {
      tPointX = x1;
      tPointY = y1;
      handleLR(0,2)
    }
    else
    {
      tPointX = x2;
      tPointY = y2;
      handleLR(0,1)
    }
  }

  // Now drive the triangle line by line.

  #undef handleLR

  S3L_COORD splitY; // Y at which one side (L or R) changes
  S3L_COORD endY;   // bottom Y of the whole triangle
  int splitOnLeft;  // whether split happens on L or R

  if (rPointY <= lPointY)
  {
    splitY = rPointY;
    splitOnLeft = 0;
    endY = lPointY;
  }
  else
  {
    splitY = lPointY;
    splitOnLeft = 1;
    endY = rPointY;
  }

  S3L_COORD currentY = tPointY;

  /* We'll be using a slight modification of Bresenham line algorithm (a one
     that draws a _non-continous_ line). */

  int16_t
    /* triangle side:
    left     right */
    lX,      rX,        // current x position
    lDx,     rDx,       // dx (end point - start point)
    lDy,     rDy,       // dy (end point - start point)
    lInc,    rInc,      // direction in which to increment (1 or -1)
    lErr,    rErr,      // current error (Bresenham)
    lErrAdd, rErrAdd,   // error value to add in each Bresenham cycle
    lErrSub, rErrSub;   // error value to substract when moving in x direction

  S3L_UNIT
    lSideUnitStep, rSideUnitStep,
    lSideUnitPos,  rSideUnitPos;

  int16_t helperDxAbs;

  #define initSide(v,p1,p2, down)\
    v##X = p1##PointX;\
    v##Dx = p2##PointX - p1##PointX;\
    v##Dy = p2##PointY - p1##PointY;\
    v##SideUnitStep = S3L_FRACTIONS_PER_UNIT / (v##Dy != 0 ? v##Dy : 1);\
    v##SideUnitPos = 0;\
    if (!down)\
    {\
      v##SideUnitPos = S3L_FRACTIONS_PER_UNIT;\
      v##SideUnitStep *= -1;\
    }\
    helperDxAbs = S3L_abs(v##Dx);\
    v##Inc = v##Dx >= 0 ? 1 : -1;\
    v##Err = 2 * helperDxAbs - v##Dy;\
    v##ErrAdd = 2 * helperDxAbs;\
    v##ErrSub = 2 * v##Dy;\
    v##ErrSub = v##ErrSub != 0 ? v##ErrSub : 1; /* don't allow 0, could lead
                                                   to an infinite substracting
                                                   loop */
  #define stepSide(s)\
    while (s##Err > 0)\
    {\
      s##X += s##Inc;\
      s##Err -= s##ErrSub;\
    }\
    s##Err += s##ErrAdd;

  initSide(r,t,r,1)
  initSide(l,t,l,1)

  S3L_PixelInfo p;

  p.barycentricA = 0;
  p.barycentricB = 0;
  p.barycentricC = 0;

  S3L_UNIT *barycentric1 = &p.barycentricA;
  S3L_UNIT *barycentric2 = &p.barycentricB;
  S3L_UNIT *barycentric3 = &p.barycentricC;

  while (currentY <= endY)
  {
    if (currentY == splitY)
    {
      if (splitOnLeft)
      {
        initSide(l,l,r,0);

        barycentric1 = &p.barycentricC;
        barycentric3 = &p.barycentricA;

        rSideUnitPos = S3L_FRACTIONS_PER_UNIT - rSideUnitPos;
        rSideUnitStep *= -1;
      }
      else
      {
        initSide(r,r,l,0);

        barycentric2 = &p.barycentricC;
        barycentric3 = &p.barycentricB;

        lSideUnitPos = S3L_FRACTIONS_PER_UNIT - lSideUnitPos;
        lSideUnitStep *= -1;
      }
    }

    p.y = currentY;

    // draw the line

    S3L_UNIT tMax = rX - lX;
    tMax = tMax != 0 ? tMax : 1; // prevent division by zero

    S3L_UNIT t1 = 0;
    S3L_UNIT t2 = tMax;

    for (S3L_COORD x = lX; x <= rX; ++x)
    {
      *barycentric1 = S3L_interpolateFrom0(rSideUnitPos,t1,tMax);
      *barycentric2 = S3L_interpolateFrom0(lSideUnitPos,t2,tMax);
      *barycentric3 = S3L_FRACTIONS_PER_UNIT - *barycentric1 - *barycentric2;

      p.x = x;
      S3L_PIXEL_FUNCTION(&p);

      ++t1;
      --t2;
    }

    stepSide(r)
    stepSide(l)

    lSideUnitPos += lSideUnitStep;
    rSideUnitPos += rSideUnitStep;

    ++currentY;
  }

  #undef initSide
  #undef stepSide
}

#endif