small3dlib/s3l.h

/*
  WIP

  Simple realtime 3D software rasterization library. It is fast, focused on
  resource-limited computers, located in a single C header file, with no
  dependencies, using only integer arithmetic.

  author: Miloslav Ciz
  license: CC0 1.0

  --------------------

  CONVENTIONS:

  Angles are in S3L_Units, a full angle (2 pi) is S3L_FRACTIONS_PER_UNITs.

  COORDINATE SYSTEMS:

  In 3D space, a left-handed coord. system is used. One spatial unit is split
  into S3L_FRACTIONS_PER_UNIT fractions.

     y ^
       |   _ 
       |   /| z
       |  /
       | /
  [0,0,0]-------> x

  Untransformed camera is placed at [0,0,0], looking forward along +z axis. The
  projection plane is centered at [0,0,0], stretrinch from
  -S3L_FRACTIONS_PER_UNIT to S3L_FRACTIONS_PER_UNIT horizontally (x),
  vertical size (y) depends on the camera aspect ratio. Camera FOV is defined
  by focal length.

           y ^
             |  _
             |  /| z
         ____|_/__
        |    |/   |
     -----[0,0,0]-|-----> x
        |____|____|
             |    
             |

  Coordinates of pixels on screen start typically at the top left.
*/

#ifndef S3L_H
#define S3L_H

#include <stdint.h>

typedef int16_t S3L_Unit; /**< Units of measurement in 3D space. There is
                               S3L_FRACTIONS_PER_UNIT in one spatial unit.
                               By dividing the unit into fractions we
                               effectively achieve fixed point arithmetic.
                               The number of fractions is a constant that
                               serves as 1.0 in floating point arithmetic
                               (normalization etc.). */

#define S3L_FRACTIONS_PER_UNIT 1024

#define S3L_SIN_TABLE_LENGTH 128
static const S3L_Unit S3L_sinTable[S3L_SIN_TABLE_LENGTH] =
{
  0, 12, 25, 37, 50, 62, 75, 87, 100, 112, 125, 137, 150, 162, 175, 187, 199,
  212, 224, 236, 248, 260, 273, 285, 297, 309, 321, 333, 344, 356, 368, 380,
  391, 403, 414, 426, 437, 449, 460, 471, 482, 493, 504, 515, 526, 537, 547,
  558, 568, 579, 589, 599, 609, 620, 629, 639, 649, 659, 668, 678, 687, 696,
  706, 715, 724, 732, 741, 750, 758, 767, 775, 783, 791, 799, 807, 814, 822,
  829, 837, 844, 851, 858, 865, 871, 878, 884, 890, 897, 903, 908, 914, 920,
  925, 930, 936, 941, 946, 950, 955, 959, 964, 968, 972, 976, 979, 983, 986,
  990, 993, 996, 999, 1001, 1004, 1006, 1008, 1010, 1012, 1014, 1016, 1017,
  1019, 1020, 1021, 1022, 1022, 1023, 1023, 1023
};

#define S3L_SIN_TABLE_UNIT_STEP\
  (S3L_FRACTIONS_PER_UNIT / (S3L_SIN_TABLE_LENGTH * 4))

typedef int16_t S3L_ScreenCoord;
typedef uint16_t S3L_Index;

typedef struct
{
  S3L_Unit x;
  S3L_Unit y;
  S3L_Unit z;
} S3L_Vec3;

static inline void S3L_initVec3(S3L_Vec3 *v)
{
  v->x = 0; v->y = 0; v->z = 0;
}

typedef struct
{
  S3L_Vec3 offset;
  S3L_Vec3 rotation; /**< Euler angles. Rortation is applied in this order:
                          1. z = around z (roll) CW looking along z+
                          2. x = around x (pitch) CW looking along x+
                          3. y = around y (yaw) CW looking along y+ */
  S3L_Vec3 scale;
} S3L_Transform3D;

static inline void S3L_initTransoform3D(S3L_Transform3D *t)
{
  S3L_initVec3(&(t->offset));
  S3L_initVec3(&(t->rotation));
  t->scale.x = S3L_FRACTIONS_PER_UNIT;
  t->scale.y = S3L_FRACTIONS_PER_UNIT;
  t->scale.z = S3L_FRACTIONS_PER_UNIT;
}

typedef struct
{
  uint16_t resolutionX;
  uint16_t resolutionY;
  S3L_Unit focalLength;       ///< Defines the field of view (FOV).
  S3L_Transform3D transform;
} S3L_Camera;

static inline void S3L_initCamera(S3L_Camera *c)
{
  c->resolutionX = 128;
  c->resolutionY = 64;
  c->focalLength = S3L_FRACTIONS_PER_UNIT;
  S3L_initTransoform3D(&(c->transform));
}

typedef struct
{
  S3L_ScreenCoord x;          ///< Screen X coordinate.
  S3L_ScreenCoord y;          ///< Screen Y coordinate.

  S3L_Unit barycentric0; /**< Barycentric coord 0 (corresponds to 1st vertex).
                              Together with 1 and 2 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 barycentric1; ///< Baryc. coord 1 (corresponds to 2nd vertex).
  S3L_Unit barycentric2; ///< Baryc. coord 2 (corresponds to 3rd vertex).
  S3L_Index triangleID;
} S3L_PixelInfo;

static inline void S3L_initPixelInfo(S3L_PixelInfo *p)
{
  p->x = 0;
  p->y = 0;
  p->barycentric0 = S3L_FRACTIONS_PER_UNIT;
  p->barycentric1 = 0;
  p->barycentric2 = 0;
  p->triangleID = 0;
}

#define S3L_BACKFACE_CULLING_NONE 0
#define S3L_BACKFACE_CULLING_CW 1
#define S3L_BACKFACE_CULLING_CCW 2

#define S3L_MODE_TRIANGLES 0
#define S3L_MODE_LINES 1
#define S3L_MODE_POINTS 2

typedef struct
{
  int backfaceCulling;
  int mode;
} S3L_DrawConfig;

void S3L_PIXEL_FUNCTION(S3L_PixelInfo *pixel); // forward decl

typedef struct
{
  int16_t steps;
  int16_t err;
  S3L_ScreenCoord x;
  S3L_ScreenCoord y;

  int16_t *majorCoord;
  int16_t *minorCoord;
  int16_t majorIncrement;
  int16_t minorIncrement;
  int16_t majorDiff;
  int16_t minorDiff; 
} S3L_BresenhamState; ///< State of drawing a line with Bresenham algorithm.

/**
  Returns a value interpolated between the three triangle vertices based on
  barycentric coordinates.
*/
static inline S3L_Unit S3L_interpolateBarycentric(
  S3L_Unit value0, S3L_Unit value1, S3L_Unit value2,
  S3L_Unit barycentric0, S3L_Unit barycentric1, S3L_Unit barycentric2)
{
  return
    (
      (value0 * barycentric0) +
      (value1 * barycentric1) +
      (value2 * barycentric2)
    ) / S3L_FRACTIONS_PER_UNIT;
}

// general helper functions

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;
}

static inline S3L_Unit S3L_wrap(S3L_Unit value, S3L_Unit mod)
{
  return value >= 0 ? (value % mod) : (mod + (value % mod) - 1);
}

static inline S3L_Unit S3L_nonZero(S3L_Unit value)
{
  return value != 0 ? value : 1;
}

static inline S3L_Unit S3L_sin(S3L_Unit x)
{
  x = S3L_wrap(x / S3L_SIN_TABLE_UNIT_STEP,S3L_SIN_TABLE_LENGTH * 4);
  int8_t positive = 1;

  if (x < S3L_SIN_TABLE_LENGTH)
    x = x;
  else if (x < S3L_SIN_TABLE_LENGTH * 2)
    x = S3L_SIN_TABLE_LENGTH * 2 - x - 1;
  else if (x < S3L_SIN_TABLE_LENGTH * 3)
  {
    x = x - S3L_SIN_TABLE_LENGTH * 2;
    positive = 0;
  }
  else
  {
    x = S3L_SIN_TABLE_LENGTH - (x - S3L_SIN_TABLE_LENGTH * 3) - 1;
    positive = 0;
  }

  return positive ? S3L_sinTable[x] : -1 * S3L_sinTable[x];
}

static inline S3L_Unit S3L_cos(S3L_Unit x)
{
  return S3L_sin(x - S3L_FRACTIONS_PER_UNIT / 4);
}

/**
  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(
  S3L_ScreenCoord x0, S3L_ScreenCoord y0,
  S3L_ScreenCoord x1, S3L_ScreenCoord y1,
  S3L_ScreenCoord x2, S3L_ScreenCoord y2,
  S3L_DrawConfig config,
  S3L_Index triangleID)
{
  if (config.backfaceCulling != S3L_BACKFACE_CULLING_NONE)
  {
    int cw = // matrix determinant
      x0 * y1 + y0 * x2 + x1 * y2 - y1 * x2 - y0 * x1 - x0 * y2 > 0;

    if ((config.backfaceCulling == S3L_BACKFACE_CULLING_CW && !cw) ||
        (config.backfaceCulling == S3L_BACKFACE_CULLING_CCW && cw))
      return;
  }

  S3L_PixelInfo p;
  S3L_initPixelInfo(&p);
  p.triangleID = triangleID;

  // point mode

  if (config.mode == S3L_MODE_POINTS)
  {
    p.x = x0; p.y = y0; p.barycentric0 = S3L_FRACTIONS_PER_UNIT;
    p.barycentric1 = 0; p.barycentric2 = 0;
    S3L_PIXEL_FUNCTION(&p);

    p.x = x1; p.y = y1; p.barycentric0 = 0;
    p.barycentric1 = S3L_FRACTIONS_PER_UNIT; p.barycentric2 = 0;
    S3L_PIXEL_FUNCTION(&p);

    p.x = x2; p.y = y2; p.barycentric0 = 0;
    p.barycentric1 = 0; p.barycentric2 = S3L_FRACTIONS_PER_UNIT;
    S3L_PIXEL_FUNCTION(&p);
 
    return;
  }

  // line mode

  if (config.mode == S3L_MODE_LINES)
  {
    S3L_BresenhamState line;
    S3L_Unit lineLen;

    #define drawLine(p1,p2)\
      S3L_bresenhamInit(&line,x##p1,y##p1,x##p2,y##p2);\
      p.barycentric0 = 0;\
      p.barycentric1 = 0;\
      p.barycentric2 = 0;\
      lineLen = S3L_nonZero(line.steps);\
      do\
      {\
        p.x = line.x; p.y = line.y;\
        p.barycentric##p1 = S3L_interpolateFrom0(\
          S3L_FRACTIONS_PER_UNIT,line.steps,lineLen);  \
        p.barycentric##p2 = S3L_FRACTIONS_PER_UNIT - p.barycentric##p1;\
        S3L_PIXEL_FUNCTION(&p);\
      } while (S3L_bresenhamStep(&line));
   
    drawLine(0,1)
    drawLine(2,0)
    drawLine(1,2)

    #undef drawLine

    return;
  }

  // triangle mode

  S3L_ScreenCoord
    tPointX, tPointY,     // top triangle point coords
    lPointX, lPointY,     // left triangle point coords
    rPointX, rPointY;     // right triangle point coords

  S3L_Unit *barycentric0; // bar. coord that gets higher from L to R
  S3L_Unit *barycentric1; // bar. coord that gets higher from R to L
  S3L_Unit *barycentric2; // bar. coord that gets higher from bottom up

  // Sort the points.

  #define handleLR(t,a,b)\
    int16_t aDx = x##a - x##t;\
    int16_t bDx = x##b - x##t;\
    int16_t aDy = S3L_nonZero(y##a - y##t);\
    int16_t bDy = S3L_nonZero(y##b - y##t);\
    if ((aDx << 4) / aDy < (bDx << 4) / bDy)\
    /*if (x##a <= x##b)*/\
    {\
      lPointX = x##a; lPointY = y##a;\
      rPointX = x##b; rPointY = y##b;\
      barycentric0 = &p.barycentric##b;\
      barycentric1 = &p.barycentric##a;\
    }\
    else\
    {\
      lPointX = x##b; lPointY = y##b;\
      rPointX = x##a; rPointY = y##a;\
      barycentric0 = &p.barycentric##a;\
      barycentric1 = &p.barycentric##b;\
    }

  if (y0 <= y1)
  {
    if (y0 <= y2)
    {
      tPointX = x0;
      tPointY = y0;
      barycentric2 = &p.barycentric0;
      handleLR(0,1,2)
    }
    else
    {
      tPointX = x2;
      tPointY = y2;
      barycentric2 = &p.barycentric2;
      handleLR(2,0,1)
    }
  }
  else
  {
    if (y1 <= y2)
    {
      tPointX = x1;
      tPointY = y1;
      barycentric2 = &p.barycentric1;
      handleLR(1,0,2)
    }
    else
    {
      tPointX = x2;
      tPointY = y2;
      barycentric2 = &p.barycentric2;
      handleLR(2,0,1)
    }
  }

  // Now draw the triangle line by line.

  #undef handleLR

  S3L_ScreenCoord splitY; // Y at which one side (L or R) changes
  S3L_ScreenCoord 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_ScreenCoord 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)

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

        S3L_Unit *tmp = barycentric0;
        barycentric0 = barycentric2;
        barycentric2 = tmp;

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

        S3L_Unit *tmp = barycentric1;
        barycentric1 = barycentric2;
        barycentric2 = tmp;

        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_ScreenCoord x = lX; x <= rX; ++x)
    {
      *barycentric0 = S3L_interpolateFrom0(rSideUnitPos,t1,tMax);
      *barycentric1 = S3L_interpolateFrom0(lSideUnitPos,t2,tMax);
      *barycentric2 = S3L_FRACTIONS_PER_UNIT - *barycentric0 - *barycentric1;

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

      ++t1;
      --t2;
    }

    stepSide(r)
    stepSide(l)

    lSideUnitPos += lSideUnitStep;
    rSideUnitPos += rSideUnitStep;

    ++currentY;
  }

  #undef initSide
  #undef stepSide
}

static inline void S3L_rotate2DPoint(S3L_Unit *x, S3L_Unit *y, S3L_Unit angle)
{
  if (angle < S3L_SIN_TABLE_UNIT_STEP)
    return; // no visible rotation

  S3L_Unit angleSin = S3L_sin(angle);
  S3L_Unit angleCos = S3L_cos(angle);

  S3L_Unit xBackup = *x;

  *x =
    (angleCos * (*x)) / S3L_FRACTIONS_PER_UNIT -
    (angleSin * (*y)) / S3L_FRACTIONS_PER_UNIT;

  *y =
    (angleSin * xBackup) / S3L_FRACTIONS_PER_UNIT +
    (angleCos * (*y)) / S3L_FRACTIONS_PER_UNIT;
}

static inline void S3L_mapModelToWorld(S3L_Vec3 point,
  S3L_Transform3D *modelTransform, S3L_Vec3 *newPoint)
{
  newPoint->x = point.x;
  newPoint->y = point.y;
  newPoint->z = point.z;

  S3L_rotate2DPoint(&(newPoint->x),&(newPoint->y),modelTransform->rotation.z);
  S3L_rotate2DPoint(&(newPoint->z),&(newPoint->y),modelTransform->rotation.x);
  S3L_rotate2DPoint(&(newPoint->z),&(newPoint->x),modelTransform->rotation.y);

  newPoint->x += modelTransform->offset.x;
  newPoint->y += modelTransform->offset.y;
  newPoint->z += modelTransform->offset.z;
}

static inline void S3L_mapWorldToCamera(S3L_Vec3 point,
  S3L_Transform3D *cameraTransform, S3L_Vec3 *newPoint)
{
  newPoint->x = point.x - cameraTransform->offset.x;
  newPoint->y = point.y - cameraTransform->offset.y;
  newPoint->z = point.z - cameraTransform->offset.z;
}

static inline void S3L_mapCameraToScreen(S3L_Vec3 point, S3L_Camera *camera,
  S3L_ScreenCoord *screenX, S3L_ScreenCoord *screenY)
{
  uint16_t halfW = camera->resolutionX >> 1; // TODO: precompute earlier? 
  uint16_t halfH = camera->resolutionY >> 1;

  *screenX = halfW + (point.x * halfW) / point.z;
  *screenY = halfH - (point.y * halfW) / point.z;
  // ^ S3L_FRACTIONS_PER_UNIT cancel out
}

void S3L_drawModel(
  const S3L_Unit coords[],
  const S3L_Index triangleVertexIndices[],
  uint16_t triangleCount,
  S3L_Transform3D modelTransform,
  S3L_Camera camera,
  S3L_DrawConfig config)
{
  S3L_Index triangleIndex = 0;
  S3L_Index coordIndex = 0;

  S3L_ScreenCoord sX0, sY0, sX1, sY1, sX2, sY2;
  S3L_Vec3 pointModel, pointWorld, pointCamera;
  S3L_Unit indexIndex;

  while (triangleIndex < triangleCount)
  {
    #define mapCoords(n)\
      indexIndex = triangleVertexIndices[coordIndex] * 3;\
      pointModel.x = coords[indexIndex];\
      ++indexIndex; /* TODO: put into square brackets? */\
      pointModel.y = coords[indexIndex];\
      ++indexIndex;\
      pointModel.z = coords[indexIndex];\
      ++coordIndex;\
      S3L_mapModelToWorld(pointModel,&modelTransform,&pointWorld);\
      S3L_mapWorldToCamera(pointWorld,&camera.transform,&pointCamera);\
      S3L_mapCameraToScreen(pointCamera,&camera,&sX##n,&sY##n);

    mapCoords(0)
    mapCoords(1)
    mapCoords(2)

    S3L_drawTriangle(sX0,sY0,sX1,sY1,sX2,sY2,config,triangleIndex);

    ++triangleIndex;
  }
}

#endif