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small3dlib/s3l.h
Miloslav Číž 513bc419b1 Add comment
2018-11-20 15:34:27 +01:00

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/*
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;
}
// FIXME: rewrite this to just apply one matrix, EFFICIENCY!!!
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
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