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small3dlib/s3l.h
Miloslav Číž eaea810b85 Make resolution constant
2019-05-08 14:14:56 +02:00

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/*
WIP
Simple realtime 3D software rasterization renderer. It is fast, focused on
resource-limited computers, located in a single C header file, with no
dependencies, using only integer arithmetics.
author: Miloslav Ciz
license: CC0 1.0 + additional waiver of all IP
--------------------
This work's goal is to never be encumbered by any exclusive intellectual
property rights. The work is therefore provided under CC0 1.0 + additional
WAIVER OF ALL INTELLECTUAL PROPERTY RIGHTS that waives the rest of
intellectual property rights not already waived by CC0 1.0. The WAIVER OF ALL
INTELLECTUAL PROPERTY RGHTS is as follows:
Each contributor to this work agrees that they waive any exclusive rights,
including but not limited to copyright, patents, trademark, trade dress,
industrial design, plant varieties and trade secrets, to any and all ideas,
concepts, processes, discoveries, improvements and inventions conceived,
discovered, made, designed, researched or developed by the contributor either
solely or jointly with others, which relate to this work or result from this
work. Should any waiver of such right be judged legally invalid or
ineffective under applicable law, the contributor hereby grants to each
affected person a royalty-free, non transferable, non sublicensable, non
exclusive, irrevocable and unconditional license to this right.
--------------------
CONVENTIONS:
Angles are in S3L_Units, a full angle (2 pi) is S3L_FRACTIONS_PER_UNITs.
We use row vectors.
COORDINATE SYSTEMS:
In 3D space, a left-handed coord. system is used. One spatial unit is split
into S3L_FRACTIONS_PER_UNIT fractions (fixed point arithmetic).
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, from [0,0].
Triangle rasterization rules are these (mostly same as OpenGL, D3D etc.):
- Let's define:
- left side:
- not exactly horizontal, and on the left side of triangle
- exactly horizontal and above the topmost
(in other words: its normal points at least a little to the left or
completely up)
- right side: not left side
- Pixel centers are at integer coordinates and triangle for drawing are
specified with integer coordinates of pixel centers.
- A pixel is rasterized:
- if its center is inside the triangle OR
- if its center is exactly on the triangle side which is left and at the
same time is not on the side that's right (case of a triangle that's on
a single line) OR
- if its center is exactly on the triangle corner of sides neither of which
is right.
These rules imply among others:
- Adjacent triangles don't have any overlapping pixels, nor gaps between.
- Triangles of points that lie on a single line are NOT rasterized.
- A single "long" triangle CAN be rasterized as non-continuous.
- Transforming (e.g. mirroring, rotating by 90 degrees etc.) a result of
rasterizing triangle A is NOT generally equal to applying the same
transformation to triangle A first and then rasterizing it. Even the number
of rasterized pixels is usually different.
- If specifying a triangle with integer coordinates, then:
- The bottom-most corner (or side) of a triangle is never rasterized
(because it is connected to a right side).
- The top-most corner can only be rasterized on completely horizontal side
(otherwise it is connected to a right side).
- Vertically middle corner is rasterized if and only if it is on the left
of the triangle and at the same time is also not the bottom-most corner.
*/
#ifndef S3L_H
#define S3L_H
#include <stdint.h>
#ifndef S3L_RESOLUTION_X
#define S3L_RESOLUTION_X 640 //< Redefine to your screen x resolution.
#endif
#ifndef S3L_RESOLUTION_Y
#define S3L_RESOLUTION_Y 480 //< Redefine to your screen y resolution.
#endif
#define S3L_HALF_RESOLUTION_X (S3L_RESOLUTION_X >> 1)
#define S3L_HALF_RESOLUTION_Y (S3L_RESOLUTION_Y >> 1)
typedef int32_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 512 /**< How many fractions a spatial unit is
split into. WARNING: if setting
higher than 1024, you'll probably
have to modify a sin table otherwise
it will overflow. Also other things
may overflow, so rather don't do it. */
#ifndef S3L_LERP_QUALITY
#define S3L_LERP_QUALITY 8 /**< Quality (scaling) of SOME linear
interpolations. 0 will most likely be faster,
but artifacts can occur for bigger tris,
while higher values can fix this -- in theory
all higher values will have the same speed
(it is a shift value), but it mustn't be too
high to prevent overflow. */
#endif
#define S3L_nonzero(value) ((value) != 0 ? (value) : 1) /**< prevents division
by zero */
/** Predefined vertices of a cube to simply insert in an array. These come with
S3L_CUBE_TRIANGLES and S3L_CUBE_TEXCOORDS. */
#define S3L_CUBE_VERTICES\
/* 0 front, bottom, right */\
S3L_FRACTIONS_PER_UNIT/2,-S3L_FRACTIONS_PER_UNIT/2,-S3L_FRACTIONS_PER_UNIT/2,\
/* 1 front, bottom, left */\
-S3L_FRACTIONS_PER_UNIT/2,-S3L_FRACTIONS_PER_UNIT/2,-S3L_FRACTIONS_PER_UNIT/2,\
/* 2 front, top, right */\
S3L_FRACTIONS_PER_UNIT/2,S3L_FRACTIONS_PER_UNIT/2,-S3L_FRACTIONS_PER_UNIT/2,\
/* 3 front, top, left */\
-S3L_FRACTIONS_PER_UNIT/2,S3L_FRACTIONS_PER_UNIT/2,-S3L_FRACTIONS_PER_UNIT/2,\
/* 4 back, bottom, right */\
S3L_FRACTIONS_PER_UNIT/2,-S3L_FRACTIONS_PER_UNIT/2,S3L_FRACTIONS_PER_UNIT/2,\
/* 5 back, bottom, left */\
-S3L_FRACTIONS_PER_UNIT/2,-S3L_FRACTIONS_PER_UNIT/2,S3L_FRACTIONS_PER_UNIT/2,\
/* 6 back, top, right */\
S3L_FRACTIONS_PER_UNIT/2,S3L_FRACTIONS_PER_UNIT/2,S3L_FRACTIONS_PER_UNIT/2,\
/* 7 back, top, left */\
-S3L_FRACTIONS_PER_UNIT/2,S3L_FRACTIONS_PER_UNIT/2,S3L_FRACTIONS_PER_UNIT/2
/** Predefined triangle indices of a cube, to be used with S3L_CUBE_VERTICES
and S3L_CUBE_TEXCOORDS. */
#define S3L_CUBE_TRIANGLES\
0, 3, 2, /* front */\
0, 1, 3,\
4, 0, 2, /* right */\
4, 2, 6,\
5, 4, 6, /* back */\
6, 7, 5,\
7, 3, 1, /* left */\
7, 1, 5,\
3, 6, 2, /* top */\
3, 7, 6,\
4, 1, 0, /* bottom */\
4, 5, 1
/** Predefined texture coordinates of a cube, corresponding to triangles (NOT
vertices), to be used with S3L_CUBE_VERTICES and S3L_CUBE_TRIANGLES. */
#define S3L_CUBE_TEXCOORDS\
1,1, 0,0, 1,0,\
1,1, 0,1, 0,0,\
1,0, 1,1, 0,1,\
1,0, 0,1, 0,0,\
0,0, 1,0, 1,1,\
1,1, 0,1, 0,0,\
0,1, 0,0, 1,0,\
0,1, 1,0, 1,1,\
1,1, 0,0, 1,0,\
1,1, 0,1, 0,0,\
0,1, 1,0, 1,1,\
0,1, 0,0, 1,0
#define S3L_SIN_TABLE_LENGTH 128
static const S3L_Unit S3L_sinTable[S3L_SIN_TABLE_LENGTH] =
{
/* 511 was chosen here as a highest number that doesn't overflow during
compilation for S3L_FRACTIONS_PER_UNIT == 1024 */
(0*S3L_FRACTIONS_PER_UNIT)/511, (6*S3L_FRACTIONS_PER_UNIT)/511,
(12*S3L_FRACTIONS_PER_UNIT)/511, (18*S3L_FRACTIONS_PER_UNIT)/511,
(25*S3L_FRACTIONS_PER_UNIT)/511, (31*S3L_FRACTIONS_PER_UNIT)/511,
(37*S3L_FRACTIONS_PER_UNIT)/511, (43*S3L_FRACTIONS_PER_UNIT)/511,
(50*S3L_FRACTIONS_PER_UNIT)/511, (56*S3L_FRACTIONS_PER_UNIT)/511,
(62*S3L_FRACTIONS_PER_UNIT)/511, (68*S3L_FRACTIONS_PER_UNIT)/511,
(74*S3L_FRACTIONS_PER_UNIT)/511, (81*S3L_FRACTIONS_PER_UNIT)/511,
(87*S3L_FRACTIONS_PER_UNIT)/511, (93*S3L_FRACTIONS_PER_UNIT)/511,
(99*S3L_FRACTIONS_PER_UNIT)/511, (105*S3L_FRACTIONS_PER_UNIT)/511,
(111*S3L_FRACTIONS_PER_UNIT)/511, (118*S3L_FRACTIONS_PER_UNIT)/511,
(124*S3L_FRACTIONS_PER_UNIT)/511, (130*S3L_FRACTIONS_PER_UNIT)/511,
(136*S3L_FRACTIONS_PER_UNIT)/511, (142*S3L_FRACTIONS_PER_UNIT)/511,
(148*S3L_FRACTIONS_PER_UNIT)/511, (154*S3L_FRACTIONS_PER_UNIT)/511,
(160*S3L_FRACTIONS_PER_UNIT)/511, (166*S3L_FRACTIONS_PER_UNIT)/511,
(172*S3L_FRACTIONS_PER_UNIT)/511, (178*S3L_FRACTIONS_PER_UNIT)/511,
(183*S3L_FRACTIONS_PER_UNIT)/511, (189*S3L_FRACTIONS_PER_UNIT)/511,
(195*S3L_FRACTIONS_PER_UNIT)/511, (201*S3L_FRACTIONS_PER_UNIT)/511,
(207*S3L_FRACTIONS_PER_UNIT)/511, (212*S3L_FRACTIONS_PER_UNIT)/511,
(218*S3L_FRACTIONS_PER_UNIT)/511, (224*S3L_FRACTIONS_PER_UNIT)/511,
(229*S3L_FRACTIONS_PER_UNIT)/511, (235*S3L_FRACTIONS_PER_UNIT)/511,
(240*S3L_FRACTIONS_PER_UNIT)/511, (246*S3L_FRACTIONS_PER_UNIT)/511,
(251*S3L_FRACTIONS_PER_UNIT)/511, (257*S3L_FRACTIONS_PER_UNIT)/511,
(262*S3L_FRACTIONS_PER_UNIT)/511, (268*S3L_FRACTIONS_PER_UNIT)/511,
(273*S3L_FRACTIONS_PER_UNIT)/511, (278*S3L_FRACTIONS_PER_UNIT)/511,
(283*S3L_FRACTIONS_PER_UNIT)/511, (289*S3L_FRACTIONS_PER_UNIT)/511,
(294*S3L_FRACTIONS_PER_UNIT)/511, (299*S3L_FRACTIONS_PER_UNIT)/511,
(304*S3L_FRACTIONS_PER_UNIT)/511, (309*S3L_FRACTIONS_PER_UNIT)/511,
(314*S3L_FRACTIONS_PER_UNIT)/511, (319*S3L_FRACTIONS_PER_UNIT)/511,
(324*S3L_FRACTIONS_PER_UNIT)/511, (328*S3L_FRACTIONS_PER_UNIT)/511,
(333*S3L_FRACTIONS_PER_UNIT)/511, (338*S3L_FRACTIONS_PER_UNIT)/511,
(343*S3L_FRACTIONS_PER_UNIT)/511, (347*S3L_FRACTIONS_PER_UNIT)/511,
(352*S3L_FRACTIONS_PER_UNIT)/511, (356*S3L_FRACTIONS_PER_UNIT)/511,
(361*S3L_FRACTIONS_PER_UNIT)/511, (365*S3L_FRACTIONS_PER_UNIT)/511,
(370*S3L_FRACTIONS_PER_UNIT)/511, (374*S3L_FRACTIONS_PER_UNIT)/511,
(378*S3L_FRACTIONS_PER_UNIT)/511, (382*S3L_FRACTIONS_PER_UNIT)/511,
(386*S3L_FRACTIONS_PER_UNIT)/511, (391*S3L_FRACTIONS_PER_UNIT)/511,
(395*S3L_FRACTIONS_PER_UNIT)/511, (398*S3L_FRACTIONS_PER_UNIT)/511,
(402*S3L_FRACTIONS_PER_UNIT)/511, (406*S3L_FRACTIONS_PER_UNIT)/511,
(410*S3L_FRACTIONS_PER_UNIT)/511, (414*S3L_FRACTIONS_PER_UNIT)/511,
(417*S3L_FRACTIONS_PER_UNIT)/511, (421*S3L_FRACTIONS_PER_UNIT)/511,
(424*S3L_FRACTIONS_PER_UNIT)/511, (428*S3L_FRACTIONS_PER_UNIT)/511,
(431*S3L_FRACTIONS_PER_UNIT)/511, (435*S3L_FRACTIONS_PER_UNIT)/511,
(438*S3L_FRACTIONS_PER_UNIT)/511, (441*S3L_FRACTIONS_PER_UNIT)/511,
(444*S3L_FRACTIONS_PER_UNIT)/511, (447*S3L_FRACTIONS_PER_UNIT)/511,
(450*S3L_FRACTIONS_PER_UNIT)/511, (453*S3L_FRACTIONS_PER_UNIT)/511,
(456*S3L_FRACTIONS_PER_UNIT)/511, (459*S3L_FRACTIONS_PER_UNIT)/511,
(461*S3L_FRACTIONS_PER_UNIT)/511, (464*S3L_FRACTIONS_PER_UNIT)/511,
(467*S3L_FRACTIONS_PER_UNIT)/511, (469*S3L_FRACTIONS_PER_UNIT)/511,
(472*S3L_FRACTIONS_PER_UNIT)/511, (474*S3L_FRACTIONS_PER_UNIT)/511,
(476*S3L_FRACTIONS_PER_UNIT)/511, (478*S3L_FRACTIONS_PER_UNIT)/511,
(481*S3L_FRACTIONS_PER_UNIT)/511, (483*S3L_FRACTIONS_PER_UNIT)/511,
(485*S3L_FRACTIONS_PER_UNIT)/511, (487*S3L_FRACTIONS_PER_UNIT)/511,
(488*S3L_FRACTIONS_PER_UNIT)/511, (490*S3L_FRACTIONS_PER_UNIT)/511,
(492*S3L_FRACTIONS_PER_UNIT)/511, (494*S3L_FRACTIONS_PER_UNIT)/511,
(495*S3L_FRACTIONS_PER_UNIT)/511, (497*S3L_FRACTIONS_PER_UNIT)/511,
(498*S3L_FRACTIONS_PER_UNIT)/511, (499*S3L_FRACTIONS_PER_UNIT)/511,
(501*S3L_FRACTIONS_PER_UNIT)/511, (502*S3L_FRACTIONS_PER_UNIT)/511,
(503*S3L_FRACTIONS_PER_UNIT)/511, (504*S3L_FRACTIONS_PER_UNIT)/511,
(505*S3L_FRACTIONS_PER_UNIT)/511, (506*S3L_FRACTIONS_PER_UNIT)/511,
(507*S3L_FRACTIONS_PER_UNIT)/511, (507*S3L_FRACTIONS_PER_UNIT)/511,
(508*S3L_FRACTIONS_PER_UNIT)/511, (509*S3L_FRACTIONS_PER_UNIT)/511,
(509*S3L_FRACTIONS_PER_UNIT)/511, (510*S3L_FRACTIONS_PER_UNIT)/511,
(510*S3L_FRACTIONS_PER_UNIT)/511, (510*S3L_FRACTIONS_PER_UNIT)/511,
(510*S3L_FRACTIONS_PER_UNIT)/511, (510*S3L_FRACTIONS_PER_UNIT)/511
};
#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;
/**
Vector that consists of four scalars and can represent homogenous
coordinates, but is generally also used as Vec3 and Vec2.
*/
typedef struct
{
S3L_Unit x;
S3L_Unit y;
S3L_Unit z;
S3L_Unit w;
} S3L_Vec4;
#define S3L_writeVec4(v)\
printf("Vec4: %d %d %d %d\n",(v.x),(v.y),(v.z),(v.w))
static inline void S3L_initVec4(S3L_Vec4 *v)
{
v->x = 0; v->y = 0; v->z = 0; v->w = S3L_FRACTIONS_PER_UNIT;
}
typedef S3L_Unit S3L_Mat4[4][4]; /**< 4x4 matrix, used mostly for 3D
transforms. The indexing is this:
matrix[column][row]. */
#define S3L_writeMat4(m)\
printf("Mat4:\n %d %d %d %d\n %d %d %d %d\n %d %d %d %d\n %d %d %d %d\n"\
,(m)[0][0],(m)[1][0],(m)[2][0],(m)[3][0],\
(m)[0][1],(m)[1][1],(m)[2][1],(m)[3][1],\
(m)[0][2],(m)[1][2],(m)[2][2],(m)[3][2],\
(m)[0][3],(m)[1][3],(m)[2][3],(m)[3][3])
/**
Initializes a 4x4 matrix to identity.
*/
static inline void S3L_initMat4(S3L_Mat4 *m)
{
#define M(x,y) (*m)[x][y]
#define S S3L_FRACTIONS_PER_UNIT
M(0,0) = S; M(1,0) = 0; M(2,0) = 0; M(3,0) = 0;
M(0,1) = 0; M(1,1) = S; M(2,1) = 0; M(3,1) = 0;
M(0,2) = 0; M(1,2) = 0; M(2,2) = S; M(3,2) = 0;
M(0,3) = 0; M(1,3) = 0; M(2,3) = 0; M(3,3) = S;
#undef M
#undef S
}
/**
Multiplies a vector by a matrix with normalization by S3L_FRACTIONS_PER_UNIT.
Result is stored in the input vector.
*/
void S3L_vec4Xmat4(S3L_Vec4 *v, S3L_Mat4 *m)
{
S3L_Vec4 vBackup;
vBackup.x = v->x;
vBackup.y = v->y;
vBackup.z = v->z;
vBackup.w = v->w;
// TODO: try alternative operation orders to optimize
#define dot(col)\
(vBackup.x * (*m)[col][0]) / S3L_FRACTIONS_PER_UNIT +\
(vBackup.y * (*m)[col][1]) / S3L_FRACTIONS_PER_UNIT +\
(vBackup.z * (*m)[col][2]) / S3L_FRACTIONS_PER_UNIT +\
(vBackup.w * (*m)[col][3]) / S3L_FRACTIONS_PER_UNIT
v->x = dot(0);
v->y = dot(1);
v->z = dot(2);
v->w = dot(3);
#undef dot
}
// 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;
}
/**
Multiplies two matrices with normalization by S3L_FRACTIONS_PER_UNIT. Result
is stored in the first matrix.
*/
void S3L_mat4Xmat4(S3L_Mat4 *m1, S3L_Mat4 *m2)
{
S3L_Mat4 mat1;
for (uint16_t row = 0; row < 4; ++row)
for (uint16_t col = 0; col < 4; ++col)
mat1[col][row] = (*m1)[col][row];
for (uint16_t row = 0; row < 4; ++row)
for (uint16_t col = 0; col < 4; ++col)
{
(*m1)[col][row] = 0;
for (uint16_t i = 0; i < 4; ++i)
(*m1)[col][row] +=
(mat1[i][row] * (*m2)[col][i]) / S3L_FRACTIONS_PER_UNIT;
}
}
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);
}
void S3L_makeTranslationMat(
S3L_Unit offsetX, S3L_Unit offsetY, S3L_Unit offsetZ, S3L_Mat4 *m)
{
#define M(x,y) (*m)[x][y]
#define S S3L_FRACTIONS_PER_UNIT
M(0,0) = S; M(1,0) = 0; M(2,0) = 0; M(3,0) = 0;
M(0,1) = 0; M(1,1) = S; M(2,1) = 0; M(3,1) = 0;
M(0,2) = 0; M(1,2) = 0; M(2,2) = S; M(3,2) = 0;
M(0,3) = offsetX; M(1,3) = offsetY; M(2,3) = offsetZ; M(3,3) = S;
#undef M
#undef S
}
/**
Makes a scaling matrix. DON'T FORGET: scale of 1.0 is set with
S3L_FRACTIONS_PER_UNIT!
*/
void S3L_makeScaleMatrix(
S3L_Unit scaleX, S3L_Unit scaleY, S3L_Unit scaleZ, S3L_Mat4 *m)
{
#define M(x,y) (*m)[x][y]
M(0,0) = scaleX; M(2,0) = 0; M(3,0) = 0;
M(0,1) = 0; M(1,1) = scaleY; M(2,1) = 0; M(3,1) = 0;
M(0,2) = 0; M(1,2) = 0; M(2,2) = scaleZ; M(3,2) = 0;
M(0,3) = 0; M(1,3) = 0; M(2,3) = 0; M(3,3) = S3L_FRACTIONS_PER_UNIT;
#undef M
}
/**
Makes a rotation matrix. For the rotation conventions (meaning, order, units)
see the appropriate structure comments.
*/
void S3L_makeRotationMatrix(
S3L_Unit aroundX, S3L_Unit aroundY, S3L_Unit aroundZ, S3L_Mat4 *m)
{
S3L_Unit sx = S3L_sin(aroundX);
S3L_Unit sy = S3L_sin(aroundY);
S3L_Unit sz = S3L_sin(aroundZ);
S3L_Unit cx = S3L_cos(aroundX);
S3L_Unit cy = S3L_cos(aroundY);
S3L_Unit cz = S3L_cos(aroundZ);
#define M(x,y) (*m)[x][y]
#define S S3L_FRACTIONS_PER_UNIT
M(0,0) = (cy * cz) / S + (sy * sx * sz) / (S * S);
M(1,0) = (cx * sz) / S;
M(2,0) = (cy * sx * sz) / (S * S) - (cz * sy) / S;
M(3,0) = 0;
M(0,1) = (cz * sy * sx) / (S * S) - (cy * sz) / S;
M(1,1) = (cx * cz) / S;
M(2,1) = (cy * cz * sx) / (S * S) + (sy * sz) / S;
M(3,1) = 0;
M(0,2) = (cx * sy) / S;
M(1,2) = -1 * sx;
M(2,2) = (cy * cx) / S;
M(3,2) = 0;
M(0,3) = 0;
M(1,3) = 0;
M(2,3) = 0;
M(3,3) = S3L_FRACTIONS_PER_UNIT;
#undef M
#undef S
}
typedef struct
{
S3L_Vec4 translation;
S3L_Vec4 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_Vec4 scale;
} S3L_Transform3D;
static inline void S3L_initTransoform3D(S3L_Transform3D *t)
{
S3L_initVec4(&(t->translation));
S3L_initVec4(&(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
{
S3L_Unit focalLength; ///< Defines the field of view (FOV).
S3L_Transform3D transform;
} S3L_Camera;
static inline void S3L_initCamera(S3L_Camera *c)
{
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_initDrawConfig(S3L_DrawConfig *config)
{
config->backfaceCulling = 1;
config->mode = S3L_MODE_TRIANGLES;
}
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;
}
/**
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_drawFilledTriangle(
S3L_ScreenCoord x0, S3L_ScreenCoord y0,
S3L_ScreenCoord x1, S3L_ScreenCoord y1,
S3L_ScreenCoord x2, S3L_ScreenCoord y2,
S3L_PixelInfo *p)
{
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 of the vertically middle point of the triangle
S3L_ScreenCoord endY; // bottom Y of the whole triangle
int splitOnLeft; // whether splitY happens on L or R side
if (rPointY <= lPointY)
{
splitY = rPointY;
splitOnLeft = 0;
endY = lPointY;
}
else
{
splitY = lPointY;
splitOnLeft = 1;
endY = rPointY;
}
S3L_ScreenCoord currentY = tPointY;
/* We'll be using an algorithm similar to Bresenham line algorithm. The
specifics of this algorithm are among others:
- drawing possibly a NON-CONTINUOUS line
- NOT tracing the line exactly, but rather rasterizing one the right
side of it, according to the pixel CENTERS, INCLUDING the pixel
centers
The principle is this:
- Move vertically by pixels and accumulate the error (abs(dx/dy)).
- If the error is greater than one (crossed the next pixel center), keep
moving horizontally and substracting 1 from the error until it is less
than 1 again.
- To make this INTEGER ONLY, scale the case so that distance between
pixels is equal to dy (instead of 1). This way the error becomes
dx/dy * dy == dx, and we're comparing the error to (and potentially
substracting) 1 * dy == dy. */
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)
lErrCmp, rErrCmp, // helper for deciding comparison (> vs >=)
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;
/* init side for the algorithm, params:
s - which side (l or r)
p1 - point from (t, l or r)
p2 - point to (t, l or r)
down - whether the side coordinate goes top-down or vice versa
*/
#define initSide(s,p1,p2,down)\
s##X = p1##PointX;\
s##Dx = p2##PointX - p1##PointX;\
s##Dy = p2##PointY - p1##PointY;\
s##SideUnitStep = (S3L_FRACTIONS_PER_UNIT << S3L_LERP_QUALITY)\
/ (s##Dy != 0 ? s##Dy : 1);\
s##SideUnitPos = 0;\
if (!down)\
{\
s##SideUnitPos = S3L_FRACTIONS_PER_UNIT << S3L_LERP_QUALITY;\
s##SideUnitStep *= -1;\
}\
s##Inc = s##Dx >= 0 ? 1 : -1;\
if (s##Dx < 0)\
{s##Err = 0; s##ErrCmp = 0;}\
else\
{s##Err = s##Dy; s##ErrCmp = 1;}\
s##ErrAdd = S3L_abs(s##Dx);\
s##ErrSub = s##Dy != 0 ? s##Dy : 1; /* don't allow 0, could lead to an
infinite substracting loop */
#define stepSide(s)\
while (s##Err - s##Dy >= s##ErrCmp)\
{\
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) /* draw the triangle from top to bottom -- the
bottom-most row is left out because, following
from the rasterization rules (see top of the
source), it is to never be rasterized. */
{
if (currentY == splitY) // reached a vertical split of the triangle?
{ // then reinit one side
if (splitOnLeft)
{
initSide(l,l,r,0);
S3L_Unit *tmp = barycentric0;
barycentric0 = barycentric2;
barycentric2 = tmp;
rSideUnitPos = (S3L_FRACTIONS_PER_UNIT << S3L_LERP_QUALITY)
- rSideUnitPos;
rSideUnitStep *= -1;
}
else
{
initSide(r,r,l,0);
S3L_Unit *tmp = barycentric1;
barycentric1 = barycentric2;
barycentric2 = tmp;
lSideUnitPos = (S3L_FRACTIONS_PER_UNIT << S3L_LERP_QUALITY)
- lSideUnitPos;
lSideUnitStep *= -1;
}
}
stepSide(r)
stepSide(l)
p->y = currentY;
// draw the horizontal line
S3L_Unit rowLength = S3L_nonzero(rX - lX - 1); // prevent zero div
S3L_Unit b0 = 0;
S3L_Unit b1 = lSideUnitPos;
S3L_Unit b0Step = rSideUnitPos / rowLength;
S3L_Unit b1Step = lSideUnitPos / rowLength;
for (S3L_ScreenCoord x = lX; x < rX; ++x)
{
*barycentric0 = b0 >> S3L_LERP_QUALITY;
*barycentric1 = b1 >> S3L_LERP_QUALITY;
*barycentric2 = S3L_FRACTIONS_PER_UNIT - *barycentric0 - *barycentric1;
p->x = x;
S3L_PIXEL_FUNCTION(p);
b0 += b0Step;
b1 -= b1Step;
}
lSideUnitPos += lSideUnitStep;
rSideUnitPos += rSideUnitStep;
++currentY;
}
#undef initSide
#undef stepSide
}
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;
if (config.mode == S3L_MODE_TRIANGLES) // triangle mode
{
_S3L_drawFilledTriangle(x0,y0,x1,y1,x2,y2,&p);
}
else if (config.mode == S3L_MODE_LINES) // line mode
{
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
}
else // point mode
{
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);
}
}
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;
}
void S3L_makeWorldMatrix(S3L_Transform3D worldTransform, S3L_Mat4 *m)
{
S3L_makeScaleMatrix(
worldTransform.scale.x,
worldTransform.scale.y,
worldTransform.scale.z,
m
);
S3L_Mat4 t;
S3L_makeRotationMatrix(
worldTransform.rotation.x,
worldTransform.rotation.y,
worldTransform.rotation.z,
&t);
S3L_mat4Xmat4(m,&t);
S3L_makeTranslationMat(
worldTransform.translation.x,
worldTransform.translation.y,
worldTransform.translation.z,
&t);
S3L_mat4Xmat4(m,&t);
}
void S3L_makeCameraMatrix(S3L_Transform3D cameraTransform, S3L_Mat4 *m)
{
S3L_makeTranslationMat(
-1 * cameraTransform.translation.x,
-1 * cameraTransform.translation.y,
-1 * cameraTransform.translation.z,
m);
}
static inline void S3L_mapCameraToScreen(S3L_Vec4 point, S3L_Camera *camera,
S3L_ScreenCoord *screenX, S3L_ScreenCoord *screenY)
{
*screenX =
S3L_HALF_RESOLUTION_X + (point.x * S3L_HALF_RESOLUTION_X) / point.z;
*screenY =
S3L_HALF_RESOLUTION_Y - (point.y * S3L_HALF_RESOLUTION_X) / point.z;
// ^ S3L_FRACTIONS_PER_UNIT cancel out
}
/*
Helper function to interpolate texture coordinates based on barycentric
coordinates. If you're going for max performance, you may want to compute
these values yourself -- some specific cases may be possible to compute
faster.
*/
void S3L_interpolateTexCoords(
S3L_Unit u0,
S3L_Unit v0,
S3L_Unit u1,
S3L_Unit v1,
S3L_Unit u2,
S3L_Unit v2,
S3L_PixelInfo *p,
S3L_Unit *u,
S3L_Unit *v
)
{
*u = (p->barycentric0 * u0 + p->barycentric1 * u1 + p->barycentric2 * u2) /
S3L_FRACTIONS_PER_UNIT;
*v = (p->barycentric0 * v0 + p->barycentric1 * v1 + p->barycentric2 * v2) /
S3L_FRACTIONS_PER_UNIT;
}
void S3L_drawModelIndexed(
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_Vec4 pointModel;
S3L_Unit indexIndex;
pointModel.w = S3L_FRACTIONS_PER_UNIT; // has to be "1.0" for translation
S3L_Mat4 mat1, mat2;
S3L_makeWorldMatrix(modelTransform,&mat1);
S3L_makeCameraMatrix(camera.transform,&mat2);
S3L_mat4Xmat4(&mat1,&mat2);
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_vec4Xmat4(&pointModel,&mat1);\
S3L_mapCameraToScreen(pointModel,&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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